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Chapter 36: Q. 4 (page 1059)
A baseball pitcher can throw a ball with a speed of . He is in the back of a pickup truck that is driving away from you. He throws the ball in your direction, and it floats toward you at a lazy . What is the speed of the truck?
The speed of the truck is
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Let’s 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′ 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′.
b. Use the Lorentz velocity transformation to find the velocities and the Newtonian momenta of B and C in S′.
c. What is the total final momentum in S′?
d. Newtonian momentum was conserved in frame S. Is it conserved in frame S′?
What is the speed, as a fraction of , of a particle whose momentum is ?
You are flying your personal rocket craft at from Star toward Star The distance between the stars, in the stars’ reference frame, is Both stars happen to explode simultaneously in your reference frame at the instant you are exactly halfway between them. Do you see the flashes simultaneously? If not, which do you see first, and what is the time difference between the two?
Bianca is standing at .Firecracker at the origin, and firecracker, at explode simultaneously. The flash from firecracker reaches Bianca’s eye at .At what time does she see the flash from firecracker?
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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