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Chapter 37: 35P (page 1147)
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?
The tuning frequency to receive the report on Earth is 22.9 MHz.
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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 rest energy and total energy, respectively, of three particles, expressed in terms of a basic amount A are (1) A, 2A; (2) A, 3A; (3) 3A, 4A. Without written calculation, rank the particles according to their (a) mass, (b) kinetic energy, (c) Lorentz factor, and (d) speed, greatest first.
The car-in-the-garage problem. Carman has just purchased the world’s longest stretch limo, which has a proper length of . In Fig. 37-32a, it is shown parked in front of a garage with a proper length of . The garage has a front door (shown open) and a back door (shown closed).The limo is obviously longer than the garage. Still, Garageman, who owns the garage and knows something about relativistic length contraction, makes a bet with Carman that the limo can fit in the garage with both doors closed. Carman, who dropped his physics course before reaching special relativity, says such a thing, even in principle, is impossible.
To analyze Garageman’s scheme, an axis is attached to the limo, with at the rear bumper, and an axis is attached to the garage, with at the (now open) front door. Then Carman is to drive the limo directly toward the front door at a velocity of (which is, of course, both technically and financially impossible). Carman is stationary in the reference frame; Garageman is stationary in the role="math" localid="1663064422721" reference frame.
There are two events to consider. Event 1: When the rear bumper clears the front door, the front door is closed. Let the time of this event be zero to both Carman and Garageman: . The event occurs at . Figure 37-32b shows event 1 according to the reference frame. Event 2: When the front bumper reaches the back door, that door opens. Figure 37-32c shows event 2 according to the reference frame.
According to Garageman, (a) what is the length of the limo, and what are the spacetime coordinates (b) and (c) of event 2? (d) For how long is the limo temporarily “trapped” inside the garage with both doors shut? Now consider the situation from the reference frame, in which the garage comes racing past the limo at a velocity of . According to Carman, (e) what is the length of the passing garage, what are the spacetime coordinates (f) and (g) of event 2, (h) is the limo ever in the garage with both doors shut, and (i) which event occurs first? (j) Sketch events 1 and 2 as seen by Carman. (k) Are the events causally related; that is, does one of them cause the other? (l) Finally, who wins the bet?
Figure 37-17 shows two clocks in stationary frame (they are synchronized in that frame) and one clock in moving frame . Clocks and read zero when they pass each other. When clocks and pass each other, (a) which clock has the smaller reading and (b) which clock measures a proper time?
A rod is to move at constant speed along the axis of reference frame , with the rod’s length parallel to that axis. An observer in frame is to measure the length of the rod. Figure 37-23 given length versus speed parameter for a range of values for . The vertical axis scale is set by . What is if ?
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