Chapter 26 Solutions

Chapter 26 Solutions - Chapter 26 RELATIVITY Conceptual...

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975 Chapter 26 RELATIVITY Conceptual Questions 1. (a) According to Galilean relativity, the following quantities are invariant: displacement, length, time interval, acceleration, force, and mass. The position, velocity, momentum, kinetic energy, and speed of light in vacuum are not invariant. (b) According to Einstein’s Special Relativity, of all the quantities listed only mass and the speed of light in vacuum are invariant. 2. Whether something is obvious depends on our common sense about it. In everyday experience we only observe objects in motion with speeds much smaller than the speed of light. We have no experience with, and hence no common sense about, objects moving close to the speed of light. Therefore, it is not obvious that moving clocks don’t run slow or that lengths don’t shorten when the speeds involved approach the speed of light. 3. The acceleration of the electron is much less than F / m . This must be the case because the electron is already moving at nearly the speed of light, and it cannot ever actually reach the speed of light. More specifically, in any time interval t , the change in the electron’s momentum is given by p = F t . Since , p mv γ = and the mass is constant, / ( ) / . F m v t γ = ∆ For an object moving close to the speed of light, γ is a very large number. Therefore, / ( ) / / . a v t v t F m γ = ∆ ∆ < ∆ ∆ = 4. The proper time interval between two events is defined as the time interval measured in a frame in which the two events occur at the same place. Therefore, the sprinter’s reference frame is the one in which an observer would measure the proper time. The proper length of an object is the length as measured in a frame in which the object is at rest. Therefore, an observer who is at rest with respect to the track would measure the proper length. 5. The cell phone’s battery loses stored chemical energy as the phone is used. Since its energy decreases, its mass decreases as well (albeit by a very small amount). 6. There is no limit on either the momentum or the kinetic energy of a particle. This can be seen by noting that p = γ mv , K = ( γ 1) mc 2 , and as v approaches c , γ approaches infinity. 7. The astronaut would measure about 52 beats per minute. He is in his own rest frame, so he measures the proper time between heartbeats—the same as if he were taking his pulse back on Earth. 8. + Time Velocity Acceleration Momentum
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Chapter 26: Relativity College Physics 976 9. The observer on the train is in an inertial reference frame for either state of motion. The principle of relativity states that the laws of physics must be identical in all inertial frames. Thus, there is no experiment that the observer could perform to determine the train’s state of motion. 10. The observer has a positive velocity with respect to the room directed toward Sally. The observer would therefore find that the two flashes were not simultaneous, but instead that the flash from Sally’s camera occurred first.
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