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Chapter 36: Q. 38 (page 1060)
At what speed, as a fraction of , must an electron move so that its total energy is more than its rest mass energy?
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Let鈥檚 examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: . Consider an object A of mass 3m at rest in reference frame S. Object A explodes into two pieces: object B, of mass m, that is shot to the left at a speed of c/2 and object C, of mass 2m, that, to conserve momentum, is shot to the right at a speed of c/4. Suppose this explosion is observed in reference frame S鈥� that is moving to the right at half the speed of light.
a. Use the Lorentz velocity transformation to find the velocity and the Newtonian momentum of A in S鈥�.
b. Use the Lorentz velocity transformation to find the velocities and the Newtonian momenta of B and C in S鈥�.
c. What is the total final momentum in S鈥�?
d. Newtonian momentum was conserved in frame S. Is it conserved in frame S鈥�?
An astronaut travels to a star system away at a speed of Assume that the time needed to accelerate and decelerate is negligible.
a. How long does the journey take according to Mission Control on earth?
b. How long does the journey take according to the astronaut?
c. How much time elapses between the launch and the arrival of the first radio message from the astronaut saying that she has arrived?
A modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 * 1044 J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?
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?
A rocket is fired from the earth to the moon at a speed of . Let two events be 鈥渞ocket leaves earth鈥� and 鈥渞ocket hits moon.鈥� a. In the earth鈥檚 reference frame, calculate 鈭唜, 鈭唗, and the space time interval s for these events.
b. In the rocket鈥檚 reference frame, calculate 鈭唜鈥�, 鈭唗鈥�, and the space time interval s鈥� for these events.
c. Repeat your calculations of part a if the rocket is replaced with a laser beam.
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