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Chapter 36: Q. 32 (page 1060)
A proton is accelerated to 0.999c.
a. What is the proton’s momentum?
b. By what factor does the proton’s momentum exceed its Newtonian momentum?
The relativistic momentum is and the ratio of relativistic momentum and Newtonian momentum is 22.4.
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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.
At , a firecracker explodes at in reference frame S. Four seconds later, a second firecracker explodes at . Reference frame S′ moves in the x-direction at a speed of . What are the positions and times of these two events in frame S′?
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 ?
The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply . The mass of a proton, to four significant figures, is , and the mass of a helium nucleus is known to be .
a. How much energy is released in each fusion?
b. What fraction of the initial rest mass energy is this energy?
Some particle accelerators allow protonsand antiprotonsto circulate at equal speeds in opposite directions in a device called a storage ring. The particle beams cross each other at various points to causecollisions. In one collision, the outcome is, where g represents a high-energy gamma-ray photon. The electron and positron are ejected from the collision atand the gamma-ray photon wavelengths are found to be. What were the proton and antiproton speeds, as a fraction of , prior to the collision?
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