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Chapter 36: Q. 10 (page 1058)
Particle A has half the mass and twice the speed of particle B. Is the momentum less than, greater than, or equal to ? Explain.
Momentum A is greater than momentum of B.
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At what speed, as a fraction of , will a moving rod have a length that of an identical rod at rest?
At what speed, as a fraction of , is a particle鈥檚 total energy twice its rest energy?
This chapter has assumed that lengths perpendicular to the direction of motion are not affected by the motion. That is, motion in the -direction does not cause length contraction along the or axes. To find out if this is really true, consider two spray-paint nozzles attached to rods perpendicular to the axis. It has been confirmed that, when both rods are at rest, both nozzles are exactly 1 m above the base of the rod. One rod is placed in the reference frame with its base on the axis; the other is placed in the reference frame with its base on the axis. The rods then swoop past each other and, as FIGURE P36.60 shows, each paints a stripe across the other rod.
We will use proof by contradiction. Assume that objects perpendicular to the motion are contracted. An experimenter in frame finds that the nozzle, as it goes past, is less than above the axis. The principle of relativity says that an experiment carried out in two different inertial reference frames will have the same outcome in both.
a. Pursue this line of reasoning and show that you end up with a logical contradiction, two mutually incompatible situations.
b. What can you conclude from this contradiction?
Two rockets, and , approach the earth from opposite directions at speed of . The length of each rocket measured in its rest frame is . What is the length of rocket as measured by the crew of rocket ?
FIGURE Q36.6 shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket鈥檚 frame) hits both trees.
a. Do the light fleshes reach the rocket pilot simultaneously? If not, which reaches her first? Explain
b. A student was sitting on the ground halfway between the trees as the rocket passed overhead. According to the student, were the lightning strikes simultaneous? If not, which tree was hit first? Explain.
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