Wind chimes produce clear, pure tones when struck by a mallet or suspended clapper. A wind chime usually consists of a set of individual alloy rods, tuned by length to a series of intervals considered pleasant. These are suspended from a devised frame in such a way that a centrally suspended clapper can reach and impact all the rods. When the wind blows, the clapper is set in motion and randomly strikes one or more of the suspended rods-- causing the rod to vibrate and emit a tone.
The pitch of said tone is governed by the length of the rod, but the perceived loudness is affected by many determinants: the force of the clappers impact, the alloy's density and structure, and the speed and direction of the wind (to name a few). Also affecting the loudness is the lack of resonating chamber or hard connection between rods and frame. The chime would certainly be louder, for instance, if the rods were built with the inclusion of small chambers containing a volume of air whose fundamental harmonic was the same as that of the rod-- when struck, the rod would transfer vibration to the enclosed air as well as directly to the atmosphere, resulting in a louder tone. A hard connection between rods and frame would also accomplish this result somewhat; the vibrations of each seperate rod would be commuted to the others, resulting in more vibrating surface area (and hence, more volume).
The transmission of the chime's sound without the abovementioned alterations is quite simple; each rod releases longitudinal waves radially from it's longest axis (excepting deviances caused by deformation or impurity of the metal), which travel until they are absorbed or reflected by an independent surface. These waves travel at a speed governed by the temperature of the atmosphere-- the colder the air, the more immediate the transmission.
The waves that are not absorbed can be perceived by the human ear; of equal importance to the directly intercepted waves are those reflected before interception, as these allow an animal or human to identify the physical relationship of self to sound-emitter. These intercepted waves (reflected or not) are processed by the ear in an amazing process.
Sound waves vibrate the ear-drum, causing the minute movement of three microscopic bones (hammer, then anvil, then stirrup) in the middle ear. The bone chain, having transferred air vibration to physical vibration, systematically disturbs the fluid (perilymph) in the inner ear (cochlea). Hair cells along the basilar membrane (which runs the length of the cochlea) perceive the disturbances and interpret them as auditory signals to be transmitted to the nervous system. With pure tones such as those created by a wind chime, certain groups of hair cells are agitated more than others-- and the position of that group along the basilar membrane can be directly correlated to the relative pitch of the tone.
Saturday 12 January 2013
What is Physics
Physics, a branch of science, is traditionally defined as the study of
matter, energy, and the relation between them. The interaction between matter
and energy is found everywhere. In order for matter to move, it requires some
form of energy.
Sports show many good examples of the relationship between matter and energy.
For instance, a pitcher requires energy to throw a baseball at the incredible speed
and accuracy that is needed to keep the batter from using his energy to try and hit
the ball. The batter exhibits the need for a certain trajectory because he/she needs
to hit the ball hard enough and keep it high enough to sail over the outfield wall.
On the other hand, the batter must be certain to keep the trajectory low enough so
that the ball will reach the fence. Trajectory is also seen in basketball, where
players must shoot the ball with enough arch to get over the front of the rim, and go
through the hoop. The energy required to do this comes from not only the arms, but
the legs as well.
The medical field has seen enormous breakthroughs because of principles of physics.
Doctors are now able to use lasers for surgery. Lasers are based on the physical principle
of light, and are devices for the creation and amplification of a narrow, intense beam of
coherent light. New laser microsurgery can actually alter the shape of the cornea in the
eye so the patient's eyesight can return to normal, and he/she will no longer need those
bothersome glasses. Ultrasound is used in the medical field for destroying various unwanted
substances in the body such as kidney stones. Ultrasound uses sound waves to dissolve these
foreign bodies. If not for physics, ultrasounds would never have been discovered and utilized.
MRI scans, another new discovery, are able to show a complete three dimensional picture of the
interior structure of the body, and are extremely valuable in hospitals. These scans are based
on the principles of electromagnetism, and the phenomenon that nuclei of some atoms line up in
the presence of an electromagnetic field.
Understanding the dark matter of the universe, which has remained a mystery for quite some time,
is based primarily on theories of physics. We have yet to see a black hole, but physics has
explained what one is, and why we cannot see it. Otherwise we would have never known that it is
an extremely small region of space-time with a gravitational field so intense that nothing can
escape, not even light. Physics help to understand the dark matter of the universe, because it
applies theories to what the dark matter is. We are also able to look at distant spots in the
universe with new telescopes because of the principles of magnification and amplification of light.
Not only can physics better your baseball game and explain the dark matter of the universe,
but it can save lives. It remains a very important part of us and our world.
matter, energy, and the relation between them. The interaction between matter
and energy is found everywhere. In order for matter to move, it requires some
form of energy.
Sports show many good examples of the relationship between matter and energy.
For instance, a pitcher requires energy to throw a baseball at the incredible speed
and accuracy that is needed to keep the batter from using his energy to try and hit
the ball. The batter exhibits the need for a certain trajectory because he/she needs
to hit the ball hard enough and keep it high enough to sail over the outfield wall.
On the other hand, the batter must be certain to keep the trajectory low enough so
that the ball will reach the fence. Trajectory is also seen in basketball, where
players must shoot the ball with enough arch to get over the front of the rim, and go
through the hoop. The energy required to do this comes from not only the arms, but
the legs as well.
The medical field has seen enormous breakthroughs because of principles of physics.
Doctors are now able to use lasers for surgery. Lasers are based on the physical principle
of light, and are devices for the creation and amplification of a narrow, intense beam of
coherent light. New laser microsurgery can actually alter the shape of the cornea in the
eye so the patient's eyesight can return to normal, and he/she will no longer need those
bothersome glasses. Ultrasound is used in the medical field for destroying various unwanted
substances in the body such as kidney stones. Ultrasound uses sound waves to dissolve these
foreign bodies. If not for physics, ultrasounds would never have been discovered and utilized.
MRI scans, another new discovery, are able to show a complete three dimensional picture of the
interior structure of the body, and are extremely valuable in hospitals. These scans are based
on the principles of electromagnetism, and the phenomenon that nuclei of some atoms line up in
the presence of an electromagnetic field.
Understanding the dark matter of the universe, which has remained a mystery for quite some time,
is based primarily on theories of physics. We have yet to see a black hole, but physics has
explained what one is, and why we cannot see it. Otherwise we would have never known that it is
an extremely small region of space-time with a gravitational field so intense that nothing can
escape, not even light. Physics help to understand the dark matter of the universe, because it
applies theories to what the dark matter is. We are also able to look at distant spots in the
universe with new telescopes because of the principles of magnification and amplification of light.
Not only can physics better your baseball game and explain the dark matter of the universe,
but it can save lives. It remains a very important part of us and our world.
Nuklear Power Our miusunderstood Freind
At first nuclear power was only seen as a means of destruction but after World War II a major effort was made to apply nuclear energy to peacetime uses. Nuclear power if made when a nucleus of an atom is split to release a powerful burst of energy. Though technological advancements nuclear power now supplies us with new medical aids, a new power source and new ways to do scientific research.
New medical advancements are being produced rapidly due to nuclear power. Nuclear material is now being used to treat diseases. Pacients suffering from cancer can then be exposed to the healing effects of the radiation under controlled conditions. The radiation of the nuclear energy can help in medical tests. Radioactive phosphorus is an important diagnostic aid. It is injected into the veins of a patient, it concentrates in the cells of certain brain tumors. Thyroid gland strongly attracts iodine. Radioactive iodine is used both in diagnosing and in treating diseases of the thyroid. Nuclear power is changing the face of medicine with new cures and tests that will cure millions..
Nuclear power can be converted into strong and efficient nuclear energy and be used for many purposes. Nuclear power reactors generates heat that is converted into steam. The steam can be used directly for energy. This energy is used in transportation. Most military subs are now ran by nuclear energy. The most used purpose of nuclear energy can also be used to generate electric power for example in a commercial nuclear power plant. Another way to produce nuclear energy is by gas-cooled reactors with either carbon dioxide or helium as the coolant instead of water. This method is used mainly in commercial nuclear plants in the United Kingdom and France due to the lack of freshwater. With growing popularity nuclear energy will definitely of the future with new ways to use this energy in a positive manner.
Scientists can now use nuclear power for biological research to help understand life more. Radioactive isotopes have been described as the most useful research tool since the invention of the microscope. Physiologists use them to learn where and at what speed physical and chemical processes occur in the human body. Isotopes are also used for agricultural Biologists use radioactive isotopes to see how plants absorb chemicals as they grow. With radioactive cobalt, botanists can produce new types of plants. Structural variations that normally take years of selective breeding to develop can be made to occur in a few months.
Many believe that nuclear power is too destructive and as such should be destroyed. Although it does have it's negative aspects, nuclear power is not evil in anyway. Nuclear power is an inanimate object, it does not live nor have a mind of it's own. It is the human race that decided that the best way to use this power was to use it as an instrument of war. Nuclear Power should be seen as a positive and humanity can blame no one for its destructive manner but themselves. It was our decision to use it for death, it is now our responsibility to use it for life.
New medical advancements are being produced rapidly due to nuclear power. Nuclear material is now being used to treat diseases. Pacients suffering from cancer can then be exposed to the healing effects of the radiation under controlled conditions. The radiation of the nuclear energy can help in medical tests. Radioactive phosphorus is an important diagnostic aid. It is injected into the veins of a patient, it concentrates in the cells of certain brain tumors. Thyroid gland strongly attracts iodine. Radioactive iodine is used both in diagnosing and in treating diseases of the thyroid. Nuclear power is changing the face of medicine with new cures and tests that will cure millions..
Nuclear power can be converted into strong and efficient nuclear energy and be used for many purposes. Nuclear power reactors generates heat that is converted into steam. The steam can be used directly for energy. This energy is used in transportation. Most military subs are now ran by nuclear energy. The most used purpose of nuclear energy can also be used to generate electric power for example in a commercial nuclear power plant. Another way to produce nuclear energy is by gas-cooled reactors with either carbon dioxide or helium as the coolant instead of water. This method is used mainly in commercial nuclear plants in the United Kingdom and France due to the lack of freshwater. With growing popularity nuclear energy will definitely of the future with new ways to use this energy in a positive manner.
Scientists can now use nuclear power for biological research to help understand life more. Radioactive isotopes have been described as the most useful research tool since the invention of the microscope. Physiologists use them to learn where and at what speed physical and chemical processes occur in the human body. Isotopes are also used for agricultural Biologists use radioactive isotopes to see how plants absorb chemicals as they grow. With radioactive cobalt, botanists can produce new types of plants. Structural variations that normally take years of selective breeding to develop can be made to occur in a few months.
Many believe that nuclear power is too destructive and as such should be destroyed. Although it does have it's negative aspects, nuclear power is not evil in anyway. Nuclear power is an inanimate object, it does not live nor have a mind of it's own. It is the human race that decided that the best way to use this power was to use it as an instrument of war. Nuclear Power should be seen as a positive and humanity can blame no one for its destructive manner but themselves. It was our decision to use it for death, it is now our responsibility to use it for life.
Saturday 5 January 2013
Indirect Proofs
Hypothesis - I think the dice has 2 dots and by indirect proof I think we will be able to prove it.
Data:
Indirect Proof Work:
a) Total number of faces seen: 1 face x 180
Trials = 180
b) Total number of dots seen: 145
c) Average number of dots per cube: 145/180 = 0.81
d) Average number of dots per cube: 0.81 X 6 = 4.9 (5)
Actual number of dots = 5
Data:
Indirect Proof Work:
a) Total number of faces seen: 1 face x 180
Trials = 180
b) Total number of dots seen: 145
c) Average number of dots per cube: 145/180 = 0.81
d) Average number of dots per cube: 0.81 X 6 = 4.9 (5)
Actual number of dots = 5
How the laws of balnce aplly to sports
Billy Moore
Physics
Sports Page
In sports balance and stability are used to increase performance of the athlete or the athletes equipment. In Racecar driving, balance is used to stabalize the racecar. The wheels are wide and extrude from the base of the car. This gives the car a wider support base which increases the stability. The race cars are flat and low to the ground. This moves the center of gravity lower which also increases the stability of the car.
In foot ball you need to keep your balance while your running so that you can resist a tackle. Foot ball players do this by crouching down and keeping their center of mass over their feet which is there support base.
Physics
Sports Page
In sports balance and stability are used to increase performance of the athlete or the athletes equipment. In Racecar driving, balance is used to stabalize the racecar. The wheels are wide and extrude from the base of the car. This gives the car a wider support base which increases the stability. The race cars are flat and low to the ground. This moves the center of gravity lower which also increases the stability of the car.
In foot ball you need to keep your balance while your running so that you can resist a tackle. Foot ball players do this by crouching down and keeping their center of mass over their feet which is there support base.
hot to make a rocket launcher
How to Make Rocket Launchers
Making a rocket launcher may not be easy but it is worth it. The first thing needed is the model rocket set. The set comes with the engine and all other parts to make the rocket. The instructions to make the rocket must be followed. After making the rocket, a three foot PVC tube and cap must be purchased at a piping store, such as Lowes. In the cap of the PVC tube a one-fourth inch hole must be drilled. Electrical wire, that can be found at any hardware store, must be purchased. A four inch wire must be inserted through the hole in the cap. An electrical igniter must be attached to the end of the four inches of wire. Instructions that came with the rocket set need to be followed to connect the igniter to the rocket engine. One pole of a nine-volt battery, which can be purchased at any Radio Shack, should be connected to one pole of any momentary switch. The two unconnected wires from the cap must be connected to the open poles of the switch and battery. It is ready to fire the rocket launcher. Making a rocket launcher is never easy but the show is worth it.
Making a rocket launcher may not be easy but it is worth it. The first thing needed is the model rocket set. The set comes with the engine and all other parts to make the rocket. The instructions to make the rocket must be followed. After making the rocket, a three foot PVC tube and cap must be purchased at a piping store, such as Lowes. In the cap of the PVC tube a one-fourth inch hole must be drilled. Electrical wire, that can be found at any hardware store, must be purchased. A four inch wire must be inserted through the hole in the cap. An electrical igniter must be attached to the end of the four inches of wire. Instructions that came with the rocket set need to be followed to connect the igniter to the rocket engine. One pole of a nine-volt battery, which can be purchased at any Radio Shack, should be connected to one pole of any momentary switch. The two unconnected wires from the cap must be connected to the open poles of the switch and battery. It is ready to fire the rocket launcher. Making a rocket launcher is never easy but the show is worth it.
Chlorophyll
CHLOROPHYLL
NAME
Biology
November. 19
A. Chlorophyll belongs to the Plant Kingdom. Chlorophyll is not found in the Animal Kingdom. Chlorophyll is found inside of Chloroplasts, and Chloroplasts are found inside of plant cells.
B. Chlorophyll is a pigment that makes plants green. It is important because it converts sunlight to split water into hydrogen and oxygen.
C. Chlorophyll is found inside the chloroplast which is located near the cell wall. It is located here because the suns rays might not penetrate deep into the plant, and the plant needs the suns rays to generate hydrogen and oxygen.
D. If a plant did not have chlorophyll then the plant would be unable to get the energy from the sun, and it would slowly die. There are no diseases or dysfunction's of chlorophyll. If there were plants would have a serious problem.
E. I once had a friend named Bill,
and he was green with Chlorophyll,
He Didn't have to eat,
not a beat or any meat,
Instead of going to dine he would feast on sunshine
Bill went to the Land of the Midnight Sun
and there he was done.
NAME
Biology
November. 19
A. Chlorophyll belongs to the Plant Kingdom. Chlorophyll is not found in the Animal Kingdom. Chlorophyll is found inside of Chloroplasts, and Chloroplasts are found inside of plant cells.
B. Chlorophyll is a pigment that makes plants green. It is important because it converts sunlight to split water into hydrogen and oxygen.
C. Chlorophyll is found inside the chloroplast which is located near the cell wall. It is located here because the suns rays might not penetrate deep into the plant, and the plant needs the suns rays to generate hydrogen and oxygen.
D. If a plant did not have chlorophyll then the plant would be unable to get the energy from the sun, and it would slowly die. There are no diseases or dysfunction's of chlorophyll. If there were plants would have a serious problem.
E. I once had a friend named Bill,
and he was green with Chlorophyll,
He Didn't have to eat,
not a beat or any meat,
Instead of going to dine he would feast on sunshine
Bill went to the Land of the Midnight Sun
and there he was done.
Friday 4 January 2013
Steam Turbines
Steam Turbines
The invention of the water turbine was so successful that eventually, the idea came about
for extracting power from steam. Steam has one great advantage over water-it expands in
volume with tremendous velocity. To be the most effective, a steam turbine must run at a very
high speed. No wheel made can revolve at any speed approaching the velocity that a steam
turbine can. By utilizing the kinetic energy of steam flow, the turbine could achieve a higher
efficiency. As a result, the steam turbine has supplanted the reciprocating engine as a prime
mover in large electricity-generating plants and is also used as a means of jet propulsion.
The action of the steam turbine is based on the thermodynamic principle that when a vapor
is allowed to expand, its temperature drops. In turn, its internal energy is decreased. This
reduction in internal energy is transformed into mechanical energy in the form of an acceleration
of the particles of vapor. The transformation that occurs, provides a large amount of available
work energy.
The essential parts of all steam turbines consist of nozzles or jets through which the steam
can flow and expand. Thus, the temperature drops, and kinetic energy is gained. In addition,
there are blades, on which high pressure steam is exerted. Stationary blades shift the steam onto
rotating blades, which provide power. Also, turbines are equipped with wheels or drums where
the blades are mounted. A shaft for these wheels or drums is also a basic component, as well as
an outer casing that confines the steam to the area of the turbine proper. In order to efficiently
use this contraption, it is necessary to have a number of stages. In each of these stages, a small
amount of thermal energy is converted to kinetic energy. If the entire conversion of energy took
place at once, the rotative speed of the turbine wheel would be way too excessive.
Steam turbines are really quite simple machines, that have only one major moving part, the
rotor. However, auxiliary equipment is necessary for their operation. Journal bearings support
the shaft, and an oil system provides lubrication to these bearings. A special seal system prevents
steam from leaking out, or outside air, from leaking in. A modern multistage steam turbine is
inherently high in expansion efficiency, because of the ability to recover losses of one stage
downstream. This is done through the process of reheating.
Steam turbines are still in heavy use today, providing power to ships as well as many other
things. They are used in the generation of nuclear power and they can operate with fuel-fired
boilers for power generation. In factories, industrial units are used to power machines, pumps,
compressors, electrical generators.
The invention of the water turbine was so successful that eventually, the idea came about
for extracting power from steam. Steam has one great advantage over water-it expands in
volume with tremendous velocity. To be the most effective, a steam turbine must run at a very
high speed. No wheel made can revolve at any speed approaching the velocity that a steam
turbine can. By utilizing the kinetic energy of steam flow, the turbine could achieve a higher
efficiency. As a result, the steam turbine has supplanted the reciprocating engine as a prime
mover in large electricity-generating plants and is also used as a means of jet propulsion.
The action of the steam turbine is based on the thermodynamic principle that when a vapor
is allowed to expand, its temperature drops. In turn, its internal energy is decreased. This
reduction in internal energy is transformed into mechanical energy in the form of an acceleration
of the particles of vapor. The transformation that occurs, provides a large amount of available
work energy.
The essential parts of all steam turbines consist of nozzles or jets through which the steam
can flow and expand. Thus, the temperature drops, and kinetic energy is gained. In addition,
there are blades, on which high pressure steam is exerted. Stationary blades shift the steam onto
rotating blades, which provide power. Also, turbines are equipped with wheels or drums where
the blades are mounted. A shaft for these wheels or drums is also a basic component, as well as
an outer casing that confines the steam to the area of the turbine proper. In order to efficiently
use this contraption, it is necessary to have a number of stages. In each of these stages, a small
amount of thermal energy is converted to kinetic energy. If the entire conversion of energy took
place at once, the rotative speed of the turbine wheel would be way too excessive.
Steam turbines are really quite simple machines, that have only one major moving part, the
rotor. However, auxiliary equipment is necessary for their operation. Journal bearings support
the shaft, and an oil system provides lubrication to these bearings. A special seal system prevents
steam from leaking out, or outside air, from leaking in. A modern multistage steam turbine is
inherently high in expansion efficiency, because of the ability to recover losses of one stage
downstream. This is done through the process of reheating.
Steam turbines are still in heavy use today, providing power to ships as well as many other
things. They are used in the generation of nuclear power and they can operate with fuel-fired
boilers for power generation. In factories, industrial units are used to power machines, pumps,
compressors, electrical generators.
Thursday 3 January 2013
Telephones
The telephone itself is a rather simple appliance. A microphone, called the transmitter, and an earphone, called the receiver, are contained in the handset. The microphone converts speech into its direct electrical analog, which is transmitted as an electrical signal; the earphone converts received electrical signals back to sound. The switch hook determines whether current flows to the telephone, thereby signaling the central office that the telephone is in use. The ringer responds to a signal sent by the central office that causes the telephone to ring. As simple a device as the telephone, had a mighty big impact on society during the 30's. This was due to the fact that, it was during the 30's when telephone service became economically feasible and also reliable.
Men and women alike were captivated by the intrique and fascination of talking to relatives and friends, miles and miles away. Not only did the telephone pamper to individual woes, but it provided a very useful industrial service. It allows commercial companies to expand their horizons infinitely easier than ever before. It became possible to set up meetings and discuss business matters with partners thousands of miles away. Companies that posessed a telephone had a enormous advantage over the rest. And in a time as economically troubled as the 30's depression, everyone was looking for a competitive edge.
The telephone wasn't invented in the thirties, nor was the first transatlantic line built then, but the thirties represents a time in history when the world was changing incredible fast and much of that change was made possible by the the telephone. Without the telephone, progress would have been much slower and people might not have been so receptive to change. We owe a great deal to Alexander Graham Bell, the inventor of the telephone, for his invention has served mankind well and will continue to offer society a valuable service for years to come.
Men and women alike were captivated by the intrique and fascination of talking to relatives and friends, miles and miles away. Not only did the telephone pamper to individual woes, but it provided a very useful industrial service. It allows commercial companies to expand their horizons infinitely easier than ever before. It became possible to set up meetings and discuss business matters with partners thousands of miles away. Companies that posessed a telephone had a enormous advantage over the rest. And in a time as economically troubled as the 30's depression, everyone was looking for a competitive edge.
The telephone wasn't invented in the thirties, nor was the first transatlantic line built then, but the thirties represents a time in history when the world was changing incredible fast and much of that change was made possible by the the telephone. Without the telephone, progress would have been much slower and people might not have been so receptive to change. We owe a great deal to Alexander Graham Bell, the inventor of the telephone, for his invention has served mankind well and will continue to offer society a valuable service for years to come.
Stratospheric Observatory For Infrared Astronomy
Stratospheric Observatory For Infrared Astronomy
The Stratospheric Observatory For Infrared Astronomy (SOFIA) will be a 2.5 meter, optical/infrared/sub-millimeter telescopemounted in a Boeing 747, to be used for many advanced astronomical observations performed at stratospheric altitudes. The Observatory will accommodate installation of different focal plane instruments, with in-flight accessibility, provided by
investigators selected from the international science community. The Observatory objective is to have an operational lifetime in excess of 20 years.
The SOFIA project is in the early full-scale stage. The start of detailed system design is anticipated in the Fall of 1996. The German Space Agency (DARA) is a partner with NASA in the SOFIA project. DARA will provide the telescope and NASA will provide the rest of the facility including the 747 aircraft, aircraft modifications, on-board mission control system, ground
facilities and support equipment, overall management, system integration and operations.
The SOFIA project is currently moving forward with evaluation of proposals for prime contracts for the U.S. and German portions of the program. Final approval for program implementation has been received from the U.S. Congress and NASA management. The observatory will begin flight operations by the year 2001.
The Stratospheric Observatory For Infrared Astronomy (SOFIA) will be a 2.5 meter, optical/infrared/sub-millimeter telescopemounted in a Boeing 747, to be used for many advanced astronomical observations performed at stratospheric altitudes. The Observatory will accommodate installation of different focal plane instruments, with in-flight accessibility, provided by
investigators selected from the international science community. The Observatory objective is to have an operational lifetime in excess of 20 years.
The SOFIA project is in the early full-scale stage. The start of detailed system design is anticipated in the Fall of 1996. The German Space Agency (DARA) is a partner with NASA in the SOFIA project. DARA will provide the telescope and NASA will provide the rest of the facility including the 747 aircraft, aircraft modifications, on-board mission control system, ground
facilities and support equipment, overall management, system integration and operations.
The SOFIA project is currently moving forward with evaluation of proposals for prime contracts for the U.S. and German portions of the program. Final approval for program implementation has been received from the U.S. Congress and NASA management. The observatory will begin flight operations by the year 2001.
Newtons Method A Computer Project
Newton's Method: A Computer Project
Newton's Method is used to find the root of an equation provided that the function f[x] is equal to zero. Newton Method is an equation created before the days of calculators and was
used to find approximate roots to numbers. The roots of the function are where the function crosses the x axis. The basic principle behind Newton's Method is that the root can be found by subtracting the
function divided by its derivative from the initial guess of the root.
Newtons Method worked well because an initial guess was given to put into the equation. This is important because a wrong initial guess may give you the wrong root for the function.
With Mathematica, a program for Newton's method can be produced and a graph of the function can be made. From the graph, the a good initial guess can be made.
Although Newton's Method works to find roots for many functions, it does have its disadvantages. The root sometimes cannot be found by using Newton's Method. The reason it
sometimes cannot be found is because when the function is equal to zero, there is no slope to the tangent line.
As seen in experimentation's, it is important to select an initial guess close to the root because some functions have multiple roots. Failure to choose an initial value that is close to the root
could result in finding a the wrong root or wasting a lot of time doing multiple iterations while getting close to the actual root.
On some occasions, the program cannot find a root to an initial guess that is placed into the program. In some instances Mathmatica could not find the root to the function, like if it is a
parabola with its vertex is placed right on the y axis with its roots an equal distance away in both directions. In a case like this, the computer could not decide which root to work towards so it gave an
indeterminate answer.
Although Newton's Method does have its disadvantages, it is very effective for finding the roots of most equations. The advantages definitely outweigh the slight disadvantages, and that is
why it is still used to this day.
Newton's Method is used to find the root of an equation provided that the function f[x] is equal to zero. Newton Method is an equation created before the days of calculators and was
used to find approximate roots to numbers. The roots of the function are where the function crosses the x axis. The basic principle behind Newton's Method is that the root can be found by subtracting the
function divided by its derivative from the initial guess of the root.
Newtons Method worked well because an initial guess was given to put into the equation. This is important because a wrong initial guess may give you the wrong root for the function.
With Mathematica, a program for Newton's method can be produced and a graph of the function can be made. From the graph, the a good initial guess can be made.
Although Newton's Method works to find roots for many functions, it does have its disadvantages. The root sometimes cannot be found by using Newton's Method. The reason it
sometimes cannot be found is because when the function is equal to zero, there is no slope to the tangent line.
As seen in experimentation's, it is important to select an initial guess close to the root because some functions have multiple roots. Failure to choose an initial value that is close to the root
could result in finding a the wrong root or wasting a lot of time doing multiple iterations while getting close to the actual root.
On some occasions, the program cannot find a root to an initial guess that is placed into the program. In some instances Mathmatica could not find the root to the function, like if it is a
parabola with its vertex is placed right on the y axis with its roots an equal distance away in both directions. In a case like this, the computer could not decide which root to work towards so it gave an
indeterminate answer.
Although Newton's Method does have its disadvantages, it is very effective for finding the roots of most equations. The advantages definitely outweigh the slight disadvantages, and that is
why it is still used to this day.
Newtons First Law of Motion
Newton's First Law of Motion
Sir Isaac Newton was in my mind one of the greatest people who ever lived. He was born in 1642 and died in 1727. He formulated three laws of motion that help explain some very important principles of physics. Some of Newton's laws could only be proved under certain conditions; actual observations and experiments made sure that they are true. Newton's laws tell us how objects move by describing the relationship between force and motion. I am going to try to explain his first law in more simple terms.
Newton's first law of motion states: A body continues in its state of rest or uniform motion unless an unbalanced force acts on it. When a body is at rest or in uniform motion this is called inertia.
Let's say that someone parks a car on a flat road and forgets to put the vehicle into park. The car should stay in that spot. This state of being is called inertia. All of a sudden the wind picks up or some kid crashes into the car with a bike. Both the wind and the kid's bike crashing into the bike are unbalanced forces. The car should start to move. The car might accelerate to two miles per hour. Now we would all assume that the car would come to a stop sometime. We assume this because it is true. It is true because there is friction between the tires and the road. The car now has inertia in uniform motion. Since there is friction, the car cannot keep moving forever because friction is an unbalanced force acting upon the tires.
What if there was not any friction? The car would keep going forever. That is if there was not any wind or a hill or any unbalanced force acting upon the car. This is rather weird just to think about. Because this usually would not happen in our customary world today. You just would not see a car go on forever.
An easy experiment to demonstrate this law is to take a glass jar and put an index or a heavier than paper card over the top of the glass jar. Next, place a coin on the index card. Be sure that the index card is strong enough to support the penny without bending itself. Now place your finger about three centimeters away from the card and flick the card out from underneath the coin. The coin should fall into the glass jar. The inertia of the coin keeps it in place even when the card is moving underneath it.
Sir Isaac Newton was in my mind one of the greatest people who ever lived. He was born in 1642 and died in 1727. He formulated three laws of motion that help explain some very important principles of physics. Some of Newton's laws could only be proved under certain conditions; actual observations and experiments made sure that they are true. Newton's laws tell us how objects move by describing the relationship between force and motion. I am going to try to explain his first law in more simple terms.
Newton's first law of motion states: A body continues in its state of rest or uniform motion unless an unbalanced force acts on it. When a body is at rest or in uniform motion this is called inertia.
Let's say that someone parks a car on a flat road and forgets to put the vehicle into park. The car should stay in that spot. This state of being is called inertia. All of a sudden the wind picks up or some kid crashes into the car with a bike. Both the wind and the kid's bike crashing into the bike are unbalanced forces. The car should start to move. The car might accelerate to two miles per hour. Now we would all assume that the car would come to a stop sometime. We assume this because it is true. It is true because there is friction between the tires and the road. The car now has inertia in uniform motion. Since there is friction, the car cannot keep moving forever because friction is an unbalanced force acting upon the tires.
What if there was not any friction? The car would keep going forever. That is if there was not any wind or a hill or any unbalanced force acting upon the car. This is rather weird just to think about. Because this usually would not happen in our customary world today. You just would not see a car go on forever.
An easy experiment to demonstrate this law is to take a glass jar and put an index or a heavier than paper card over the top of the glass jar. Next, place a coin on the index card. Be sure that the index card is strong enough to support the penny without bending itself. Now place your finger about three centimeters away from the card and flick the card out from underneath the coin. The coin should fall into the glass jar. The inertia of the coin keeps it in place even when the card is moving underneath it.
Luminescence of Black Light
The Luminescence of Black Light
Black Light. What is it? It is a portion of the Ultra-Violet Spectrum that is invisible to our eyes. We can
not distinguish it. However, when this radiation impinges on certain materials visible light is emitted and this is
known as "fluorescence." Fluorescence is visible to the human eye, in that it makes an object appear to "glow in
the dark."
There are several sources of ultra-violet light. These sources are: the sun, carbon arcs, mercury arcs, and black
lights. In most cases, the production of ultra-violet light creates a reasonable amount of heat.
Many materials exhibit the peculiar characteristic of giving off light or radiant energy when ultra-violet light is
allowed to fall upon them. This is called luminescence. In most cases, the wave length of the light radiated is longer
than that of the ultra-violet excitation but a few exceptions have been found.
The quantum theory attempts to explain this property by contending that a certain outside excitation
causes an electron to jump from one orbit to another. It is then in an unstable environment causing it to fall back into
its original orbit. This process releases energy, and if it is in the visible part of the spectrum, we have a transient
light phenomenon. Ultra-violet light is an exciting agent which causes luminescence to occur.
There are many materials which exhibit fluorescent characteristics. Many of which are even organic. Teeth,
eyes, some portions of the skin, and even blood exhibit fluorescent qualities. Naturally occurring minerals such as:
agate, calcite, chalcedony, curtisite, fluorite, gypsum, hackmanite, halite, opal scheelite, and willemite, also have
similar characteristics. These materials can be used in industries.
The radiance of ultraviolet light is measured in units called "Angstrom." The intensity of ultraviolet fluorescence
is the greatest between the 5000 and 6000 range. This being the range between the green and yellow hues.
Ultra violet light is not readily visible. It is not visible because certain materials reflect it. Ultra-violet light is
made visible due to the fact that it causes a reaction at the atomic level. When it strikes the atom, some of the
electrons are sent into other orbits. This then creates an unstable situation which causes the electron to fall back
into its place. This process produces energy, and this is what is seen. This discharge of energy is what creates the
"glow" that is seen. I had no idea that light could cause such an strong reaction on something. That something
being an atom is even more profound. Ultraviolet light causes the atom to lose a subatomic particle then regain it,
and give off energy in the form of visible light. This is just amazing.
Black Light. What is it? It is a portion of the Ultra-Violet Spectrum that is invisible to our eyes. We can
not distinguish it. However, when this radiation impinges on certain materials visible light is emitted and this is
known as "fluorescence." Fluorescence is visible to the human eye, in that it makes an object appear to "glow in
the dark."
There are several sources of ultra-violet light. These sources are: the sun, carbon arcs, mercury arcs, and black
lights. In most cases, the production of ultra-violet light creates a reasonable amount of heat.
Many materials exhibit the peculiar characteristic of giving off light or radiant energy when ultra-violet light is
allowed to fall upon them. This is called luminescence. In most cases, the wave length of the light radiated is longer
than that of the ultra-violet excitation but a few exceptions have been found.
The quantum theory attempts to explain this property by contending that a certain outside excitation
causes an electron to jump from one orbit to another. It is then in an unstable environment causing it to fall back into
its original orbit. This process releases energy, and if it is in the visible part of the spectrum, we have a transient
light phenomenon. Ultra-violet light is an exciting agent which causes luminescence to occur.
There are many materials which exhibit fluorescent characteristics. Many of which are even organic. Teeth,
eyes, some portions of the skin, and even blood exhibit fluorescent qualities. Naturally occurring minerals such as:
agate, calcite, chalcedony, curtisite, fluorite, gypsum, hackmanite, halite, opal scheelite, and willemite, also have
similar characteristics. These materials can be used in industries.
The radiance of ultraviolet light is measured in units called "Angstrom." The intensity of ultraviolet fluorescence
is the greatest between the 5000 and 6000 range. This being the range between the green and yellow hues.
Ultra violet light is not readily visible. It is not visible because certain materials reflect it. Ultra-violet light is
made visible due to the fact that it causes a reaction at the atomic level. When it strikes the atom, some of the
electrons are sent into other orbits. This then creates an unstable situation which causes the electron to fall back
into its place. This process produces energy, and this is what is seen. This discharge of energy is what creates the
"glow" that is seen. I had no idea that light could cause such an strong reaction on something. That something
being an atom is even more profound. Ultraviolet light causes the atom to lose a subatomic particle then regain it,
and give off energy in the form of visible light. This is just amazing.
Wednesday 2 January 2013
Scientific Report On Heat Transfer
Heat Transfer
Aim: Our Aim Is To Record The Temperature Of The Water After We Have
Left The Nut In There For A Designated Period Of Time.
Hypothesis: If We Put The Heated Nut Into The Water Then The Water
Temperature Will Rise.
Apparatus: For This Experiment We Need: Container, 200ml Of Water,
Thermometer, Bunsen Burner, Stop Watch, Matches And A Metal Tong
Method:
1. Light The Bunsen Burner
2. Change The Bunsen Burners Flame To Blue
3. Combine The Metal Tongs With The Nut And Wire
4. Hold It Over The Bunsen Burner For The Designated Amount Of
Time
5. Take It Off The Bunsen Burner And Place It Straight Into The
Water
6. Leave It In For The Designated Amount Of Time
7. Place The Thermometer In And Let It Sit There For About 30
Seconds
8. Take The Thermometer Reading And Put It In The Results Section
Diagram
Heat Transfer
Results: Time In Bunsen Burner Water Temperature
30 Seconds 3.1 Degrees
1 Minute 3.3 Degrees
2 Minutes 3.7 Degrees
Conclusion: Our Results Prove Our Hypothesis Is True " If We Put The
Heated Nut Into The Water Then The Water Temperature Will Rise ". Also
We Porved That Water IS A Very Poor Conducter Of Heat
Aim: Our Aim Is To Record The Temperature Of The Water After We Have
Left The Nut In There For A Designated Period Of Time.
Hypothesis: If We Put The Heated Nut Into The Water Then The Water
Temperature Will Rise.
Apparatus: For This Experiment We Need: Container, 200ml Of Water,
Thermometer, Bunsen Burner, Stop Watch, Matches And A Metal Tong
Method:
1. Light The Bunsen Burner
2. Change The Bunsen Burners Flame To Blue
3. Combine The Metal Tongs With The Nut And Wire
4. Hold It Over The Bunsen Burner For The Designated Amount Of
Time
5. Take It Off The Bunsen Burner And Place It Straight Into The
Water
6. Leave It In For The Designated Amount Of Time
7. Place The Thermometer In And Let It Sit There For About 30
Seconds
8. Take The Thermometer Reading And Put It In The Results Section
Diagram
Heat Transfer
Results: Time In Bunsen Burner Water Temperature
30 Seconds 3.1 Degrees
1 Minute 3.3 Degrees
2 Minutes 3.7 Degrees
Conclusion: Our Results Prove Our Hypothesis Is True " If We Put The
Heated Nut Into The Water Then The Water Temperature Will Rise ". Also
We Porved That Water IS A Very Poor Conducter Of Heat
Indirect Proofs
Hypothesis - I think the dice has 2 dots and by indirect proof I think we will be able to prove it.
Data:
Indirect Proof Work:
a) Total number of faces seen: 1 face x 180
Trials = 180
b) Total number of dots seen: 145
c) Average number of dots per cube: 145/180 = 0.81
d) Average number of dots per cube: 0.81 X 6 = 4.9 (5)
Actual number of dots = 5
Data:
Indirect Proof Work:
a) Total number of faces seen: 1 face x 180
Trials = 180
b) Total number of dots seen: 145
c) Average number of dots per cube: 145/180 = 0.81
d) Average number of dots per cube: 0.81 X 6 = 4.9 (5)
Actual number of dots = 5
How the laws of balnce aplly to sports
Billy Moore
Physics
Sports Page
In sports balance and stability are used to increase performance of the athlete or the athletes equipment. In Racecar driving, balance is used to stabalize the racecar. The wheels are wide and extrude from the base of the car. This gives the car a wider support base which increases the stability. The race cars are flat and low to the ground. This moves the center of gravity lower which also increases the stability of the car.
In foot ball you need to keep your balance while your running so that you can resist a tackle. Foot ball players do this by crouching down and keeping their center of mass over their feet which is there support base.
Physics
Sports Page
In sports balance and stability are used to increase performance of the athlete or the athletes equipment. In Racecar driving, balance is used to stabalize the racecar. The wheels are wide and extrude from the base of the car. This gives the car a wider support base which increases the stability. The race cars are flat and low to the ground. This moves the center of gravity lower which also increases the stability of the car.
In foot ball you need to keep your balance while your running so that you can resist a tackle. Foot ball players do this by crouching down and keeping their center of mass over their feet which is there support base.
hot to make a rocket launcher
How to Make Rocket Launchers
Making a rocket launcher may not be easy but it is worth it. The first thing needed is the model rocket set. The set comes with the engine and all other parts to make the rocket. The instructions to make the rocket must be followed. After making the rocket, a three foot PVC tube and cap must be purchased at a piping store, such as Lowes. In the cap of the PVC tube a one-fourth inch hole must be drilled. Electrical wire, that can be found at any hardware store, must be purchased. A four inch wire must be inserted through the hole in the cap. An electrical igniter must be attached to the end of the four inches of wire. Instructions that came with the rocket set need to be followed to connect the igniter to the rocket engine. One pole of a nine-volt battery, which can be purchased at any Radio Shack, should be connected to one pole of any momentary switch. The two unconnected wires from the cap must be connected to the open poles of the switch and battery. It is ready to fire the rocket launcher. Making a rocket launcher is never easy but the show is worth it.
Making a rocket launcher may not be easy but it is worth it. The first thing needed is the model rocket set. The set comes with the engine and all other parts to make the rocket. The instructions to make the rocket must be followed. After making the rocket, a three foot PVC tube and cap must be purchased at a piping store, such as Lowes. In the cap of the PVC tube a one-fourth inch hole must be drilled. Electrical wire, that can be found at any hardware store, must be purchased. A four inch wire must be inserted through the hole in the cap. An electrical igniter must be attached to the end of the four inches of wire. Instructions that came with the rocket set need to be followed to connect the igniter to the rocket engine. One pole of a nine-volt battery, which can be purchased at any Radio Shack, should be connected to one pole of any momentary switch. The two unconnected wires from the cap must be connected to the open poles of the switch and battery. It is ready to fire the rocket launcher. Making a rocket launcher is never easy but the show is worth it.
Tuesday 1 January 2013
Gun Physics
How Guns Work
A gun is a weapon that uses the force of an explosive propellant to project a missile.
Guns or firearms are classified by the diameter of the barrel opening. This is known as the calibre of the gun. Anything with a calibre up to and including .60 calibre(0.6 inches) is known as a firearm.
The precise origin of the gun is unknown, although they were in use by the early 14th century and were common place in Europe by mid-century. These early guns were nothing more than large calibre cylinders of wrought iron or cast bronze, closed at one end and loaded by placing gunpowder and projectile in the muzzle, or open end.
Nowadays firearms are a little more sophisticated.
However, the physics behind all guns remain the same. Weapons such as cannons, shotguns and rifles, work on the basic idea of conservation of momentum and the change in energy from potential to kinetic.
When the trigger is pulled the hammer hits the firing pin. The firing pin then hits the primer which causes the powder to burn hence producing lots of gases. This causes the volume behind the bullet to fill with extremely high pressure gas. The gas pushes on every surface it encounters, including the bullet in front of it and the base of the gun barrel behind it. The increase in pressure caused by the gases causes the bullet to be forced into the barrel hence causing the bullet to come out the muzzle at very high speeds. Once the bullet is fired, it remains in motion from its momentum. The momentum will carry the bullet until it strikes an object or gravity pulls the bullet towards the earth.
Firearms change potential chemical energy into kinetic energy in the actual firing of the gun. Many people do not realise that the force imparted by accelerating the bullet is not the only force acting on the gun, or the shooter. Grains of burned gun powder are sent out the muzzle at high velocity. When the trigger is pulled, the hammer strikes a small charge at the end of the shell, the ammunition. This charge ignites black gun powder packed behind the lead ball bearings. When the black gun powder burns, it produces gas that rapidly expands with the burning of more black gun powder. High pressure gases exert forces on the back of the bullet and on the gun. The only way for the gas to escape is to push the bullet out of its way through the end of the barrel. This is how a bullet is fired from a gun.
Conservation of momentum is the law that is held true when the gun is fired and a "kick" is felt. When a bullet is fired from a gun, total momentum before is zero since nothing is moving. After firing the bullet there is a momentum in the forward direction. The gun must therefore have the same magnitude of momentum but in the opposite direction so that they cancel each other out leaving the total momentum still equal to zero. For this reason the gun must have a recoil velocity after the bullet is fired(i.e. the gun 'jumps' backwards and a 'kick' is felt) .
As the bullet is propelled through the barrel, it gains momentum. In order for the entire system of the gun and the ammunition to have equal momentum, the gun must gain momentum in the opposite direction from the bullet. Momentum is a vector quantity, having both a direction and a direction. The faster an object is moving or the more mass it has, the more momentum it has in the direction of its motion(momentum = mass velocity). Because momentum is a conserved quantity, it cannot be created or destroyed(momentum before = momentum after). It can only be transferred between objects. Momentum is conserved because of Newton's third law of motion.
When one object exerts a force on a second object for a certain amount of time, the second object exerts an equal but oppositely directed force on the first object for exactly the same amount of time. The momentum lost by the first object is exactly equal to the momentum gained by the second object. Momentum is transferred from the first object to the second object. In this case, if a gun exerts a force on a bullet when firing it forward then the bullet will exert an equal force in the opposite direction on the gun causing it to move backwards or recoil. Although the action and reaction forces are equal in size the effect on the gun and the bullet are not the same since the mass of the gun is far greater than the mass of the bullet. The acceleration of the bullet while moving along the gun barrel would be much greater than the acceleration of the gun(acceleration = force mass).
The conservation of momentum is also demonstrated when the bullet hits an object. The object that it strikes absorbs the kinetic energy, energy from motion and momentum. If the force of momentum from the bullet is great enough to overcome the mass of the object, the target will be moved along the same vector as the bullet.
To increase the accuracy of the flight of the bullet, a technique called rifling can be used. Rifling is where the barrel of the gun and or the bullet is creased with spiral grooves that allow air to pass through. When the bullet is fired, the air passes through these curved grooves and spins the bullet. This spinning action allows the bullet to cut through the air more efficiently and fly on a more true course, thus stabilising its trajectory.
A gun is a weapon that uses the force of an explosive propellant to project a missile.
Guns or firearms are classified by the diameter of the barrel opening. This is known as the calibre of the gun. Anything with a calibre up to and including .60 calibre(0.6 inches) is known as a firearm.
The precise origin of the gun is unknown, although they were in use by the early 14th century and were common place in Europe by mid-century. These early guns were nothing more than large calibre cylinders of wrought iron or cast bronze, closed at one end and loaded by placing gunpowder and projectile in the muzzle, or open end.
Nowadays firearms are a little more sophisticated.
However, the physics behind all guns remain the same. Weapons such as cannons, shotguns and rifles, work on the basic idea of conservation of momentum and the change in energy from potential to kinetic.
When the trigger is pulled the hammer hits the firing pin. The firing pin then hits the primer which causes the powder to burn hence producing lots of gases. This causes the volume behind the bullet to fill with extremely high pressure gas. The gas pushes on every surface it encounters, including the bullet in front of it and the base of the gun barrel behind it. The increase in pressure caused by the gases causes the bullet to be forced into the barrel hence causing the bullet to come out the muzzle at very high speeds. Once the bullet is fired, it remains in motion from its momentum. The momentum will carry the bullet until it strikes an object or gravity pulls the bullet towards the earth.
Firearms change potential chemical energy into kinetic energy in the actual firing of the gun. Many people do not realise that the force imparted by accelerating the bullet is not the only force acting on the gun, or the shooter. Grains of burned gun powder are sent out the muzzle at high velocity. When the trigger is pulled, the hammer strikes a small charge at the end of the shell, the ammunition. This charge ignites black gun powder packed behind the lead ball bearings. When the black gun powder burns, it produces gas that rapidly expands with the burning of more black gun powder. High pressure gases exert forces on the back of the bullet and on the gun. The only way for the gas to escape is to push the bullet out of its way through the end of the barrel. This is how a bullet is fired from a gun.
Conservation of momentum is the law that is held true when the gun is fired and a "kick" is felt. When a bullet is fired from a gun, total momentum before is zero since nothing is moving. After firing the bullet there is a momentum in the forward direction. The gun must therefore have the same magnitude of momentum but in the opposite direction so that they cancel each other out leaving the total momentum still equal to zero. For this reason the gun must have a recoil velocity after the bullet is fired(i.e. the gun 'jumps' backwards and a 'kick' is felt) .
As the bullet is propelled through the barrel, it gains momentum. In order for the entire system of the gun and the ammunition to have equal momentum, the gun must gain momentum in the opposite direction from the bullet. Momentum is a vector quantity, having both a direction and a direction. The faster an object is moving or the more mass it has, the more momentum it has in the direction of its motion(momentum = mass velocity). Because momentum is a conserved quantity, it cannot be created or destroyed(momentum before = momentum after). It can only be transferred between objects. Momentum is conserved because of Newton's third law of motion.
When one object exerts a force on a second object for a certain amount of time, the second object exerts an equal but oppositely directed force on the first object for exactly the same amount of time. The momentum lost by the first object is exactly equal to the momentum gained by the second object. Momentum is transferred from the first object to the second object. In this case, if a gun exerts a force on a bullet when firing it forward then the bullet will exert an equal force in the opposite direction on the gun causing it to move backwards or recoil. Although the action and reaction forces are equal in size the effect on the gun and the bullet are not the same since the mass of the gun is far greater than the mass of the bullet. The acceleration of the bullet while moving along the gun barrel would be much greater than the acceleration of the gun(acceleration = force mass).
The conservation of momentum is also demonstrated when the bullet hits an object. The object that it strikes absorbs the kinetic energy, energy from motion and momentum. If the force of momentum from the bullet is great enough to overcome the mass of the object, the target will be moved along the same vector as the bullet.
To increase the accuracy of the flight of the bullet, a technique called rifling can be used. Rifling is where the barrel of the gun and or the bullet is creased with spiral grooves that allow air to pass through. When the bullet is fired, the air passes through these curved grooves and spins the bullet. This spinning action allows the bullet to cut through the air more efficiently and fly on a more true course, thus stabilising its trajectory.
GeigerMueller Tube
In the Geiger-Muller tube, particles ionize gas atoms. The tube contains a gas at low pressure. At one end of the tube is a very thin "window" through which charged particles or gamma rays pass. Inside the tube is a copper cylinder with a negative charge. A rigid wire with a positive charge runs down the center of this cylinder. The voltage across the wire and cylinder is kept just below the point at which a spontaneous discharge, or spark, occurs. When a charged particle or gamma ray enters the tube , it ionizes a gas atom between the copper cylinder and the wire. The positive ion produced is accelerated toward the copper cylinder by the potential difference. The electron is accelerated toward the positive wire. As these new particles move toward the electrodes, they strike other atoms and form even more ion in their path.
Thus an avalanche of charged particles is created and a pulse of current flows through the tube. The current causes a potential difference across a resistor in the circuit. The voltage is amplified and registers the arrival of a particle by advancing a counter or producing an audible signal, such as a click. The potential difference across the tube so that the current flow stops. Thus the tube is ready for the beginning of a new avalanche when another particle or gamma ray enters it
Thus an avalanche of charged particles is created and a pulse of current flows through the tube. The current causes a potential difference across a resistor in the circuit. The voltage is amplified and registers the arrival of a particle by advancing a counter or producing an audible signal, such as a click. The potential difference across the tube so that the current flow stops. Thus the tube is ready for the beginning of a new avalanche when another particle or gamma ray enters it
Fire Retardant Fabrics
Purpose: To find which fabric is most flammable. (Which fabric will catch fire fastest)
Materials:
Lighter
safety goggles
Stop Watch
5cm x 5cm piece of Denim
5cm x 5cm piece of Nylon
5cm x 5cm piece of Polyester
5cm x 5cm piece of Cotton
5cm x 5cm piece of Rayon
5cm x 5cm piece of Acrylic
Procedure:
1) Place a piece fabric under flame. Make sure that each time you do this, the flame is placed at an equal distance from the fabric.
2) As soon as fabric is exposed to flame, begin timing with the stop watch
3) Stop timing when fabric ignites.
4) Put out the fire. Try not to destroy the fabric, it can be used for presentation.
5) Record the time it took for the fabric to ignite
6) Repeat steps 1 to 5 three times for each piece of fabric.
Hypothesis: We think that the Polyester will ignite the fastest, because it is very light, and delicate. We think that the Nylon will ignite in the longest time because it is much like a plastic.
Results: In order to control all of the variables, we burned and timed each type fabric three times. Below is a table showing our results in seconds.
Next Page
Fabric 1st Time 2nd Time 3rd Time Average
Denim 5.3 sec 4.8 sec 5 sec 5.03 sec
Nylon 4 sec 3.3 sec 4.1 sec 3.8 sec
Polyester 0.5 sec 0.7 sec 0.7 sec 0.63 sec
Cotton 4.6 sec 4.2 sec 5 sec 4.6 sec
Rayon 3.5 sec 3 sec 2.4 sec 2.97 sec
Acrylic 4.7 sec 5 sec 4.1 sec 4.6 sec
Conclusion:
The Polyester ignited the fastest, which is what we hypothesized. The flame was nearly an inch away from the fabric, when it ignited. It burned up in a flash. The majority of the fabric was burned to ashes in a matter of split seconds. The Denim ignited in the longest amount of time. If we were testing which fabric is safest to wear near a flame, it would be Denim. The Polyester is extremely dangerous to wear near a fire.
Research:
Denim: Denim is a heavy cotton twilled fabric, usually colored; coarser weaves are used for overalls, etc.; finer, for drapery and upholstery. The name comes from French town of Nimes (serge de Nimes).
Nylon: Nylon is used for several purposes. Clothing is just one. Nylon was invented in 1938 by a team of researchers, led by organic chemist Wallace H. The production of common nylon (nylon-6,6) begins when the basic hydrocarbons, under pressure and heat, are synthesized into the chemicals adipic acid and hexamethylene diamine. (The production of other nylons may require slightly different acids and amines.) These are mixed to form a substance called nylon salt. This concentrated salt solution is heated in huge kettles, called autoclaves. Here the acid and amine molecules link up alternately to form a nylon superpolymer (long-chain molecule). The molten nylon then pours over a giant casting wheel. A swift spray of cold water turns the molten ribbon of nylon into a hard, translucent sheet, which is then chopped into small flakes called nylon chips.
If the nylon is intended for sheets, rods, bristles, coatings, or molds, it is sent to factories in the form of chips. The chips are melted and turned into final products. Nylon intended for yarn must undergo further treatment. In a process called melt spinning, the chips are melted, and the melt is pumped through a spinneret, a perforated plate with tiny holes equal in number to the filaments, or single threads, desired in the finished yarn. The filaments form as soon as they strike cool air outside the spinneret.
Polyester: Polyester is very similar to Nylon. In fact, when we looked polyester up in an encyclopedia, it said see nylon. Through our experiment we discovered that polyester is much more delicate than Nylon. Nylon fabric is more like a plastic, which is why Nylon clothing is water proof. On the other hand, Polyester is extremely delicate and light. Polyester is usually either transparent, or translucent.
Cotton: Cotton is used in some way, every day of our lives. Cotton is used for both warm and cold clothing. Cotton is made from the cotton plant. The cotton plant is a warm-climate crop. To develop fully, the plant usually needs a growing season of 150 days free from frost. The cotton planting season ranges from February 1 in southern to early June. To get warmth from the sun, the seeds are planted shallowly, from one to two inches deep. Some farmers plant their seed in hills, some in furrows, and others in flat seed beds. Cotton was the leading industry in the USA during the 1800's and early 1900's, and it still is in some counties.
Rayon: Rayon or Chardonnet silk is a vegetable fiber (cellulose). Rayon is produced mechanically from wood pulp. The fabric is fairly light, and delicate. Rayon is used in many types of clothes.
Acrylic: Acrylic is a man made fabric. The process for making Acrylic is extremely complicated, and is made using a formula (e.g. H2O). Acrylic is very heavy, and is much like wool. The sample of Acrylic that we used came from a sweater.
COPY AS IS, AND PASTE IN MS WORD. IT WILL MAKE MORE SENCE!
Materials:
Lighter
safety goggles
Stop Watch
5cm x 5cm piece of Denim
5cm x 5cm piece of Nylon
5cm x 5cm piece of Polyester
5cm x 5cm piece of Cotton
5cm x 5cm piece of Rayon
5cm x 5cm piece of Acrylic
Procedure:
1) Place a piece fabric under flame. Make sure that each time you do this, the flame is placed at an equal distance from the fabric.
2) As soon as fabric is exposed to flame, begin timing with the stop watch
3) Stop timing when fabric ignites.
4) Put out the fire. Try not to destroy the fabric, it can be used for presentation.
5) Record the time it took for the fabric to ignite
6) Repeat steps 1 to 5 three times for each piece of fabric.
Hypothesis: We think that the Polyester will ignite the fastest, because it is very light, and delicate. We think that the Nylon will ignite in the longest time because it is much like a plastic.
Results: In order to control all of the variables, we burned and timed each type fabric three times. Below is a table showing our results in seconds.
Next Page
Fabric 1st Time 2nd Time 3rd Time Average
Denim 5.3 sec 4.8 sec 5 sec 5.03 sec
Nylon 4 sec 3.3 sec 4.1 sec 3.8 sec
Polyester 0.5 sec 0.7 sec 0.7 sec 0.63 sec
Cotton 4.6 sec 4.2 sec 5 sec 4.6 sec
Rayon 3.5 sec 3 sec 2.4 sec 2.97 sec
Acrylic 4.7 sec 5 sec 4.1 sec 4.6 sec
Conclusion:
The Polyester ignited the fastest, which is what we hypothesized. The flame was nearly an inch away from the fabric, when it ignited. It burned up in a flash. The majority of the fabric was burned to ashes in a matter of split seconds. The Denim ignited in the longest amount of time. If we were testing which fabric is safest to wear near a flame, it would be Denim. The Polyester is extremely dangerous to wear near a fire.
Research:
Denim: Denim is a heavy cotton twilled fabric, usually colored; coarser weaves are used for overalls, etc.; finer, for drapery and upholstery. The name comes from French town of Nimes (serge de Nimes).
Nylon: Nylon is used for several purposes. Clothing is just one. Nylon was invented in 1938 by a team of researchers, led by organic chemist Wallace H. The production of common nylon (nylon-6,6) begins when the basic hydrocarbons, under pressure and heat, are synthesized into the chemicals adipic acid and hexamethylene diamine. (The production of other nylons may require slightly different acids and amines.) These are mixed to form a substance called nylon salt. This concentrated salt solution is heated in huge kettles, called autoclaves. Here the acid and amine molecules link up alternately to form a nylon superpolymer (long-chain molecule). The molten nylon then pours over a giant casting wheel. A swift spray of cold water turns the molten ribbon of nylon into a hard, translucent sheet, which is then chopped into small flakes called nylon chips.
If the nylon is intended for sheets, rods, bristles, coatings, or molds, it is sent to factories in the form of chips. The chips are melted and turned into final products. Nylon intended for yarn must undergo further treatment. In a process called melt spinning, the chips are melted, and the melt is pumped through a spinneret, a perforated plate with tiny holes equal in number to the filaments, or single threads, desired in the finished yarn. The filaments form as soon as they strike cool air outside the spinneret.
Polyester: Polyester is very similar to Nylon. In fact, when we looked polyester up in an encyclopedia, it said see nylon. Through our experiment we discovered that polyester is much more delicate than Nylon. Nylon fabric is more like a plastic, which is why Nylon clothing is water proof. On the other hand, Polyester is extremely delicate and light. Polyester is usually either transparent, or translucent.
Cotton: Cotton is used in some way, every day of our lives. Cotton is used for both warm and cold clothing. Cotton is made from the cotton plant. The cotton plant is a warm-climate crop. To develop fully, the plant usually needs a growing season of 150 days free from frost. The cotton planting season ranges from February 1 in southern to early June. To get warmth from the sun, the seeds are planted shallowly, from one to two inches deep. Some farmers plant their seed in hills, some in furrows, and others in flat seed beds. Cotton was the leading industry in the USA during the 1800's and early 1900's, and it still is in some counties.
Rayon: Rayon or Chardonnet silk is a vegetable fiber (cellulose). Rayon is produced mechanically from wood pulp. The fabric is fairly light, and delicate. Rayon is used in many types of clothes.
Acrylic: Acrylic is a man made fabric. The process for making Acrylic is extremely complicated, and is made using a formula (e.g. H2O). Acrylic is very heavy, and is much like wool. The sample of Acrylic that we used came from a sweater.
COPY AS IS, AND PASTE IN MS WORD. IT WILL MAKE MORE SENCE!
Fibre Optics
Assignment
Many modern medical materials and equipment work on a principle which is beyond the capacity of human transducers.
Comment and discuss the working principles of an endoscope, uteroscope or a rectoscope showing the illuminating path, the image path, transmission path and the liquid transfer or operating instrument ducts, showing the position of suitable valves.
This will therefore explain how light travels through an optical fibre and show how such fibres are used in medicinal equipment either to transmit light or to bring back images from within a patient.
Contents
Fibre Optics
Fibre-Optic Bundles
Coherent and Incoherent Bundles
Transimission efficiency and resolution
Types of Fibres: Single mode or Multimode ?
Fibre Properties
Fibre-Optic Endoscopy
Introduction
The Fibre-Optic Endoscope
Some Applications for Fibre-Optic Endoscopy
References
Fibre Optics
A relatively new technology with vast potential importance, fibre optics, is the
channelled transmission of light through hair-thin glass fibres.
The clear advantages of fibre optics are too often obscured by concerns that
may have been valid during the pioneering days of fibre, but that have since been
answered by technical advances.
Fibre is fragile
An optical fibre has greater tensile strength than copper or steel fibres of the same
diameter. It is flexible, bends easily, and resists most corrosive elements that attack
copper cable. Optical cables can withstand pulling forces of more than 150 pounds.
Fibre is hard to work with
This myth derives from the early days of fibre optic connectors. Early connectors
where difficult to apply; they came with many small parts that could tax even the
nimble fingered. They needed epoxy, curing, cleaving and polishing. On top of that,
the technologies of epoxy, curing, cleaving and polishing were still evolving.
Today, connectors have fewer parts, the procedures for termination are well
understood, and the craftsperson is aided by polishing machines and curing ovens to
make the job faster and easier.
Even better, epoxyless connectors eliminate the need for the messy and time-
consuming application of epoxy. Polishing is an increasingly simple, straightforward
process. Pre-terminated cable assemblies also speed installation and reduce a once
(but no longer) labour-intensive process.
Fibre Optic Bundles
If light enters the end of a solid glass rod so that the light transmitted into the
rod strikes the side of the rod at an angle O, exceeding the critical angle, then total
internal reflection occurs. The light continues to be internally reflected
back and forth in its passage along the rod, and it emerges from the other end
with very little loss of intensity.
This is the principle in fibre optics of which long glass fibres of very small
cross-sectional area transmit light from end to end, even when bent, without much
loss of light through their side walls. Such fibres can then be combined into 'bundles'
of dozens to thousands of fibres for the efficient conveyance of light from one (often
inaccessible) point to another.
If the glass fibre comes into contact with a substance of equal or higher
refractive index, such as an adjacent glass fibre, dirt or grease, then total internal
reflection does not occur and light is lost rapidly by transmission through the area of
contact. To avoid such 'leakage' and to protect the fibres, they are clad in 'glass
skins' of refractive index lower than that of the fibre core.
As the angle of incidence I increases, R increases and O ( = (n/2) -R)
decreases. Eventually, O reaches C, the critical angle,
and any further reduction in O results in transmission through the side wall.
The expression n0 sin Imax is called the numerical aperture of the fibre. A
typical value for this might be 0.55, making Imax about 33o in air. Sometimes Imax is
referred to as the half-angle of the fibre, since it describes half the field of view
acceptably transmitted. The numerical aperture (and hence Imax) can be increased by
using a core of high refractive index. However, these glasses have a lower efficiency
of transmission, especially at the blue end of the spectrum, and are not commonly
used.
The above analysis applies only to a straight line fibre. If the fibre is curved, the angles of incidence vary as the light travels along the fibre and losses occur if the angles fall below the critical angle. In practice, a radius of curvature down to about twenty times the fibre diameter can be tolerated without significant losses.
Coherent and Incoherent Bundles
An ideal fibre transmits light independently of its neighbours, so if a bundle of
fibres is placed together in an orderly manner along its length, with the relative
positions remaining unchanged, actual images may be transmitted along the fibre.
Such an arrangement is called a coherent bundle, and consists of fibres of
very small diameter about 10 µm. The ends of the bundle are cut square and
polished smooth to prevent distortions. Each fibre transmits a small element of the
image which is seen at the other end of the coherent bundle as a mosaic. The eye has
to 'look through' the fragmented structure to appreciate a clear image.
The image to be transmitted is either in direct contact with the end of the
bundle or focused on to this surface. The image formed at the other end is viewed
using an eyepiece incorporating magnification. One novel method of magnification is
to make one end of the fibres smaller than the other. For example, if they have an
average diameter of 5µm at the image end, and 50µm at the viewing end, a
magnification of x10 is achieved.
In contrast, a bundle of fibres arranged at random is known as an incoherent bundle, (or sometimes simply a light guide) and is suitable only for the transport of light not of images. The fibres of such a bundle are relatively large having diameters of about 50-100µm.
The fibre, must be cabled - enclosed within a protective structure. This usually includes strength members and an outer buffer. The most common strength member is Kevlar aramid yarn, which adds mechanical strength. During and after installation, strength members provide crush resistance and handle the tensile stresses applied to the cable so that the fibre is not damaged. Steel and fibreglass rods are also used as strength members in multifibre bundles.
The concentric layers of an optical fibre include the light-carrying core, the cladding and the protective buffer.
Core : the inner light-carrying member.
Cladding : the middle layer, which serves to confine the light to the core.
Buffer : the outer layer which serves as a 'shock absorber' to protect the core and cladding from damage.
The buffer protects against abrasion, oil, solvents and other contaminates.
The buffer usually defines the cable's duty and flammability rating.
Transmission efficiency and resolution
Light injected into a fibre can adopt any of several zigzag paths, or modes. When a large number of modes are present they may overlap, for each mode has a different velocity along the fibre (modal dispersion). The glass fibres used in present-day fibre-optic systems are based on ultrapure fused silica. Fibre made from ordinary glass is so dirty that impurities reduce signal intensity by a factor of on million in only about 5 m (16 ft) of fibre. These impurities must be removed -- often to the parts-per-billion level - before useful long-haul fibres can be drawn. But even perfectly pure glass is not perfectly transparent.
It attenuates, or weakens, light in two ways. One, occurring at shorter wavelengths, is a scattering caused by unavoidable density fluctuations within the fibre. The other is a longer wavelength absorption by atomic vibrations (photons).
For silica, the minimum attenuation, or the maximum transparency, occurs in wavelengths in the near infrared, at about 1.5 micrometers.
In addition, there are 'end losses' which are light losses at the end faces due to partial reflection and incidence on the cladding material. Thus, light sources need to be very powerful, and even then problems can arise when viewing coloured images since different wavelengths have different transmission efficiencies.
The thinner and more numerous the fibres, the greater should be the resolution. However, when the core diameter falls below about 5µm diffraction starts to occur and transmission efficiency drops. Hence, although fibres with core diameters down to about 1µm have been used, typical diameters are nearer 10µm. A deterioration in image quality may occur for a number of reasons, for example defects in the end faces of the fibres, misalignment of fibres, broken fibres (causing black spots), or light leakage between adjacent fibres (producing 'cross-talk').
Types of fibres : Singlemode or Multimode ?
In the simplest optical fibre, the relatively large core has uniform optical properties. Termed a step-index multimode fibre, this fibre supports thousands of modes and offers the highest dispersion - and hence the lowest bandwidth.
By varying the optical properties of the core, the graded-index multimode fibre reduces dispersion and increases bandwidth. Grading makes light following longer paths travel slightly faster than light following a shorter path. Put another way, light travelling straight down the core without reflecting travels slowest.
The net result is that the light does not spread out nearly as much. Nearly all multimode fibres used in medical application have a graded index.
Fibre Properties
Numerical aperture (NA) of the fibre defines which light will be propagated and will not. NA defines the light-gathering ability of the fibre. Imagine a cone coming from the core. Light entering the core from within this cone will be propagated by total internal reflection. Light entering from outside the cone will not be propagated.
NA has an important consequence. A large NA makes it easier to inject more light into a fibre, while a small NA tends to give the fibre a higher bandwidth. A large NA allows greater modal dispersion by allowing more modes in which light can travel. A smaller NA reduces dispersion by limiting the number of modes.
Fibre-optic endoscopy
Introduction
An endoscope is an instrument designed to provide a direct view of an internal part of the body, and possibly to perform tasks such as the removal of samples, injection of fluids and diathermy. Fibre optics has extended the scope of the instrument considerably by permitting the transmission of images from inaccessible areas such as the oesophagus, stomach, intestines, heart and lungs.
The fibre-optic endoscope
The long flexible shaft of the instrument is usually constructed of steel mesh, often with a crush-resistant covering of a bronze or steel spiral, it is then sheathed with a protective, low-friction covering of PVC or some other impervious material, which forms a hermetic seal around the instrument. The shaft is about 10mm in diameter; about 0.6-1.8 m long (depending on the application) and has a short deflectable section about 50-85mm long leading to its distal tip.
Within the shaft lie:
at least one non-coherent fibre-optic bundle to transmit light from the distant light source to the distal tip;
a coherent fibre-optic bundle transmitting the image from the objective lens at the distal tip;
an irrigation channel through which water can be pumped to wash the objective lens;
(d) an operations channel for the Performance of tasks;
(e) control cables.
The viewing end of the endoscope contains:
an eyepiece, with focus controls and camera attachment;
distal tip deflection controls, giving polydirectional control up to about
200o, plus locking capability;
objective lens control which may be a push-pull wire effecting focusing;
valve controls for air aspiration, (suctioned withdrawal of body fluids through the operations channel) and lens washing and air insufflation (application of water or air jet through the irrigation channel);
operating channel valve, which controls the entry of catheters, electrodes, biopsy forceps and other flexible devices;
connection with the umbilical tube, providing light through a non-coherent fibre-optic bundle and water or air from the pump or aspirator system.
A typical Micro-video Endoscopy Unit would contain:
Optical catheter system as described above,
Colour video monitor
CO2 and fluid insufflation,
Instrumentation,
Disposables,
Miscellaneous accessories.
Some applications of Fibre-optic endoscopy
Endoscopic examination of the gastrointestinal tract has proved especially successful with the diagnosis and treatment of ulcers, cancers, constrictions, bleeding sites, and so on. The heart, respiratory system and pancreas have also been investigated.
Another application is the measurment of the proportion of haemoglobin in the blood which is combined with oxygen using an oximeter. Two incoherent bundles are introduced into the blood stream: one is used to illuminate a sample of blood and the other to assess the absorption of light by the blood.
An endoscope can also be equipped with a laser that can vaporize, coagulate, or cut structures, often with more ease and flexibility than a more rigid cutting knife. It is a less invasive method that causes less scarring and a quicker recovery time than other surgical techniques.
Common types of endoscopes are the cytoscope to view the bladder, the bronchoscope to view the lungs, the otoscope to view the ear, the arthroscope to view the knee and other joints, and the laparascope to view the female reproductive structures. The most common surgery performed through endoscopy is biopsy, the removal of tissue for microscopic study to detect a malignancy. Diagnostic hysteroscopy with directed biopsy and dilatation and curettage, removal of polyps, and removal of foreign objects and Cystourethroscopy are other important fields which endoscopy makes possible.
References:
Pope, Jean A.; Medical Physics 2nd r.e. Heinemann Educational Printers 1973.
Brown, B. H. , Smallwood R. H.; Medical Physics and Physiological Measurement;
Blackwell Scientific Publications, Billing and Son's Publishers; 1981.
Many modern medical materials and equipment work on a principle which is beyond the capacity of human transducers.
Comment and discuss the working principles of an endoscope, uteroscope or a rectoscope showing the illuminating path, the image path, transmission path and the liquid transfer or operating instrument ducts, showing the position of suitable valves.
This will therefore explain how light travels through an optical fibre and show how such fibres are used in medicinal equipment either to transmit light or to bring back images from within a patient.
Contents
Fibre Optics
Fibre-Optic Bundles
Coherent and Incoherent Bundles
Transimission efficiency and resolution
Types of Fibres: Single mode or Multimode ?
Fibre Properties
Fibre-Optic Endoscopy
Introduction
The Fibre-Optic Endoscope
Some Applications for Fibre-Optic Endoscopy
References
Fibre Optics
A relatively new technology with vast potential importance, fibre optics, is the
channelled transmission of light through hair-thin glass fibres.
The clear advantages of fibre optics are too often obscured by concerns that
may have been valid during the pioneering days of fibre, but that have since been
answered by technical advances.
Fibre is fragile
An optical fibre has greater tensile strength than copper or steel fibres of the same
diameter. It is flexible, bends easily, and resists most corrosive elements that attack
copper cable. Optical cables can withstand pulling forces of more than 150 pounds.
Fibre is hard to work with
This myth derives from the early days of fibre optic connectors. Early connectors
where difficult to apply; they came with many small parts that could tax even the
nimble fingered. They needed epoxy, curing, cleaving and polishing. On top of that,
the technologies of epoxy, curing, cleaving and polishing were still evolving.
Today, connectors have fewer parts, the procedures for termination are well
understood, and the craftsperson is aided by polishing machines and curing ovens to
make the job faster and easier.
Even better, epoxyless connectors eliminate the need for the messy and time-
consuming application of epoxy. Polishing is an increasingly simple, straightforward
process. Pre-terminated cable assemblies also speed installation and reduce a once
(but no longer) labour-intensive process.
Fibre Optic Bundles
If light enters the end of a solid glass rod so that the light transmitted into the
rod strikes the side of the rod at an angle O, exceeding the critical angle, then total
internal reflection occurs. The light continues to be internally reflected
back and forth in its passage along the rod, and it emerges from the other end
with very little loss of intensity.
This is the principle in fibre optics of which long glass fibres of very small
cross-sectional area transmit light from end to end, even when bent, without much
loss of light through their side walls. Such fibres can then be combined into 'bundles'
of dozens to thousands of fibres for the efficient conveyance of light from one (often
inaccessible) point to another.
If the glass fibre comes into contact with a substance of equal or higher
refractive index, such as an adjacent glass fibre, dirt or grease, then total internal
reflection does not occur and light is lost rapidly by transmission through the area of
contact. To avoid such 'leakage' and to protect the fibres, they are clad in 'glass
skins' of refractive index lower than that of the fibre core.
As the angle of incidence I increases, R increases and O ( = (n/2) -R)
decreases. Eventually, O reaches C, the critical angle,
and any further reduction in O results in transmission through the side wall.
The expression n0 sin Imax is called the numerical aperture of the fibre. A
typical value for this might be 0.55, making Imax about 33o in air. Sometimes Imax is
referred to as the half-angle of the fibre, since it describes half the field of view
acceptably transmitted. The numerical aperture (and hence Imax) can be increased by
using a core of high refractive index. However, these glasses have a lower efficiency
of transmission, especially at the blue end of the spectrum, and are not commonly
used.
The above analysis applies only to a straight line fibre. If the fibre is curved, the angles of incidence vary as the light travels along the fibre and losses occur if the angles fall below the critical angle. In practice, a radius of curvature down to about twenty times the fibre diameter can be tolerated without significant losses.
Coherent and Incoherent Bundles
An ideal fibre transmits light independently of its neighbours, so if a bundle of
fibres is placed together in an orderly manner along its length, with the relative
positions remaining unchanged, actual images may be transmitted along the fibre.
Such an arrangement is called a coherent bundle, and consists of fibres of
very small diameter about 10 µm. The ends of the bundle are cut square and
polished smooth to prevent distortions. Each fibre transmits a small element of the
image which is seen at the other end of the coherent bundle as a mosaic. The eye has
to 'look through' the fragmented structure to appreciate a clear image.
The image to be transmitted is either in direct contact with the end of the
bundle or focused on to this surface. The image formed at the other end is viewed
using an eyepiece incorporating magnification. One novel method of magnification is
to make one end of the fibres smaller than the other. For example, if they have an
average diameter of 5µm at the image end, and 50µm at the viewing end, a
magnification of x10 is achieved.
In contrast, a bundle of fibres arranged at random is known as an incoherent bundle, (or sometimes simply a light guide) and is suitable only for the transport of light not of images. The fibres of such a bundle are relatively large having diameters of about 50-100µm.
The fibre, must be cabled - enclosed within a protective structure. This usually includes strength members and an outer buffer. The most common strength member is Kevlar aramid yarn, which adds mechanical strength. During and after installation, strength members provide crush resistance and handle the tensile stresses applied to the cable so that the fibre is not damaged. Steel and fibreglass rods are also used as strength members in multifibre bundles.
The concentric layers of an optical fibre include the light-carrying core, the cladding and the protective buffer.
Core : the inner light-carrying member.
Cladding : the middle layer, which serves to confine the light to the core.
Buffer : the outer layer which serves as a 'shock absorber' to protect the core and cladding from damage.
The buffer protects against abrasion, oil, solvents and other contaminates.
The buffer usually defines the cable's duty and flammability rating.
Transmission efficiency and resolution
Light injected into a fibre can adopt any of several zigzag paths, or modes. When a large number of modes are present they may overlap, for each mode has a different velocity along the fibre (modal dispersion). The glass fibres used in present-day fibre-optic systems are based on ultrapure fused silica. Fibre made from ordinary glass is so dirty that impurities reduce signal intensity by a factor of on million in only about 5 m (16 ft) of fibre. These impurities must be removed -- often to the parts-per-billion level - before useful long-haul fibres can be drawn. But even perfectly pure glass is not perfectly transparent.
It attenuates, or weakens, light in two ways. One, occurring at shorter wavelengths, is a scattering caused by unavoidable density fluctuations within the fibre. The other is a longer wavelength absorption by atomic vibrations (photons).
For silica, the minimum attenuation, or the maximum transparency, occurs in wavelengths in the near infrared, at about 1.5 micrometers.
In addition, there are 'end losses' which are light losses at the end faces due to partial reflection and incidence on the cladding material. Thus, light sources need to be very powerful, and even then problems can arise when viewing coloured images since different wavelengths have different transmission efficiencies.
The thinner and more numerous the fibres, the greater should be the resolution. However, when the core diameter falls below about 5µm diffraction starts to occur and transmission efficiency drops. Hence, although fibres with core diameters down to about 1µm have been used, typical diameters are nearer 10µm. A deterioration in image quality may occur for a number of reasons, for example defects in the end faces of the fibres, misalignment of fibres, broken fibres (causing black spots), or light leakage between adjacent fibres (producing 'cross-talk').
Types of fibres : Singlemode or Multimode ?
In the simplest optical fibre, the relatively large core has uniform optical properties. Termed a step-index multimode fibre, this fibre supports thousands of modes and offers the highest dispersion - and hence the lowest bandwidth.
By varying the optical properties of the core, the graded-index multimode fibre reduces dispersion and increases bandwidth. Grading makes light following longer paths travel slightly faster than light following a shorter path. Put another way, light travelling straight down the core without reflecting travels slowest.
The net result is that the light does not spread out nearly as much. Nearly all multimode fibres used in medical application have a graded index.
Fibre Properties
Numerical aperture (NA) of the fibre defines which light will be propagated and will not. NA defines the light-gathering ability of the fibre. Imagine a cone coming from the core. Light entering the core from within this cone will be propagated by total internal reflection. Light entering from outside the cone will not be propagated.
NA has an important consequence. A large NA makes it easier to inject more light into a fibre, while a small NA tends to give the fibre a higher bandwidth. A large NA allows greater modal dispersion by allowing more modes in which light can travel. A smaller NA reduces dispersion by limiting the number of modes.
Fibre-optic endoscopy
Introduction
An endoscope is an instrument designed to provide a direct view of an internal part of the body, and possibly to perform tasks such as the removal of samples, injection of fluids and diathermy. Fibre optics has extended the scope of the instrument considerably by permitting the transmission of images from inaccessible areas such as the oesophagus, stomach, intestines, heart and lungs.
The fibre-optic endoscope
The long flexible shaft of the instrument is usually constructed of steel mesh, often with a crush-resistant covering of a bronze or steel spiral, it is then sheathed with a protective, low-friction covering of PVC or some other impervious material, which forms a hermetic seal around the instrument. The shaft is about 10mm in diameter; about 0.6-1.8 m long (depending on the application) and has a short deflectable section about 50-85mm long leading to its distal tip.
Within the shaft lie:
at least one non-coherent fibre-optic bundle to transmit light from the distant light source to the distal tip;
a coherent fibre-optic bundle transmitting the image from the objective lens at the distal tip;
an irrigation channel through which water can be pumped to wash the objective lens;
(d) an operations channel for the Performance of tasks;
(e) control cables.
The viewing end of the endoscope contains:
an eyepiece, with focus controls and camera attachment;
distal tip deflection controls, giving polydirectional control up to about
200o, plus locking capability;
objective lens control which may be a push-pull wire effecting focusing;
valve controls for air aspiration, (suctioned withdrawal of body fluids through the operations channel) and lens washing and air insufflation (application of water or air jet through the irrigation channel);
operating channel valve, which controls the entry of catheters, electrodes, biopsy forceps and other flexible devices;
connection with the umbilical tube, providing light through a non-coherent fibre-optic bundle and water or air from the pump or aspirator system.
A typical Micro-video Endoscopy Unit would contain:
Optical catheter system as described above,
Colour video monitor
CO2 and fluid insufflation,
Instrumentation,
Disposables,
Miscellaneous accessories.
Some applications of Fibre-optic endoscopy
Endoscopic examination of the gastrointestinal tract has proved especially successful with the diagnosis and treatment of ulcers, cancers, constrictions, bleeding sites, and so on. The heart, respiratory system and pancreas have also been investigated.
Another application is the measurment of the proportion of haemoglobin in the blood which is combined with oxygen using an oximeter. Two incoherent bundles are introduced into the blood stream: one is used to illuminate a sample of blood and the other to assess the absorption of light by the blood.
An endoscope can also be equipped with a laser that can vaporize, coagulate, or cut structures, often with more ease and flexibility than a more rigid cutting knife. It is a less invasive method that causes less scarring and a quicker recovery time than other surgical techniques.
Common types of endoscopes are the cytoscope to view the bladder, the bronchoscope to view the lungs, the otoscope to view the ear, the arthroscope to view the knee and other joints, and the laparascope to view the female reproductive structures. The most common surgery performed through endoscopy is biopsy, the removal of tissue for microscopic study to detect a malignancy. Diagnostic hysteroscopy with directed biopsy and dilatation and curettage, removal of polyps, and removal of foreign objects and Cystourethroscopy are other important fields which endoscopy makes possible.
References:
Pope, Jean A.; Medical Physics 2nd r.e. Heinemann Educational Printers 1973.
Brown, B. H. , Smallwood R. H.; Medical Physics and Physiological Measurement;
Blackwell Scientific Publications, Billing and Son's Publishers; 1981.
Einsteins theory of relativity basic
Innehållsförteckning:
Innehållsförteckning 1
Inledning
1. Syfte och tillvägagångssätt 2
2. Begränsningar 2
3. Sammanfattning 2
Kap. 1, Relativistiska effekter, Ljuset.
1.1 Begynnelsen 3
1.2 Ljusets hastighet 3
1.3 Ljushastigheten är konstant 3
1.4 Teorin 4
1.5 Konsekvens 4
Kap. 2, Relativistiska effekter, Tiden.
2.1 Tidsdilationen 5
2.2 Bevis 5
2.3 Tolkning 5
2.4 Experimentella belägg för tidsdilationen 6
Kap. 3, Relativistiska effekter, Paradoxer.
3.1 Skenbara paradoxer 7
3.2 Tvillingparadoxen 7
3.3 Myonerna 7
3.4 The train experiment 7
Kap. 4, Relativistiska effekter, Massa & Energi.
4.1 Massans hastighetsberoende 8
4.2 Rörelseenergi 8
4.3 Massa och energi 8
Register.
1. Ordlista 9
2. Formler och konstanter 9
3. Källförteckning 10
4. Litteratur tips/ Författar tips 10
Bilagor
1. Tabell och diagram
över ökningen av rörelseenergi vid hastigheter nära ljushastigheten. 11
Inledning
1. Syfte och tillvägagångssätt
Syftet med rapporten är att på ett så lättförståeligt och enkelt sätt som möjligt redogöra, samt väcka intresse för, de mest basala idéerna och teorierna inom den Speciella Relativitetsteorin, med de avgränsningar som nämns. Materialet i rapporten är sekundärdata tagna och bearbetade från redovisad litteratur.
2. Begränsningar
Rapporten är begränsad till de grundläggande tankegångar kring den speciella relativitetsteorin, som man kan finna praktisk tillämpning för i det dagliga livet, samt för förståelsen av omvärlden. Ämnen som tagits upp är ljushastighetens konstans, tidsdilation samt effekter på massa och energi.
3. Sammanfattning
År 1905 utvecklade Albert Einstein sin speciella relativitetsteori. Denna berör föremål som rör sig i höga hastigheter, hastigheter närmare ljusets, och de fenomen som följer av hastigheten.
Ljushastigheten har, experimentellt och teoretiskt, beräknats vara konstant. Detta leder till konstaterandet att uppfattningar som tid och rum är relativa, d.v.s. att sinnesintryck såsom tid och längd är subjektiva uppfattningar och kan variera från en iakttagare till en annan beroende på vilka referenssystem som används. Det leder även till konstaterandet att massa, även det, är en relativ uppfattning, samt att massa och energi i grunden är samma sak. Detta kan sägas få långtgående konsekvenser inom t.ex. rymdforskningen då massan ökar med hastigheten för att nära ljushastigheten närma sig oändligheten och därigenom få till följd att resor i ljusets hastighet, med dagens kunskap, ej är möjligt då; tiden är icke existerande i ljushastigheten samt att massan blir oändlig och därigenom en acceleration till nämnda hastighet är omöjlig.
Kap. 1, Relativistiska effekter: Ljuset.
1.1 Begynnelsen
"The first stirrings of the theory came when, as a boy of fourteen, he wondered what the world would look like if he could ride on a beam of light." (Albert Einstein)
1.2 Ljusets hastighet för olika iakttagare
· En pistolkula som avlossas framåt från en bil i rörelse får högre hastighet relativt marken än om bilen står stilla. Kulans hastighet kommer i detta fallet att bli lika med kulans utgångshastighet plus bilens hastighet. Om bilen har hastigheten 180 km/ h (50 m/s) och kulan har utgångshastighet 200 m/s kommer kulans hastighet i förhållande till marken att bli 50+200=250 m/s (900 km/h).
· Antag att det efter en stund börjar skymma och vi slår på strålkastarna, kommer vi att på samma sätt kunna mäta hastigheten hos ljuset? I detta fall kommer vi inte att kunna mäta om det föreligger någon skillnad p.g.a. att differensen hos hastigheterna är så stor men om vi förelägger ett annat exempel kommer vi till klarhet.
· Jorden kretsar kring solen med en fart av 30 km/s, hur inverkar den farten på det värde man får då man mäter hastigheten hos det infallande ljuset från en avlägsen stjärna? En observatör mäter hastigheten hos det infallande ljuset när jorden står i läge A, ett halvår senare mäter han återigen hastigheten hos ljuset från samma stjärna. Om nu resonemanget från exemplet med bilen skulle kunna tillämpas här skulle vi få en högre hastighet hos ljuset i läge B än i läge A, så är inte fallet.
1.3 Ljushastigheten är konstant!
"Enligt Einsteins relativitetsteori är ljusets hastighet alltid densamma i förhållande till observatören -oavsett hur de förhåller sig till ljuskällan." Man har verifierat detta vid avancerade mätningar av mycket snabba partiklar och även där funnit att det inte spelar någon roll var i referenssystemet man befinner sig , ljushastigheten i vakuum är alltid konstant, 299 792 458 m/s. Detta kan vid en första tanke vara svårt att acceptera, men svårigheterna beror enbart på att vi är vana vid de förhållanden som råder på jorden och inte de extrema förhållanden som råder nära ljusets.
1.4 Teorin
"Einstein avvisade Newtons tanke på ett 'absolut rum' i rymden. Det går inte att tala om absolut rörelse, eftersom allt i universum rör sig- planeterna, solen, stjärnorna, galaxerna. När vetenskapsmannen mäter hastighet på något måste det ske i förhållande till något annat."
Albert Einstein byggde upp sin teori med utgångspunkt från principen om ljushastighetens konstans. Dessutom förutsatte han att varje skeende skall kunna förutsägas och beskrivas med samma fysikaliska lagar av observatörer i alla referenssystem, som rör sig med konstant hastighet i förhållande till varandra. Han "visade också att det inte finns någon absolut eller 'sann' tid. Liksom hastigheten måste tid relateras till något. Att sluta tänka i absolut tid var oerhört svårt har Einstein berättat."
1.5 Konsekvens
Konsekvensen av att ljushastigheten är konstant i vakuum är att tider, längder och massor kan vara olika stora för iakttagare som rör sig relativt varandra. En annan följd är att två händelser kan inträffa samtidigt för en iakttagare men vid olika tidpunkter för en annan.
Kap. 2, Relativistiska effekter: Tiden.
2.1 Tidsdilationen
"En av konsekvenserna av lagen om ljushastighetens konstans är att tiden måste gå olika fort för iakttagare som rör sig i förhållande till varandra.
· Antag att ett rymdskepp med hög fart passerar en observatör och att en ljusblixt just då sänds från rymdskeppets 'tak' mot dess 'golv', där en spegel reflekterar den tillbaka mot taket."
Förflyttning
vt
fig. A fig. B
Blixt Blixt
ct ct ct0 J
2 2 2
Rymdskepp J Rymdskepp
· Om vi tillämpar lagen att ljushastigheten är lika stor för båda observatörerna måste observatören utanför rymdskeppet, fig. A, uppmäta en längre tid för ljusblixtens färd än iakttagaren i rymdskeppet fig. B. Detta är en logisk konsekvens om man använder Pytagoras sats och ljushastighetens konstans, ty vägen som blixten vandrar, sett utifrån(fig. A), är längre än den vägen en iakttagare inuti skeppet uppmäter(fig. B).
2.2 Bevis a
Pytagoras sats; c² = a² + b² :
b c
Likformighet: (ct/2)2 = (ct0/2)2 + (vt/2)2 Þ t = (t0) / (û (1-(v2/c2)))
2.3 Tolkning
En iakttagare inuti rymdskeppet uppmäter tiden t0 för ljusblixtens gång fram och tillbaka mellan rymdskeppets golv och tak. En observatör som ser rymdskeppet svepa fram med hastigheten v uppmäter en längre tid t för samma förlopp.
Sambandet gäller för alla förlopp som sker ombord på rymdskeppet. Den tid t0 som uppmäts ombord på rymdskeppet kallas egentid och är den kortast tid som kan uppmätas för ett förlopp, förlängningen av tiden som en utomstående iakttagare kan uppmäta kallas för tidsdilation och orsakas av en relativ hastighet mellan observatören och det system där förloppet utspelas.
2.4 Experimentella belägg för tidsdilationen
På olika hög höjd i atmosfären finns det s.k. myoner, detta är mycket små partiklar som rör sig med 99,5 % av ljushastigheten. De är emellertid inte stabila utan har en halveringstid av 1,5 ms, därmed menas att efter 1,5ms återstår endast hälften av ursprungsantalet. Antag att man mäter mängden myoner på arean av en viss yta på 2000 m höjd, hur många av dessa hinner ned till havsytan innan de omvandlats?
Partiklarnas gångtid beräknas; t = s/v = 2000 m/(3,0*108 m/s) = 6,7ms.
Under den tiden hinner partiklarna halveras mer än 4 gånger, mindre än 1/16 av myonerna bör följaktligen återfinnas vid havsytan. Detta stämmer inte, betydligt mer än hälften återfinns vid havsytan. "Felet är att vi jämför tider som gäller i olika referenssystem. Tiden 6,7 ms är myonernas gångtid i ett till jorden knutet referenssystem, medan 1,5 ms är egentiden för partiklarnas halveringstid," giltig i det system som partiklarna befinner sig i. Om vi använder formeln för beräkning av tidsdilation kan vi se skillnaden i tid mellan de olika systemen.
t = (t0) / (û (1-(v2/c2))) = (1,5 ms) / (û(1-0,9952)) = 15 ms
Detta är mer än dubbla gångtiden, och med det värdet på halveringstiden stämmer det observerade antalet myoner bättre.
Kap. 3, Relativistiska effekter: Paradoxer.
3.1 Skenbara paradoxer
Det finns många frågor man kan ställa sig med anledning av tidsdilationen. Om två rymdskepp passerar varandra och besättningarna jämför de båda skeppens klockor, vilket skepp uppmäter t och vilket uppmäter t0? Om myonerna passerar genom atmosfären på endast en tiondel av den på jorden uppmätta tiden, måste då inte jordatmosfären vara 1/10 så tjock som för oss på jorden? Kan två personer verkligen se samma händelser oberoende av varandra men med olika faktiska tidsuppfattningar?
3.2 Tvillingparadoxen
Vi tänker oss att den ene av två tvillingar i unga år ger sig ut på en rymdresa med ett rymdskepp som går i hastighet nära ljusets. Långt ute i rymden vänder han rymdskeppet och far hemåt igen, den totala resan för rymdfararen har enligt hans egen tideräkning tagit 5 år men på jorden har det gått 25 år. När tvillingarna åter träffas skiljer det 20 år i livstid och den ene är en mogen man medan den andre fortfarande är en yngling. Men, kan man tycka, de båda bröderna har färdats med precis samma hastigheter relativt varandra så varför är inte åldersfördelningen tvärtom?
Nu är inte situationen precis likadan för de båda bröderna, brodern i rymdskeppet har vid starter, landningar och vid vändningen i rymden utsatts för krafter som ej hans jordbundne bror har gjort och alltså har det uppstått asymmetri mellan bröderna, och frågeställningen blir i och med det inaktuell.
3.3 Myonerna
Om myonerna passerar jordatmosfären på 1/10 av den tid vi på jorden uppmäter, har då inte jordatmosfären 1/10 av den tjocklek vi uppmäter på jorden?
Detta är ingen paradox, för svaret på frågan är ja. Det som är svårt att acceptera är faktumet att samma sträcka kan vara olika lång beroende på var i referenssystemet man befinner sig.
3.4 The Train experiment
"In one of his famous 'thought experiments' Einstein considered what would be seen if lightning struck twice along the track of a moving train, one struck in front of the train the other an equal distance behind it. Suppose an observer, who is standing on the bank next to the track, sees these two lightnings strokes happen simultaneously; will a man in the train agree? Einstein's answer is no. The light from both flashes travels towards the man in the train at the same speed. It will take longer for the flash from behind to reach him, because the train is continuing to move forward while the light is travelling towards him. The opposite will be true for the flash seen ahead. So for the man on the train the two flashes are not simultaneous."
Kap. 4, Relativistiska effekter: Massa & Energi.
4.1 Massans hastighetsberoende
En konsekvens av tidsdilationen är, att massan hos ett föremål ökar, då hastigheten hos föremålet ökar. Detta kan med utgångspunkt i ljushastighetens konstans räknas fram och får vittgående praktiska konsekvenser för framtida rymdfart. Massformeln visar klara likheter med formeln för tidsdilation och det är också härifrån denna kan härledas.
m = (m0) / (û(1-(v2/c2)))
Av massformeln ser vi att m växer mot oändligheten då v närmar sig c. Detta innebär att det skulle behövas en oändlig mängd energi för att accelerera ett föremål till ljusets hastighet. "Det betyder att ingenting kan färdas lika fort som eller fortare än ljuset." Ljushastigheten verkar vara en övre gräns för de hastigheter ett föremål kan uppnå.
4.2 Rörelseenergi
Einsteins formel för rörelseenergi ser lite annorlunda ut än den klassiska formeln gör.
Klassiska formeln: Wk = 1/2 * mv2
Einsteins formel: Wk = mc2 - m0c2
Detta har bekräftats vid experiment i USA 1964 då man accelererade elektroner genom hög spänning varefter man beräknade deras rörelseenergi ur formeln Wk = eU, Einsteins formel behöver dock inte användas i normala hastigheter. (Bilaga 1)
U Wk v
(MV) (fj) (Mm/s)
0,50 80 260
1,00 160 273
1,50 240 288
4,50 720 296
4.3 Massa och energi
När man ökar rörelseenergin Wk hos ett föremål, ökar enligt sambandet Wk = mc2 - m0c2 också dess massa m. Massan hos ett föremål är tydligen ett mått på dess energi. "Den i praktiken viktigaste konsekvensen av relativitetsteorin är utan all gensägelse ekvivalensen mellan massa och energi. Summan av massa och energi förblir konstant i ett slutet system." Massan m motsvaras av en energi W, som är produkten av massan och faktorn c2.
W = mc2
Einstein kallade uttrycket m0c2 föremålets viloenergi och mc2 dess totala energi. Skillnaden mellan dessa, Wk , kallas föremålets rörelseenergi.
Om massa och energi i grunden är samma sak, bör all energi W motsvaras av en viss massa m.
m = W/c2
Om man exempelvis värmer ett föremål, bör dess massa öka. Detta stämmer också enligt kända faktum. En sten som lyfts till en högre höjd bör också öka i massa då lägesenergin ökar, detta är dock inte påvisat men det är ett känt faktum bland studenter att böckers tyngd ökar med antalet trappor de skall bäras uppför.
Register
1. Ordlista:
Ord Betydelse Hänvisning
Absolut Något fast, oföränderligt, fix 1.4
Differens Skillnad 1.2
Effekt Verkan, Påföljd Inl.2
Ekvivalens Likvärdig, Fullgod ersättning 4.3
Energi Arbetsförmåga, Kraft Inl.2-3, Bil.1, 4.1-3
Formel Uttryck för att förklara eller bestämma något 2.4, 4.2, Bil.1
Gångtid Tid som förflyter från en tid till annan 2.4
Halveringstid Något halveras på viss fix tid 2.4
Konsekvens Följd, Följdriktighet Inl.3, 1.5, 2.1, 4.1, 4.3
Konstant Oföränderlig Inl.3, 1.3-5, 4.3
Oändlig Motsats till ändlig Inl.3, 4.1
Paradox Skenbart motsägelsefull sats/ företeelse Kap.3
Referenssystem Miljö som används som referens Inl.3, 1.3-4, 2.4, 3.3
Relativ Föränderlig, I jämförelse med Hela Rapporten
Sinnesintryck Uppfattningar som inhämtats genom sinnena Inl.3
Subjektiv Personlig uppfattning Inl.3
Tidsdilation Förskjutning, Böjning av tiden Inl.2, 2.1, 2.3-4, 3.1, 4.1
2. Formler och konstanter:
Benämning Formel/ Förkortning Enhet Hänvisning
Arbete a = F*s Joule
Coulombs lag F = k((Q1Q2)/r2) F, Kraften mellan två punktformiga laddningar
Einsteins formel Wk = mc2 - m0c2 Joule 4.2
Elektrisk spänning = U 1 Volt = 1 Joule/ Coulomb
Elektrisk ström I = Q/t 1 Ampere = 1 Coulomb/ sekund
Elementarladdning = e 1,6022*10-19 Coulomb (Ampere*sekund)
Energi W = mc2 Joule 4.3
Hastighet v = s/t meter/ sekund Kap.1
Joule = J 1 Joule = 1 Newtonmeter (Nm)
Klassiska formeln Wk = 1/2*mv2 Joule 4.2
Coulombs konstant = k 8,988*109 Nm2/C2
Kraft = F N, (Newton)
Laddning = Q C, (Coulomb)
Laddningsavstånd = r meter
Ljushastigheten c = 299792485 (m/s), meter/ sekund Kap.1
Massa = m kg, (kilogram)
Massformeln m = (m0)/(Ö(1-(v2/c2))) kg 4.1
Pytagoras sats c2 = a2 + b2 2.1-2
Rörelseenergi = Wk Joule 4.2-3, Bil.1
Sträcka = s meter
Tid = t sekund
Tidsdilation t = (t0)/(Ö(1-(v2/c2))) sekunder Kap.2
3. Källförteckning
· Almqvist & Wiksell/ Gebers Förlag AB, Focus-Materien, Stockholm, MCMLXV.
· Alphonce, Björkman, Gunnvald, Lindahl, Fysik för gymnasieskolan 3: Kapitel 26, Biblioteksförlaget, 1993.
· Hildingsson Kaj, Vetenskapens Profiler, Natur och Kultur, Stockholm, 1989.
· Lindberg Yngve, Gymnasieskolans Tabeller och formler, Liber Läromedel, 1986.
· They made our world, Broadside Books ltd., 1991.
4. Litteratur tips/ Författar tips:
· Asimov Isac, Svarta hål och kosmiska ägg, Prisma Magnum,1983.
· Boschke Friedrich L., Det outforskade, Bernces.
· Ferris Timothy, Mot universums gränser, Forum, 1978.
· Hawking Stephen W. A Brief History Of Time; from the big bang to black holes, Guild Publishing London, 1990.
· Moore Patrick, Planeterna och universum, Generalstabens Litografiska Anstalts Förlag, 1978.
· Sagan Carl, Kosmos, Askild & Kärnekull, 1981.
· Semitiov Eugen
Bilagor
1. Tabell och diagram över ökningen av rörelseenergin vid hastigheter nära ljushastigheten.
Energi 1 är rörelseenergi beräknad med formeln Wk = 1/2 * mv2 och tar ej hänsyn till ljushastigheten. Energi 2 är rörelseenergi beräknad med formeln Wk = mc2 - m0c2 och tar hänsyn till ljushastigheten.
Energi 1 Massa Hastighet Energi 2 Massa0 Massa* Hastighet
Massa* är uträknad enligt massformeln
Massa anges i kg
Energi anges i Joule
Hastighet anges m/s
Innehållsförteckning 1
Inledning
1. Syfte och tillvägagångssätt 2
2. Begränsningar 2
3. Sammanfattning 2
Kap. 1, Relativistiska effekter, Ljuset.
1.1 Begynnelsen 3
1.2 Ljusets hastighet 3
1.3 Ljushastigheten är konstant 3
1.4 Teorin 4
1.5 Konsekvens 4
Kap. 2, Relativistiska effekter, Tiden.
2.1 Tidsdilationen 5
2.2 Bevis 5
2.3 Tolkning 5
2.4 Experimentella belägg för tidsdilationen 6
Kap. 3, Relativistiska effekter, Paradoxer.
3.1 Skenbara paradoxer 7
3.2 Tvillingparadoxen 7
3.3 Myonerna 7
3.4 The train experiment 7
Kap. 4, Relativistiska effekter, Massa & Energi.
4.1 Massans hastighetsberoende 8
4.2 Rörelseenergi 8
4.3 Massa och energi 8
Register.
1. Ordlista 9
2. Formler och konstanter 9
3. Källförteckning 10
4. Litteratur tips/ Författar tips 10
Bilagor
1. Tabell och diagram
över ökningen av rörelseenergi vid hastigheter nära ljushastigheten. 11
Inledning
1. Syfte och tillvägagångssätt
Syftet med rapporten är att på ett så lättförståeligt och enkelt sätt som möjligt redogöra, samt väcka intresse för, de mest basala idéerna och teorierna inom den Speciella Relativitetsteorin, med de avgränsningar som nämns. Materialet i rapporten är sekundärdata tagna och bearbetade från redovisad litteratur.
2. Begränsningar
Rapporten är begränsad till de grundläggande tankegångar kring den speciella relativitetsteorin, som man kan finna praktisk tillämpning för i det dagliga livet, samt för förståelsen av omvärlden. Ämnen som tagits upp är ljushastighetens konstans, tidsdilation samt effekter på massa och energi.
3. Sammanfattning
År 1905 utvecklade Albert Einstein sin speciella relativitetsteori. Denna berör föremål som rör sig i höga hastigheter, hastigheter närmare ljusets, och de fenomen som följer av hastigheten.
Ljushastigheten har, experimentellt och teoretiskt, beräknats vara konstant. Detta leder till konstaterandet att uppfattningar som tid och rum är relativa, d.v.s. att sinnesintryck såsom tid och längd är subjektiva uppfattningar och kan variera från en iakttagare till en annan beroende på vilka referenssystem som används. Det leder även till konstaterandet att massa, även det, är en relativ uppfattning, samt att massa och energi i grunden är samma sak. Detta kan sägas få långtgående konsekvenser inom t.ex. rymdforskningen då massan ökar med hastigheten för att nära ljushastigheten närma sig oändligheten och därigenom få till följd att resor i ljusets hastighet, med dagens kunskap, ej är möjligt då; tiden är icke existerande i ljushastigheten samt att massan blir oändlig och därigenom en acceleration till nämnda hastighet är omöjlig.
Kap. 1, Relativistiska effekter: Ljuset.
1.1 Begynnelsen
"The first stirrings of the theory came when, as a boy of fourteen, he wondered what the world would look like if he could ride on a beam of light." (Albert Einstein)
1.2 Ljusets hastighet för olika iakttagare
· En pistolkula som avlossas framåt från en bil i rörelse får högre hastighet relativt marken än om bilen står stilla. Kulans hastighet kommer i detta fallet att bli lika med kulans utgångshastighet plus bilens hastighet. Om bilen har hastigheten 180 km/ h (50 m/s) och kulan har utgångshastighet 200 m/s kommer kulans hastighet i förhållande till marken att bli 50+200=250 m/s (900 km/h).
· Antag att det efter en stund börjar skymma och vi slår på strålkastarna, kommer vi att på samma sätt kunna mäta hastigheten hos ljuset? I detta fall kommer vi inte att kunna mäta om det föreligger någon skillnad p.g.a. att differensen hos hastigheterna är så stor men om vi förelägger ett annat exempel kommer vi till klarhet.
· Jorden kretsar kring solen med en fart av 30 km/s, hur inverkar den farten på det värde man får då man mäter hastigheten hos det infallande ljuset från en avlägsen stjärna? En observatör mäter hastigheten hos det infallande ljuset när jorden står i läge A, ett halvår senare mäter han återigen hastigheten hos ljuset från samma stjärna. Om nu resonemanget från exemplet med bilen skulle kunna tillämpas här skulle vi få en högre hastighet hos ljuset i läge B än i läge A, så är inte fallet.
1.3 Ljushastigheten är konstant!
"Enligt Einsteins relativitetsteori är ljusets hastighet alltid densamma i förhållande till observatören -oavsett hur de förhåller sig till ljuskällan." Man har verifierat detta vid avancerade mätningar av mycket snabba partiklar och även där funnit att det inte spelar någon roll var i referenssystemet man befinner sig , ljushastigheten i vakuum är alltid konstant, 299 792 458 m/s. Detta kan vid en första tanke vara svårt att acceptera, men svårigheterna beror enbart på att vi är vana vid de förhållanden som råder på jorden och inte de extrema förhållanden som råder nära ljusets.
1.4 Teorin
"Einstein avvisade Newtons tanke på ett 'absolut rum' i rymden. Det går inte att tala om absolut rörelse, eftersom allt i universum rör sig- planeterna, solen, stjärnorna, galaxerna. När vetenskapsmannen mäter hastighet på något måste det ske i förhållande till något annat."
Albert Einstein byggde upp sin teori med utgångspunkt från principen om ljushastighetens konstans. Dessutom förutsatte han att varje skeende skall kunna förutsägas och beskrivas med samma fysikaliska lagar av observatörer i alla referenssystem, som rör sig med konstant hastighet i förhållande till varandra. Han "visade också att det inte finns någon absolut eller 'sann' tid. Liksom hastigheten måste tid relateras till något. Att sluta tänka i absolut tid var oerhört svårt har Einstein berättat."
1.5 Konsekvens
Konsekvensen av att ljushastigheten är konstant i vakuum är att tider, längder och massor kan vara olika stora för iakttagare som rör sig relativt varandra. En annan följd är att två händelser kan inträffa samtidigt för en iakttagare men vid olika tidpunkter för en annan.
Kap. 2, Relativistiska effekter: Tiden.
2.1 Tidsdilationen
"En av konsekvenserna av lagen om ljushastighetens konstans är att tiden måste gå olika fort för iakttagare som rör sig i förhållande till varandra.
· Antag att ett rymdskepp med hög fart passerar en observatör och att en ljusblixt just då sänds från rymdskeppets 'tak' mot dess 'golv', där en spegel reflekterar den tillbaka mot taket."
Förflyttning
vt
fig. A fig. B
Blixt Blixt
ct ct ct0 J
2 2 2
Rymdskepp J Rymdskepp
· Om vi tillämpar lagen att ljushastigheten är lika stor för båda observatörerna måste observatören utanför rymdskeppet, fig. A, uppmäta en längre tid för ljusblixtens färd än iakttagaren i rymdskeppet fig. B. Detta är en logisk konsekvens om man använder Pytagoras sats och ljushastighetens konstans, ty vägen som blixten vandrar, sett utifrån(fig. A), är längre än den vägen en iakttagare inuti skeppet uppmäter(fig. B).
2.2 Bevis a
Pytagoras sats; c² = a² + b² :
b c
Likformighet: (ct/2)2 = (ct0/2)2 + (vt/2)2 Þ t = (t0) / (û (1-(v2/c2)))
2.3 Tolkning
En iakttagare inuti rymdskeppet uppmäter tiden t0 för ljusblixtens gång fram och tillbaka mellan rymdskeppets golv och tak. En observatör som ser rymdskeppet svepa fram med hastigheten v uppmäter en längre tid t för samma förlopp.
Sambandet gäller för alla förlopp som sker ombord på rymdskeppet. Den tid t0 som uppmäts ombord på rymdskeppet kallas egentid och är den kortast tid som kan uppmätas för ett förlopp, förlängningen av tiden som en utomstående iakttagare kan uppmäta kallas för tidsdilation och orsakas av en relativ hastighet mellan observatören och det system där förloppet utspelas.
2.4 Experimentella belägg för tidsdilationen
På olika hög höjd i atmosfären finns det s.k. myoner, detta är mycket små partiklar som rör sig med 99,5 % av ljushastigheten. De är emellertid inte stabila utan har en halveringstid av 1,5 ms, därmed menas att efter 1,5ms återstår endast hälften av ursprungsantalet. Antag att man mäter mängden myoner på arean av en viss yta på 2000 m höjd, hur många av dessa hinner ned till havsytan innan de omvandlats?
Partiklarnas gångtid beräknas; t = s/v = 2000 m/(3,0*108 m/s) = 6,7ms.
Under den tiden hinner partiklarna halveras mer än 4 gånger, mindre än 1/16 av myonerna bör följaktligen återfinnas vid havsytan. Detta stämmer inte, betydligt mer än hälften återfinns vid havsytan. "Felet är att vi jämför tider som gäller i olika referenssystem. Tiden 6,7 ms är myonernas gångtid i ett till jorden knutet referenssystem, medan 1,5 ms är egentiden för partiklarnas halveringstid," giltig i det system som partiklarna befinner sig i. Om vi använder formeln för beräkning av tidsdilation kan vi se skillnaden i tid mellan de olika systemen.
t = (t0) / (û (1-(v2/c2))) = (1,5 ms) / (û(1-0,9952)) = 15 ms
Detta är mer än dubbla gångtiden, och med det värdet på halveringstiden stämmer det observerade antalet myoner bättre.
Kap. 3, Relativistiska effekter: Paradoxer.
3.1 Skenbara paradoxer
Det finns många frågor man kan ställa sig med anledning av tidsdilationen. Om två rymdskepp passerar varandra och besättningarna jämför de båda skeppens klockor, vilket skepp uppmäter t och vilket uppmäter t0? Om myonerna passerar genom atmosfären på endast en tiondel av den på jorden uppmätta tiden, måste då inte jordatmosfären vara 1/10 så tjock som för oss på jorden? Kan två personer verkligen se samma händelser oberoende av varandra men med olika faktiska tidsuppfattningar?
3.2 Tvillingparadoxen
Vi tänker oss att den ene av två tvillingar i unga år ger sig ut på en rymdresa med ett rymdskepp som går i hastighet nära ljusets. Långt ute i rymden vänder han rymdskeppet och far hemåt igen, den totala resan för rymdfararen har enligt hans egen tideräkning tagit 5 år men på jorden har det gått 25 år. När tvillingarna åter träffas skiljer det 20 år i livstid och den ene är en mogen man medan den andre fortfarande är en yngling. Men, kan man tycka, de båda bröderna har färdats med precis samma hastigheter relativt varandra så varför är inte åldersfördelningen tvärtom?
Nu är inte situationen precis likadan för de båda bröderna, brodern i rymdskeppet har vid starter, landningar och vid vändningen i rymden utsatts för krafter som ej hans jordbundne bror har gjort och alltså har det uppstått asymmetri mellan bröderna, och frågeställningen blir i och med det inaktuell.
3.3 Myonerna
Om myonerna passerar jordatmosfären på 1/10 av den tid vi på jorden uppmäter, har då inte jordatmosfären 1/10 av den tjocklek vi uppmäter på jorden?
Detta är ingen paradox, för svaret på frågan är ja. Det som är svårt att acceptera är faktumet att samma sträcka kan vara olika lång beroende på var i referenssystemet man befinner sig.
3.4 The Train experiment
"In one of his famous 'thought experiments' Einstein considered what would be seen if lightning struck twice along the track of a moving train, one struck in front of the train the other an equal distance behind it. Suppose an observer, who is standing on the bank next to the track, sees these two lightnings strokes happen simultaneously; will a man in the train agree? Einstein's answer is no. The light from both flashes travels towards the man in the train at the same speed. It will take longer for the flash from behind to reach him, because the train is continuing to move forward while the light is travelling towards him. The opposite will be true for the flash seen ahead. So for the man on the train the two flashes are not simultaneous."
Kap. 4, Relativistiska effekter: Massa & Energi.
4.1 Massans hastighetsberoende
En konsekvens av tidsdilationen är, att massan hos ett föremål ökar, då hastigheten hos föremålet ökar. Detta kan med utgångspunkt i ljushastighetens konstans räknas fram och får vittgående praktiska konsekvenser för framtida rymdfart. Massformeln visar klara likheter med formeln för tidsdilation och det är också härifrån denna kan härledas.
m = (m0) / (û(1-(v2/c2)))
Av massformeln ser vi att m växer mot oändligheten då v närmar sig c. Detta innebär att det skulle behövas en oändlig mängd energi för att accelerera ett föremål till ljusets hastighet. "Det betyder att ingenting kan färdas lika fort som eller fortare än ljuset." Ljushastigheten verkar vara en övre gräns för de hastigheter ett föremål kan uppnå.
4.2 Rörelseenergi
Einsteins formel för rörelseenergi ser lite annorlunda ut än den klassiska formeln gör.
Klassiska formeln: Wk = 1/2 * mv2
Einsteins formel: Wk = mc2 - m0c2
Detta har bekräftats vid experiment i USA 1964 då man accelererade elektroner genom hög spänning varefter man beräknade deras rörelseenergi ur formeln Wk = eU, Einsteins formel behöver dock inte användas i normala hastigheter. (Bilaga 1)
U Wk v
(MV) (fj) (Mm/s)
0,50 80 260
1,00 160 273
1,50 240 288
4,50 720 296
4.3 Massa och energi
När man ökar rörelseenergin Wk hos ett föremål, ökar enligt sambandet Wk = mc2 - m0c2 också dess massa m. Massan hos ett föremål är tydligen ett mått på dess energi. "Den i praktiken viktigaste konsekvensen av relativitetsteorin är utan all gensägelse ekvivalensen mellan massa och energi. Summan av massa och energi förblir konstant i ett slutet system." Massan m motsvaras av en energi W, som är produkten av massan och faktorn c2.
W = mc2
Einstein kallade uttrycket m0c2 föremålets viloenergi och mc2 dess totala energi. Skillnaden mellan dessa, Wk , kallas föremålets rörelseenergi.
Om massa och energi i grunden är samma sak, bör all energi W motsvaras av en viss massa m.
m = W/c2
Om man exempelvis värmer ett föremål, bör dess massa öka. Detta stämmer också enligt kända faktum. En sten som lyfts till en högre höjd bör också öka i massa då lägesenergin ökar, detta är dock inte påvisat men det är ett känt faktum bland studenter att böckers tyngd ökar med antalet trappor de skall bäras uppför.
Register
1. Ordlista:
Ord Betydelse Hänvisning
Absolut Något fast, oföränderligt, fix 1.4
Differens Skillnad 1.2
Effekt Verkan, Påföljd Inl.2
Ekvivalens Likvärdig, Fullgod ersättning 4.3
Energi Arbetsförmåga, Kraft Inl.2-3, Bil.1, 4.1-3
Formel Uttryck för att förklara eller bestämma något 2.4, 4.2, Bil.1
Gångtid Tid som förflyter från en tid till annan 2.4
Halveringstid Något halveras på viss fix tid 2.4
Konsekvens Följd, Följdriktighet Inl.3, 1.5, 2.1, 4.1, 4.3
Konstant Oföränderlig Inl.3, 1.3-5, 4.3
Oändlig Motsats till ändlig Inl.3, 4.1
Paradox Skenbart motsägelsefull sats/ företeelse Kap.3
Referenssystem Miljö som används som referens Inl.3, 1.3-4, 2.4, 3.3
Relativ Föränderlig, I jämförelse med Hela Rapporten
Sinnesintryck Uppfattningar som inhämtats genom sinnena Inl.3
Subjektiv Personlig uppfattning Inl.3
Tidsdilation Förskjutning, Böjning av tiden Inl.2, 2.1, 2.3-4, 3.1, 4.1
2. Formler och konstanter:
Benämning Formel/ Förkortning Enhet Hänvisning
Arbete a = F*s Joule
Coulombs lag F = k((Q1Q2)/r2) F, Kraften mellan två punktformiga laddningar
Einsteins formel Wk = mc2 - m0c2 Joule 4.2
Elektrisk spänning = U 1 Volt = 1 Joule/ Coulomb
Elektrisk ström I = Q/t 1 Ampere = 1 Coulomb/ sekund
Elementarladdning = e 1,6022*10-19 Coulomb (Ampere*sekund)
Energi W = mc2 Joule 4.3
Hastighet v = s/t meter/ sekund Kap.1
Joule = J 1 Joule = 1 Newtonmeter (Nm)
Klassiska formeln Wk = 1/2*mv2 Joule 4.2
Coulombs konstant = k 8,988*109 Nm2/C2
Kraft = F N, (Newton)
Laddning = Q C, (Coulomb)
Laddningsavstånd = r meter
Ljushastigheten c = 299792485 (m/s), meter/ sekund Kap.1
Massa = m kg, (kilogram)
Massformeln m = (m0)/(Ö(1-(v2/c2))) kg 4.1
Pytagoras sats c2 = a2 + b2 2.1-2
Rörelseenergi = Wk Joule 4.2-3, Bil.1
Sträcka = s meter
Tid = t sekund
Tidsdilation t = (t0)/(Ö(1-(v2/c2))) sekunder Kap.2
3. Källförteckning
· Almqvist & Wiksell/ Gebers Förlag AB, Focus-Materien, Stockholm, MCMLXV.
· Alphonce, Björkman, Gunnvald, Lindahl, Fysik för gymnasieskolan 3: Kapitel 26, Biblioteksförlaget, 1993.
· Hildingsson Kaj, Vetenskapens Profiler, Natur och Kultur, Stockholm, 1989.
· Lindberg Yngve, Gymnasieskolans Tabeller och formler, Liber Läromedel, 1986.
· They made our world, Broadside Books ltd., 1991.
4. Litteratur tips/ Författar tips:
· Asimov Isac, Svarta hål och kosmiska ägg, Prisma Magnum,1983.
· Boschke Friedrich L., Det outforskade, Bernces.
· Ferris Timothy, Mot universums gränser, Forum, 1978.
· Hawking Stephen W. A Brief History Of Time; from the big bang to black holes, Guild Publishing London, 1990.
· Moore Patrick, Planeterna och universum, Generalstabens Litografiska Anstalts Förlag, 1978.
· Sagan Carl, Kosmos, Askild & Kärnekull, 1981.
· Semitiov Eugen
Bilagor
1. Tabell och diagram över ökningen av rörelseenergin vid hastigheter nära ljushastigheten.
Energi 1 är rörelseenergi beräknad med formeln Wk = 1/2 * mv2 och tar ej hänsyn till ljushastigheten. Energi 2 är rörelseenergi beräknad med formeln Wk = mc2 - m0c2 och tar hänsyn till ljushastigheten.
Energi 1 Massa Hastighet Energi 2 Massa0 Massa* Hastighet
Massa* är uträknad enligt massformeln
Massa anges i kg
Energi anges i Joule
Hastighet anges m/s
Einstein
Sida 2
INNEHÅLLSFÖRTECKNING:
Sida 1 - Titelsida
Sida 2 - Innehållsförteckning
Sida 3 - Bakgrund, syfte, avgränsning
och metod
Sida 4-6 - Inledning på huvudtexten -
Renässansen
Sida 7-12 - Leonardo da Vinci´s liv
Sida 13-15 - Leonardo da Vinci´s
uppfinningar
Sida 16-18 - Leonardo da Vinci´s musik och
konstverk
Sida 19-21 - Leonardo da Vinci´s "Mona Lisa"
Sida 22 - Subjektiv sammanfattning
Sida 23 - Källförteckning
Sida 3
BAKGRUND:
Jag har alltid varit intresserad av
historia och då speciellt av lärda män som
Leonardo da Vinci.
SYFTE:
Att undersöka om Leonardo da Vinci var
typisk för sin tid.
AVGRÄNSNING:
Jag har valt att börja med en kort inledning
om vad renässansmänniska är för något. Sen
tänkte jag berätta om Leonardos uppväxt och
till sist om hans uppfinningar och hans
konstverk.
METOD:
Metoderna har varit att låna böcker på
biblioteket, slå i uppslagsverk och leta i
tidsskrifter.
Sida 4
INLEDNING PÅ HUVUDTEXTEN -
RENÄSSANSEN
Renässansen började under mitten av 1300-
talet och slutade ungefär vid 1600-talets
början.
Rinascità (italienska), renaissance
(franska) är ordet renässans på de olika
språken.
Ordet renäsans betyder pånyttfödelse och
syftar på italienarnas återuppväckande av
det antika kulturarvet efter det långa
avbrottet under medeltiden.
Renässansen var närmast en skördetid för
tankar och ideér som vuxit fram under
medeltiden och som skulle förändra Europas
kulturbild mellan 1300- och 1600-talet.
Det man nu skapade var en ny människosyn,
som utmärktes av naturvetenskapen, de
geografiska upptäckterna, antik- och
språkintresset och de tekniska
uppfinningarna.
Vad som var typiskt för en sann renässans
människa var att han (det var mest män)
skulle kunna lite av allt. Han skulle kunna
vilka de främsta konstnärerna, musikerna,
äventyrarna mm. var. Sen fanns det ju dem
som var experter på alla områdena och
naturligtvis var ju Leonardo den störste av
dem.
Han var ju känd redan under sin tid.
Vad som också var utmärkande var att man
Sida 5
utrustade stora skepp att segla iväg och
hitta nya landområden med mycket guld och
silver.
Många av skeppen kom aldrig tillbaka.
Sida 7
LEONARDO DA VINCI´S LIV:
Leonardo föddes den 15 april 1452 i den
lilla staden Vinci i Italien.
Han arbetade som målare, bildhuggare,
fortifikationsingenjör, vattenbyggare,
kartritare och teknisk konstruktör, men i
grund och botten experimenterade han bara
för sina egna syften.
Under sin tid var han känd som den stora
impulsgivaren och skaparen av två fresker
(målningar):
"Nattvarden" och "Anghiarislaget", båda två
är förstörda idag.
Den enda personen som stod Leonardo nära var
hans vän och lärljunge Melzi, som har
bevarat Leonardos teckningar, studier,
planer, uppfinningar och tankar till
eftervärlden.
Leonardo da Vinci (Leonardo från Vinci) har
fått sitt efternnamn från sin födelsestad.
Vinci betyder "betesmarker" och det har fått
sitt namn efter landskapet med dess
vingårdar och marker.
Leonardos far, Ser Piero, härstammade från
(på den tiden) en berömd florentinsk familj.
Man kan följa släkten tillbaka till 1200-
talet och ättlingar till Leonardos bröder
levde ända in på 1900-talet. Det var ett
segt och starkt släkte.
Sida 8
Släktens medlemmar var oftast väldigt stora
och starka, det var även Leonardo. Man har
hört berättas att Leonardo utan ansträngning
kunde böja ihop en hästsko med bara ena
handen.
Han far, Ser Piero, ägde en liten lantgård i
Vinci och hela familjen var välmående.
Leonardos mor var en bondkvinna. Man vet
bara hennes förnamn och det var Catarina.
Catarina överlämnade sonen i faderns vård
och gifte sig med en enkel man från Vinci.
Leonardo föddes utom äktenskapet men på den
tiden var det ingen skam att vara av oäkta
börd.
Ser Piero gifte sig fyra gånger med först i
det tredje och fjärde äktenskapet blev det
barn, sammanlagt elva stycken. Leonardos
farbror Francesco tog hand om pojken, som
den mycket strängt sysselsattefadern
knappast hade tid med. Men man vet med stor
säkerhet att Leonardos uppväxt var mycket
lycklig.
Han levde nära naturen, där det fanns mycket
att beskåda bland djur, växter och konstigt
formade stenar.
Han konstnärliga begåvning framträdde
tidigt. Han tecknade, knåpade och
modellerade. Hans far satte honom som
fjortonåring i lära hos Verrocchio (som var
en berömd konstnär i Italien), sedan han
Sida 9
visat några prov på Leonardos skicklighet
och frågat honom om han trodde att pojken
hade några framtidsutsikter som målare.
"Helt säkert" lär mästaren ha svarat. Så
blev Leonardo lärling i Verrocchio verkstad.
Han fick hjälpa till vid utförandet av
gravstenar och förfärdiga silverskålar,
mosaikarbeten, bronstatyer och
altarmålningar.
Leonardo hade här grunden till sitt tekniska
kunnande.
Det tog Leonardo sex år innan han fick sitt
mästarbrev.
Hos Verrocchio intresserade man sig också
för matematiken och den nyupptäckta
perspektivläran, som ett medel att återge
verklighetens former. Leonardo påverkades
av de nya teorierna och ägnade matematiken
ett lidelsefullt intresse.
Man har inget tillförlitligt porträtt av
honom som barn, men man har sannolikt med
viss rätt velat se hans drag i ärkeängeln
Mikaels huvud i Botticinis målning "Tobias
och ängeln", och kanske också i "Unge David"
av Verrocchio.
Leonardo ägnade sig också mycket åt musik.
Han både sjöng och spelade luta och var
berömd för sina sällskapstalanger.
Sida 10
Musiken var en konstart som på den tiden
gynnades av hovet och bäste lärare i
musikteori var Franchino Gafurio. Hans verk
om "Musikutövning" hör till de tidigast
tryckta böckerna i Milano.
I utgåvan av Gafurios arbete finns en
teckning av en orgelspelare som satts i
förbindelse med Leonardo.
Leonardo var mycket musikalisk, men bland
hans många anteckningar finns inga noter.
Hans intresse för musiken fick honom att
göra utkast till nya konstigt formade
instrument med större tonstyrka.
I sina skrifter och teckningar har Leonardo
upprepade gånger skildrat visioner av
strider, mänsklig vildhet, naturkatastrofer
och världens undergång.
Han tecknade mycket studier av unga pojkars
och äldre mäns huvuden.
"Han åstadkommer inte många målningar" säger
en av hans samtida, "ty han är aldrig
tillfreds med någonting, det må vara aldrig
så vackert".
Därför finns det endast ett fåtal verk av
honom.
Vetande skaffade han sig på alla de områden,
men han gjorde det på egen hand.
Sida 11
Leonardo strövade ibland runt i Rinardalen
och tecknade landskap.
Ett av hans största intressen var som jag
nämnde innan matematiska studier. Han
umgicks med lärda män, bland annat en läkare
och magiker som hette Paolo dal Pozz
Toscanelli, som var en av de första som
trodde på möjligheten att ta sig fram
sjövägen till Indien (han skickade faktiskt
en karta till Colombus). Det var troligen
han som väckte Leonardos intresse för
geografi. Leonardo blev med tiden (även
på detta område) en mycket skicklig
kartograf (kartritare). Han konstruerade
även ett vattenur och andra tidmätare.
Leonardo tålde inte att se djur i
fångenskap. Han köpte fåglar i bur som han
sedan öppnade och lät flyga ut.
På den tiden gick många konstnärer med
värja. Men Leonardo bar inget vapen. Trots
sin väldiga kroppsbyggnad var han stillsam
och närmast tillbakadragen. Det fanns i
hans uppträdande något skyggt och
hemlighetsfullt. Han var också väldigt rädd
att någon skulle själa hans idéer och
uppfinningar.
SIDA 12
LEONARDOS UPPFINNINGAR:
Hans ritningar på krigsmaskiner med sina
smart uttänkta detaljer är ofta bara
symboliska uttryck för Leonardos
föreställningar och känslor.
Han har gjort en ritning på en
artilleripjäs, där två mörsare (en sorts
kanoner) sköt iväg två läderbehållare med
med en massa kulor i. Dessa behållare skulle
dela sig så fort de skjutits iväg och ett
moln av kulor skulle regna över fienderna.
Varje kula skulle vara försedd med en
explosiv laddning som skulle explodera i ett
moln av små stjärnor.
Detta projekt var inget som han verkligen
gjorde utan det bara utspelades i hans
fantasi.
Att förse projektilerna med tidsinställda
tändanordningar som fick dem att explodera i
rätt ögonblick var en omöjlighet med den
tidens utveckling. Först på 1800-talet
uppfanns sådana tändanordningar.
Vapentekninken på Leonardos tid var inte
alls outvecklad. Kanongjuterierna i Milano
var mycket berömda.
Leonardo har tecknat en väldig kran och i
den hänger ett kanonrör. Som man ser på
bilden har röret en storlek som på den tiden
var omöjliga att framställa. Arbetarna som
är sysselsatta runt jättekanonen gör väldiga
Sida 13
rörelsestudier.
Leonardo har också konstruerat en filmaskin
som kunde slå filens räfflor jämnt på ett
slätt metallstycke, som sedan kunde härdas
med de metoder som man kände till då.
Den fungerade så att när en tyngd fallit
ner, lyftes en hammare för att skilja den
utskjutande kanten och kuggen, tyngden lyfts
sedan igen med hjälp av en vev och
präglingen av räfflorna på filens yta
fortsatte.
En av Leonardos mest berömda teckningar är
den av en enorm ballista (katapult) med
några avancerade egenskaper.
På nästa sida är en liten bild på den.
Teckningen är så skickligt gjord att den
blivit klassiker bland grafiska verk om
ingenjörskonst.
Leonardo återger den stora bågen i
laminerade delar för att få största möjliga
böjlighet. Bågsträngen dras tillbaka med
skruven och kugghjulet i bildens nedre högra
hörn. Där finns två avfyrningsspakar (nere
till vänster i bilden). Den översta har en
fjäderanordning som utlöses av ett slag med
en klubba, den nedersta utlöses av en
hävarm.
Sida 15
LEONARDOS MUSIK OCH
KONSTVERK:
Det enda säkra verk från Leonardos tidiga år
är det av munkarna i San Donato a Scopeto
beställda målningen som föreställer
"Konungarnas tillbedjan". Denna målning
visar att han var flera år före sin tid. Den
visar resultat som måleriet skulle uppnå
först vid sekelskiftet. Ett stort antal
studier visar hur omsorgsfullt han
förberedde sig för sitt verk.
Leonardo visar här vad han har lärt sig. Men
den glömdes bort och tack vare detta har den
blivit bevarad i oförändrat skick.
Ett annat verk från hans tidiga år var
"Hieronymus med lejonet" som aldrig
fullbordades och som återupptäcktes i början
av 1800-talet i skadat skick.
Det som utmärker Leonardos ritningar och
studier jämfört med andra ingenjörer under
hans tid är hans moderna och konstnärliga
ritningar.
Han lade in väldigt mycket konst i sina
ritningar.
Leonardo arbetade också med att måla
madonnabilder.
Det finns en hel rad med målnigar på junfru
Maria med barn, som Leonardo har målat.
En av dessa är "Madonna Litta".
Hon är hårt målad och dräkten är oskön, men
med huvudels graciösa böjningar förs tanken
Sida 16
direkt till Leonardo.
En av hans teckningar visar ett huvud som
kommer "Madonna Litta" mycket nära.
Leonardo fick så småningom elever och
medarbetare i Milano och en målarskola
började växa fram.
Under sin första Milano tid ingick han
kompanjonskap med familjen de Predis.
De fyra bröderna de Predis var mycket
duktiga konsthantverkare. En av dem var
myntgravör, en träsmidare, en miniatyrmålare
och en porträttmålare. Tillsammans med
porträttmålaren Ambrogio de Predis inledde
Leonardo underhandlingar om uppförandet av
en altartavla i kyrkan San Francesco i
Milano.
Leonardo utförde för altaruppsatsens
mittparti "Madonnan i grottan".
Den finns i två versioner, den ena finns
på Louvre Muséet i Paris och den andre finns
i London.
Den i London är förmodligen en kopia gjord
av en av Leonardos elever under hans
uppsikt.
I den versionen som finns i Louvre svävar
inga helgonglorior över figurernas huvud.
Deras hårlockar glänser och ansiktena lyser
mot bakgrunden av ljusdunklet i grottan.
Med sin tekniska begåvning och sina
talanger som festarrangör uppskattades han
Sida 17
mycket vid Moras hov.
Leonardo har skrivit många skämt, gåtor och
kurositeter som han kunde roa ett sällskap
med. Han har återgivit anekdoter som den om
målaren som man frågar varför han gjort sina
barn så fula men sina figurer på målningarna
så vackra, då svarade målaren:
- Mina tavlor gör jag ju på dagen men mina
barn på natten.
När hertig Gian Galeazzo skulle gifta sig
ritade Leonardo dekorationerna.
Den stora hallen i slottet förvandlades av
gröna grenar till en skogsinteriör. Vid
midnatt visades det ett festspel,
"Paradiset", författat av hovskalden
Bellincioni.
Sida 18
LEONARDOS "MONA LISA":
Mona Lisa är ett av Leonardos få fullbordade
konstverk, det är faktiskt den enda bevarade
målningen som man till hundra procent vet
att han har gjort. Innan våra dagar har
tavlan varit med om många episoder, bland
annat har den blivit beskuren cirka tio
centimeter på varje sida.
Mona Lisa blev engång stulen från Louvre
Muséet i Paris av en liten oansenlig
arbetsklädd italienare som hette Vinzenzo
Peruggia, han arbetade med att rama in och
sätta glas i tavlor. Vinzenzo gick helt
fräckt in på Louvre Muséet i agusti 1913 och
lyfte ner tavlan och gick ut igen.
Under två år höll han tavlan gömd i sin
vindsvåning Paris medan världspressen
rasade. 1915 förde han tavlan vidare till
Florens gömd i en låda med kläder och
verktyg. Han blev arresterad när han
försökte sälja den till en kosthandlare.
Under rättegången förklarade han att hans
enda avsikt var att föra tillbaka tavlan
till fosterlandet. Han slapp undan med sju
månaders fängelse, och tavlan återlämnades
under en högtidlig cermoni till den franska
regeringen.
Mona Lisa har blivit konsthistoriens mest
omskrivna, besjungna och kommenterade
porträtt. Hon har givit upphov till
Sida 19
noveller, romaner, lovsånger och operor.
Det mest omdiskuterade är hennes leende.
Somliga har funnit det grymt, det har
uppfattats som det "obarmhärtiga leendet hos
en kvinna som kuvat mannen". Enligt andra är
det älskligt. Enligt Walter Pater är det ett
uttryck för "den moderna själen med alla
dess sjukdomstecken".
Det finns ochså uttranden som Leonardo själv
skrivt ner i "Traktat om måleri". Han
skriver att genom lutspel och högläsning har
han framkallat detta ansiktsuttryck på sin
modell.
Man vet inte så mycket om denna modell mer
än att hon var en mycket vacker och fattig
ung flicka som gifte sig med en tjugo år
äldre rik man som var från en väl ansedd
familj. Paret fick en dotter som dog vid låg
ålder.
Modellen var runt 25 år när Leonardo började
med tavlan och det tog drygt fyra år att
göra klart den.
Sida 21
SUBJEKTIV SAMMANFATTNING
Vad jag har kommit fram till under denna tid
jag har arbetat med detta specialarbete är
att allt det negativa som hände under
medeltiden plötsligt vände och blev
någonting positivt. Alla hade ju haft det
väldigt svårt under medeltiden. Folk hade
haft en massa förbud över sig så de hade
aldrig haft chansen och verkligen göra
vad de ville. Men sen blev det för mycket
och folket gjorde "uppror" (om man nu kan
uttrycka sig så). Man började segla ut i
världen för att upptäcka nya kontineneter,
man gjorde tekniska framsteg, man målade
tavlor, man lärde sig språk, ja listan kan
göras nästan hur lång som helst.
Och den som utmärkte sig mest var ju
Leonardo da Vinci. Han blev ju expert på
vart enda område han gav sig in på. Se bara
på hans målningar och uppfinningar för att
nämna något. De är ju värda miljoner idag.
Detta arbete är något som jag verkligen
gillat att arbeta med.
Sida 22
KÄLLFÖRTECKNING:
"Leonardo Uppfinnaren" skriven av Ludwig H.
INNEHÅLLSFÖRTECKNING:
Sida 1 - Titelsida
Sida 2 - Innehållsförteckning
Sida 3 - Bakgrund, syfte, avgränsning
och metod
Sida 4-6 - Inledning på huvudtexten -
Renässansen
Sida 7-12 - Leonardo da Vinci´s liv
Sida 13-15 - Leonardo da Vinci´s
uppfinningar
Sida 16-18 - Leonardo da Vinci´s musik och
konstverk
Sida 19-21 - Leonardo da Vinci´s "Mona Lisa"
Sida 22 - Subjektiv sammanfattning
Sida 23 - Källförteckning
Sida 3
BAKGRUND:
Jag har alltid varit intresserad av
historia och då speciellt av lärda män som
Leonardo da Vinci.
SYFTE:
Att undersöka om Leonardo da Vinci var
typisk för sin tid.
AVGRÄNSNING:
Jag har valt att börja med en kort inledning
om vad renässansmänniska är för något. Sen
tänkte jag berätta om Leonardos uppväxt och
till sist om hans uppfinningar och hans
konstverk.
METOD:
Metoderna har varit att låna böcker på
biblioteket, slå i uppslagsverk och leta i
tidsskrifter.
Sida 4
INLEDNING PÅ HUVUDTEXTEN -
RENÄSSANSEN
Renässansen började under mitten av 1300-
talet och slutade ungefär vid 1600-talets
början.
Rinascità (italienska), renaissance
(franska) är ordet renässans på de olika
språken.
Ordet renäsans betyder pånyttfödelse och
syftar på italienarnas återuppväckande av
det antika kulturarvet efter det långa
avbrottet under medeltiden.
Renässansen var närmast en skördetid för
tankar och ideér som vuxit fram under
medeltiden och som skulle förändra Europas
kulturbild mellan 1300- och 1600-talet.
Det man nu skapade var en ny människosyn,
som utmärktes av naturvetenskapen, de
geografiska upptäckterna, antik- och
språkintresset och de tekniska
uppfinningarna.
Vad som var typiskt för en sann renässans
människa var att han (det var mest män)
skulle kunna lite av allt. Han skulle kunna
vilka de främsta konstnärerna, musikerna,
äventyrarna mm. var. Sen fanns det ju dem
som var experter på alla områdena och
naturligtvis var ju Leonardo den störste av
dem.
Han var ju känd redan under sin tid.
Vad som också var utmärkande var att man
Sida 5
utrustade stora skepp att segla iväg och
hitta nya landområden med mycket guld och
silver.
Många av skeppen kom aldrig tillbaka.
Sida 7
LEONARDO DA VINCI´S LIV:
Leonardo föddes den 15 april 1452 i den
lilla staden Vinci i Italien.
Han arbetade som målare, bildhuggare,
fortifikationsingenjör, vattenbyggare,
kartritare och teknisk konstruktör, men i
grund och botten experimenterade han bara
för sina egna syften.
Under sin tid var han känd som den stora
impulsgivaren och skaparen av två fresker
(målningar):
"Nattvarden" och "Anghiarislaget", båda två
är förstörda idag.
Den enda personen som stod Leonardo nära var
hans vän och lärljunge Melzi, som har
bevarat Leonardos teckningar, studier,
planer, uppfinningar och tankar till
eftervärlden.
Leonardo da Vinci (Leonardo från Vinci) har
fått sitt efternnamn från sin födelsestad.
Vinci betyder "betesmarker" och det har fått
sitt namn efter landskapet med dess
vingårdar och marker.
Leonardos far, Ser Piero, härstammade från
(på den tiden) en berömd florentinsk familj.
Man kan följa släkten tillbaka till 1200-
talet och ättlingar till Leonardos bröder
levde ända in på 1900-talet. Det var ett
segt och starkt släkte.
Sida 8
Släktens medlemmar var oftast väldigt stora
och starka, det var även Leonardo. Man har
hört berättas att Leonardo utan ansträngning
kunde böja ihop en hästsko med bara ena
handen.
Han far, Ser Piero, ägde en liten lantgård i
Vinci och hela familjen var välmående.
Leonardos mor var en bondkvinna. Man vet
bara hennes förnamn och det var Catarina.
Catarina överlämnade sonen i faderns vård
och gifte sig med en enkel man från Vinci.
Leonardo föddes utom äktenskapet men på den
tiden var det ingen skam att vara av oäkta
börd.
Ser Piero gifte sig fyra gånger med först i
det tredje och fjärde äktenskapet blev det
barn, sammanlagt elva stycken. Leonardos
farbror Francesco tog hand om pojken, som
den mycket strängt sysselsattefadern
knappast hade tid med. Men man vet med stor
säkerhet att Leonardos uppväxt var mycket
lycklig.
Han levde nära naturen, där det fanns mycket
att beskåda bland djur, växter och konstigt
formade stenar.
Han konstnärliga begåvning framträdde
tidigt. Han tecknade, knåpade och
modellerade. Hans far satte honom som
fjortonåring i lära hos Verrocchio (som var
en berömd konstnär i Italien), sedan han
Sida 9
visat några prov på Leonardos skicklighet
och frågat honom om han trodde att pojken
hade några framtidsutsikter som målare.
"Helt säkert" lär mästaren ha svarat. Så
blev Leonardo lärling i Verrocchio verkstad.
Han fick hjälpa till vid utförandet av
gravstenar och förfärdiga silverskålar,
mosaikarbeten, bronstatyer och
altarmålningar.
Leonardo hade här grunden till sitt tekniska
kunnande.
Det tog Leonardo sex år innan han fick sitt
mästarbrev.
Hos Verrocchio intresserade man sig också
för matematiken och den nyupptäckta
perspektivläran, som ett medel att återge
verklighetens former. Leonardo påverkades
av de nya teorierna och ägnade matematiken
ett lidelsefullt intresse.
Man har inget tillförlitligt porträtt av
honom som barn, men man har sannolikt med
viss rätt velat se hans drag i ärkeängeln
Mikaels huvud i Botticinis målning "Tobias
och ängeln", och kanske också i "Unge David"
av Verrocchio.
Leonardo ägnade sig också mycket åt musik.
Han både sjöng och spelade luta och var
berömd för sina sällskapstalanger.
Sida 10
Musiken var en konstart som på den tiden
gynnades av hovet och bäste lärare i
musikteori var Franchino Gafurio. Hans verk
om "Musikutövning" hör till de tidigast
tryckta böckerna i Milano.
I utgåvan av Gafurios arbete finns en
teckning av en orgelspelare som satts i
förbindelse med Leonardo.
Leonardo var mycket musikalisk, men bland
hans många anteckningar finns inga noter.
Hans intresse för musiken fick honom att
göra utkast till nya konstigt formade
instrument med större tonstyrka.
I sina skrifter och teckningar har Leonardo
upprepade gånger skildrat visioner av
strider, mänsklig vildhet, naturkatastrofer
och världens undergång.
Han tecknade mycket studier av unga pojkars
och äldre mäns huvuden.
"Han åstadkommer inte många målningar" säger
en av hans samtida, "ty han är aldrig
tillfreds med någonting, det må vara aldrig
så vackert".
Därför finns det endast ett fåtal verk av
honom.
Vetande skaffade han sig på alla de områden,
men han gjorde det på egen hand.
Sida 11
Leonardo strövade ibland runt i Rinardalen
och tecknade landskap.
Ett av hans största intressen var som jag
nämnde innan matematiska studier. Han
umgicks med lärda män, bland annat en läkare
och magiker som hette Paolo dal Pozz
Toscanelli, som var en av de första som
trodde på möjligheten att ta sig fram
sjövägen till Indien (han skickade faktiskt
en karta till Colombus). Det var troligen
han som väckte Leonardos intresse för
geografi. Leonardo blev med tiden (även
på detta område) en mycket skicklig
kartograf (kartritare). Han konstruerade
även ett vattenur och andra tidmätare.
Leonardo tålde inte att se djur i
fångenskap. Han köpte fåglar i bur som han
sedan öppnade och lät flyga ut.
På den tiden gick många konstnärer med
värja. Men Leonardo bar inget vapen. Trots
sin väldiga kroppsbyggnad var han stillsam
och närmast tillbakadragen. Det fanns i
hans uppträdande något skyggt och
hemlighetsfullt. Han var också väldigt rädd
att någon skulle själa hans idéer och
uppfinningar.
SIDA 12
LEONARDOS UPPFINNINGAR:
Hans ritningar på krigsmaskiner med sina
smart uttänkta detaljer är ofta bara
symboliska uttryck för Leonardos
föreställningar och känslor.
Han har gjort en ritning på en
artilleripjäs, där två mörsare (en sorts
kanoner) sköt iväg två läderbehållare med
med en massa kulor i. Dessa behållare skulle
dela sig så fort de skjutits iväg och ett
moln av kulor skulle regna över fienderna.
Varje kula skulle vara försedd med en
explosiv laddning som skulle explodera i ett
moln av små stjärnor.
Detta projekt var inget som han verkligen
gjorde utan det bara utspelades i hans
fantasi.
Att förse projektilerna med tidsinställda
tändanordningar som fick dem att explodera i
rätt ögonblick var en omöjlighet med den
tidens utveckling. Först på 1800-talet
uppfanns sådana tändanordningar.
Vapentekninken på Leonardos tid var inte
alls outvecklad. Kanongjuterierna i Milano
var mycket berömda.
Leonardo har tecknat en väldig kran och i
den hänger ett kanonrör. Som man ser på
bilden har röret en storlek som på den tiden
var omöjliga att framställa. Arbetarna som
är sysselsatta runt jättekanonen gör väldiga
Sida 13
rörelsestudier.
Leonardo har också konstruerat en filmaskin
som kunde slå filens räfflor jämnt på ett
slätt metallstycke, som sedan kunde härdas
med de metoder som man kände till då.
Den fungerade så att när en tyngd fallit
ner, lyftes en hammare för att skilja den
utskjutande kanten och kuggen, tyngden lyfts
sedan igen med hjälp av en vev och
präglingen av räfflorna på filens yta
fortsatte.
En av Leonardos mest berömda teckningar är
den av en enorm ballista (katapult) med
några avancerade egenskaper.
På nästa sida är en liten bild på den.
Teckningen är så skickligt gjord att den
blivit klassiker bland grafiska verk om
ingenjörskonst.
Leonardo återger den stora bågen i
laminerade delar för att få största möjliga
böjlighet. Bågsträngen dras tillbaka med
skruven och kugghjulet i bildens nedre högra
hörn. Där finns två avfyrningsspakar (nere
till vänster i bilden). Den översta har en
fjäderanordning som utlöses av ett slag med
en klubba, den nedersta utlöses av en
hävarm.
Sida 15
LEONARDOS MUSIK OCH
KONSTVERK:
Det enda säkra verk från Leonardos tidiga år
är det av munkarna i San Donato a Scopeto
beställda målningen som föreställer
"Konungarnas tillbedjan". Denna målning
visar att han var flera år före sin tid. Den
visar resultat som måleriet skulle uppnå
först vid sekelskiftet. Ett stort antal
studier visar hur omsorgsfullt han
förberedde sig för sitt verk.
Leonardo visar här vad han har lärt sig. Men
den glömdes bort och tack vare detta har den
blivit bevarad i oförändrat skick.
Ett annat verk från hans tidiga år var
"Hieronymus med lejonet" som aldrig
fullbordades och som återupptäcktes i början
av 1800-talet i skadat skick.
Det som utmärker Leonardos ritningar och
studier jämfört med andra ingenjörer under
hans tid är hans moderna och konstnärliga
ritningar.
Han lade in väldigt mycket konst i sina
ritningar.
Leonardo arbetade också med att måla
madonnabilder.
Det finns en hel rad med målnigar på junfru
Maria med barn, som Leonardo har målat.
En av dessa är "Madonna Litta".
Hon är hårt målad och dräkten är oskön, men
med huvudels graciösa böjningar förs tanken
Sida 16
direkt till Leonardo.
En av hans teckningar visar ett huvud som
kommer "Madonna Litta" mycket nära.
Leonardo fick så småningom elever och
medarbetare i Milano och en målarskola
började växa fram.
Under sin första Milano tid ingick han
kompanjonskap med familjen de Predis.
De fyra bröderna de Predis var mycket
duktiga konsthantverkare. En av dem var
myntgravör, en träsmidare, en miniatyrmålare
och en porträttmålare. Tillsammans med
porträttmålaren Ambrogio de Predis inledde
Leonardo underhandlingar om uppförandet av
en altartavla i kyrkan San Francesco i
Milano.
Leonardo utförde för altaruppsatsens
mittparti "Madonnan i grottan".
Den finns i två versioner, den ena finns
på Louvre Muséet i Paris och den andre finns
i London.
Den i London är förmodligen en kopia gjord
av en av Leonardos elever under hans
uppsikt.
I den versionen som finns i Louvre svävar
inga helgonglorior över figurernas huvud.
Deras hårlockar glänser och ansiktena lyser
mot bakgrunden av ljusdunklet i grottan.
Med sin tekniska begåvning och sina
talanger som festarrangör uppskattades han
Sida 17
mycket vid Moras hov.
Leonardo har skrivit många skämt, gåtor och
kurositeter som han kunde roa ett sällskap
med. Han har återgivit anekdoter som den om
målaren som man frågar varför han gjort sina
barn så fula men sina figurer på målningarna
så vackra, då svarade målaren:
- Mina tavlor gör jag ju på dagen men mina
barn på natten.
När hertig Gian Galeazzo skulle gifta sig
ritade Leonardo dekorationerna.
Den stora hallen i slottet förvandlades av
gröna grenar till en skogsinteriör. Vid
midnatt visades det ett festspel,
"Paradiset", författat av hovskalden
Bellincioni.
Sida 18
LEONARDOS "MONA LISA":
Mona Lisa är ett av Leonardos få fullbordade
konstverk, det är faktiskt den enda bevarade
målningen som man till hundra procent vet
att han har gjort. Innan våra dagar har
tavlan varit med om många episoder, bland
annat har den blivit beskuren cirka tio
centimeter på varje sida.
Mona Lisa blev engång stulen från Louvre
Muséet i Paris av en liten oansenlig
arbetsklädd italienare som hette Vinzenzo
Peruggia, han arbetade med att rama in och
sätta glas i tavlor. Vinzenzo gick helt
fräckt in på Louvre Muséet i agusti 1913 och
lyfte ner tavlan och gick ut igen.
Under två år höll han tavlan gömd i sin
vindsvåning Paris medan världspressen
rasade. 1915 förde han tavlan vidare till
Florens gömd i en låda med kläder och
verktyg. Han blev arresterad när han
försökte sälja den till en kosthandlare.
Under rättegången förklarade han att hans
enda avsikt var att föra tillbaka tavlan
till fosterlandet. Han slapp undan med sju
månaders fängelse, och tavlan återlämnades
under en högtidlig cermoni till den franska
regeringen.
Mona Lisa har blivit konsthistoriens mest
omskrivna, besjungna och kommenterade
porträtt. Hon har givit upphov till
Sida 19
noveller, romaner, lovsånger och operor.
Det mest omdiskuterade är hennes leende.
Somliga har funnit det grymt, det har
uppfattats som det "obarmhärtiga leendet hos
en kvinna som kuvat mannen". Enligt andra är
det älskligt. Enligt Walter Pater är det ett
uttryck för "den moderna själen med alla
dess sjukdomstecken".
Det finns ochså uttranden som Leonardo själv
skrivt ner i "Traktat om måleri". Han
skriver att genom lutspel och högläsning har
han framkallat detta ansiktsuttryck på sin
modell.
Man vet inte så mycket om denna modell mer
än att hon var en mycket vacker och fattig
ung flicka som gifte sig med en tjugo år
äldre rik man som var från en väl ansedd
familj. Paret fick en dotter som dog vid låg
ålder.
Modellen var runt 25 år när Leonardo började
med tavlan och det tog drygt fyra år att
göra klart den.
Sida 21
SUBJEKTIV SAMMANFATTNING
Vad jag har kommit fram till under denna tid
jag har arbetat med detta specialarbete är
att allt det negativa som hände under
medeltiden plötsligt vände och blev
någonting positivt. Alla hade ju haft det
väldigt svårt under medeltiden. Folk hade
haft en massa förbud över sig så de hade
aldrig haft chansen och verkligen göra
vad de ville. Men sen blev det för mycket
och folket gjorde "uppror" (om man nu kan
uttrycka sig så). Man började segla ut i
världen för att upptäcka nya kontineneter,
man gjorde tekniska framsteg, man målade
tavlor, man lärde sig språk, ja listan kan
göras nästan hur lång som helst.
Och den som utmärkte sig mest var ju
Leonardo da Vinci. Han blev ju expert på
vart enda område han gav sig in på. Se bara
på hans målningar och uppfinningar för att
nämna något. De är ju värda miljoner idag.
Detta arbete är något som jag verkligen
gillat att arbeta med.
Sida 22
KÄLLFÖRTECKNING:
"Leonardo Uppfinnaren" skriven av Ludwig H.
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