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Chapter 37: 11P (page 1116)
A rod lies parallel to the axis of the reference frame , moving along this axis at a speed of . Its rest length is 1.70 m. What will be its measured length in frame ?
The measured length in frame is .
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Figure 37-16 shows a ship (attached to reference frame ) passing us (standing in reference frame ) with velocity . A proton is fired at speed relative to the ship from the front of the ship to the rear. The proper length of the ship is . What is the temporal separation between the time the proton is fired and the time it hits the rear wall of the ship according to (a) a passenger in the ship and (b) us? Suppose that, instead, the proton is fired from the rear to the front. What then is the temporal separation between the time it is fired and the time it hits the front wall according to (c) the passenger and (d) us?
Space cruisers A and B are moving parallel to the positive direction of an x axis. Cruiser A is faster, with a relative speed of , and has a proper length of . According to the pilot of A, at the instant (t = 0) the tails of the cruisers are aligned, the noses are also. According to the pilot of B, how much later are the noses aligned?
A spaceship is moving away from Earth at speed 0.20c. A source on the rear of the ship emits light at wavelength 450 nm according to someone on the ship. What (a) wavelength and (b) color (blue, green, yellow, or red) are detected by someone on Earth watching the ship?
The plane of clocks and measuring rods in Fig. 37-19 is like that in Fig. 37-3. The clocks along the x axis are separated (center to center) by 1light-second, as are the clocks along the y axis, and all the clocks are synchronized via the procedure described in Module 37-1. When the initial synchronizing signal of t = 0 from the origin reaches (a) clock A, (b) clock B, and (c) clock C, what initial time is then set on those clocks? An event occurs at clock A when it reads 10 s. (d) how long does the signal of that event take to travel to an observer stationed at the origin? (e) What time does that observer assign to the event?
A space traveler takes off from Earth and moves at speed toward the star Vega, which is distant. How much time will have elapsed by Earth clocks (a) when the traveler reaches Vega and (b) when Earth observers receive word from the traveler that she has arrived? (c) How much older will Earth observers calculate the traveler to be (measured from her frame) when she reaches Vega than she was when she started the trip?
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