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Chapter 37: 37P (page 1147)
Assuming that Eq. 37-36 holds, find how fast you would have to go through a red light to have it appear green. Take 620 nm as the wavelength of red light and 540 nm as the wavelength of green light.
The speed of observer for variation in colour of light from red to green is 0.13c.
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A relativistic train of proper length 200 m approaches a tunnel of the same proper length, at a relative speed of 0.900c. A paint bomb in the engine room is set to explode (and cover everyone with blue paint) when the front of the train passes the far end of the tunnel (event FF). However, when the rear car passes the near end of the tunnel (event RN), a device in that car is set to send a signal to the engine room to deactivate the bomb. Train view: (a) What is the tunnel length? (b) Which event occurs first, FF or RN? (c) What is the time between those events? (d) Does the paint bomb explode? Tunnel view: (e) What is the train length? (f) Which event occurs first? (g) What is the time between those events? (h) Does the paint bomb explode? If your answers to (d) and (h) differ, you need to explain the paradox, because either the engine room is covered with blue paint or not; you cannot have it both ways. If your answers are the same, you need to explain why?
(Come) back to the future. Suppose that a father is 20.00 y older than his daughter. He wants to travel outward from Earth for 2.000 y and then back for another 2.000 y (both intervals as he measures them) such that he is then 20.00 y younger than his daughter. What constant speed parameter (relative to Earth) is required?
The length of a spaceship is measured to be exactly half its rest length. (a) To three significant figures, what is the speed parameter of the spaceship relative to the observer鈥檚 frame? (b) By what factor do the spaceship鈥檚 clocks run slow relative to clocks in the observer鈥檚 frame?
A spaceship, moving away from Earth at a speed of 0.900c, reports back by transmitting at a frequency (measured in the spaceship frame) of 100 MHz. To what frequency must Earth receivers be tuned to receive the report?
In Fig. 37-26a, particle P is to move parallel to the x and axes of reference frames S and , at a certain velocity relative to frame S. Frame " width="9">x axis of frame S at velocity v. Figure 37-26b gives the velocity localid="1664359069513" of the particle relative to frame localid="1664359072841" for a range of values for v. The vertical axis scale is set by . What value will have if (a) and (b) ?
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