At what speed, as a fraction of , must an electron move so that its total energy is more than its rest mass energy?
We have given that,
Total energy is more.
Given values are: and total energy is more.
To find the speed , we use the below given formula.
Now, put the given values in the above formula to find the speed.
In the earth’s reference frame, a tree is at the origin and a pole is at km. Lightning strikes both the tree and the pole at . The lightning strikes are observed by a rocket traveling in the -direction at .
a. What are the spacetime coordinates for these two events in the rocket’s reference frame?
b. Are the events simultaneous in the rocket’s frame? If not, which occurs first?
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?
A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.
a. What is gp, written as a fraction like a/b?
b. What is the initial total momentum? Give your answer as a fraction times mc. c. What is the initial total energy? Give your answer as a fraction times mc2 . Don’t forget that there are two balls.
d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is 2m. Instead, let the final state of the system be an unknown mass M traveling at the unknown speed uf. You have two conservation laws. Find M and uf.
Teenagers Sam and Tom are playing chicken in their rockets. As FIGURE Q36.2 shows, an experimenter on earth sees that each is traveling at as he approaches the other. Sam fires a laser beam toward Tom.
a. What is the speed of the laser beam relative to Sam?
b. What is the speed of the laser beam relative to Tom?
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