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Time Dilation, Length Contraction and Doppler. Class 2: (ThT Q). Did you complete at least 70% of Chapter 1:1-4?. Yes No. Relativity; Galilean Reference frame Events Simultaneous. Fig 39-CO, p.1244.
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Time Dilation, Length Contraction and Doppler Class 2: (ThT Q)
Did you complete at least 70% of Chapter 1:1-4? • Yes • No Relativity; GalileanReference frameEventsSimultaneous
Reading was 1.3-1.4 + App 1 Doppler, length contraction, Lorentz transforms and velocity addition • Review: Length contraction Muon decay 43: start at 16 minutes (43:16 16.17') • HW 2 helps; start with PPT: Simultaneous Events, Relative Velocity, and Momentum (Class 32: from 123 ) • Additional material to be used. • Velocities and space-time diagrams 43:14 starts at min 11.22' . • Last material; twin paradox from MU 43:20-21 starts at min 20.32' to 21:46 • Assign 43: min. 1’ 43”- 5’40” and 44: 9’15” to 14’ 30” • Supporting ppt. :Simultaneous Events, Relative Velocity, and Momentum Class 32: from 123 MU
any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship traveling at constant speed, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary. (Wikipedia)
Imagine a person inside a ship which is sailing on a perfectly smooth lake at constant speed. This passenger is in the ship's windowless hull and, despite it being a fine day, is engaged in doing mechanical experiments (such as studying the behavior of pendula and the trajectories of falling bodies). A simple question one can ask of this researcher is whether she can determine that the ship is moving (with respect to the lake shore) without going on deck or looking out a porthole. Since the ship is moving at constant speed and direction she will not feel the motion of the ship. This is the same situation as when flying on a plane: one cannot tell, without looking out one of the windows, that the plane is moving once it reaches cruising altitude (at which point the plane is flying at constant speed and direction). Still one might wonder whether the experiments being done in the ship's hull will give some indication of the its motion. Based on his experiments Galileo concluded that this is in fact impossible: all mechanical experiments done inside a ship moving at constant speed in a constant direction would give precisely the same results as similar experiments done on shore.
Galileo and Relativity Fig 39-1, p.1246
The conclusion is that one observer in a house by the shore and another in the ship will not be able to determine that the ship is moving by comparing the results of experiments done inside the house and ship. In order to determine motion these observers must look at each other. It is important to note that this is true only if the ship is sailing at constant speed and direction, should it speed up, slow down or turn the researcher inside can tell that the ship is moving. For example, if the ship turns you can see all things hanging from the roof (such as a lamp) tilting with respect to the floor Generalizing these observations Galileo postulated his relativity hypothesis: any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments
now do it with light. • ether and wind because you are going through the ether. • M& M in 1887
Special theory of relativity Postulates • The laws of physics are the same in any inertial frame of reference. • The velocity of light is the same in all inertial frames of reference.
According to a stationary observer, a moving clock runs ______ than an identical stationary clock. • faster or • slower
According to a stationary observer, a moving object is _______ than an identical stationary object. • shorter or • longer
1. (2 pts) A meter stick moves parallel to its axis with a speed of 0.96 c relative to you. (a) What would you measure for the length of the stick? (b) How long does it take for the stick to pass you?
2. (2 pts) An observer on Earth sends light with frequency 1.2× 1015 Hz to spaceship A traveling with a speed of 0.8c away from Earth. (a) What will be the frequency of the light observed on the spaceship A? (b) Spaceship A then transmits the light received from earth, at the frequency that it is observed, to spaceship B, which is traveling ahead of it, away from Earth, with a speed of 0.6c relative to spaceship A. What is the frequency of light observed by spaceship B?
3. (4 pts) Two relativistic rockets move toward each other. As seen by an observer on Earth, rocket A, of proper length 500 m, travels with a speed of 0.8c, while rocket B, of proper length 1000 m, travels with a speed of 0.6c. (a) What is the speed of the rockets relative to each other? (b) If the captain of rocket B, sitting near the nose of his rocket, sets his clock to t = 0 when the two noses pass each other, what will his clock read when he passes the tail of rocket A? (c) The earthbound observer sets her clock to t = 0 when the two noses of the rockets justs pass each other. What will the observer's clock read when the tails of the rocket's just pass each other?
4. (4 pts) The nucleus of a particular atom, initially at rest in the laboratory system, is unstable and disintegrates into two particles. Particle one moves to the left at a speed of 0.80c, and particle two moves to the right at a speed of 0.98c. (a) What is the velocity of particle one with respect to an observer at rest with particle two? (b) An observer at rest with respect to the laboratory system finds that both particles are unstable. Particle one decays after 6.6 μs. Particle two decays after 6.0 μs. What are the lifetimes of the two particles from a reference frame in which particle two is at rest?
