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Chapter 36: Q. 5 (page 1059)
An out-of-control alien spacecraft is diving into a star at a speed of . At what speed, relative to the spacecraft, is the starlight approaching?
The speed will be speed of light c.
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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鈥檚 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鈥檛 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.
What is the speed, in m/s, of a proton after being accelerated from rest through a potential difference?
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
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?
a. At what speed, as a fraction of must a rocket travel on a journey to and from a distant star so that the astronauts age years while the Mission Control workers on earth age years?
b. As measured by Mission Control, how far away is the distant star?
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