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Chapter 36: Q. 38 (page 1060)
At what speed, as a fraction of c, must an electron move so that its total energy is 10% more than its rest mass energy?
The speed of electron is 0.417c.
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Firecracker A is from you. Firecracker B is from you in the same direction. You see both explode at the same time. Define event 1 to be 鈥渇irecracker A explodes鈥� and event 2 to be 鈥渇irecracker B explodes.鈥� Does event 1 occur before, after, or at the same time as event 2? Explain.
In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which isaway, and that you want your rocket to move so fast that you age only during the round trip.
a . How fast, as a fraction of c, must the rocket travel relative to earth?
b. How much energy is needed to accelerate the rocket to this speed?
c. Compare this amount of energy to the total energy used by the United States in the year , which was roughly
The Stanford Linear Accelerator (SLAC) accelerates electrons to in a long tube. If they travel the length of the tube at full speed (they don鈥檛, because they are accelerating), how long is the tube in the electrons鈥� reference frame?
At what speed, as a fraction of c, is the kinetic energy of a particle twice its Newtonian value?
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?
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