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Chapter 36: Q. 14 (page 1059)
At what speed, as a fraction of does a moving clock tick at half the rate of an identical clock at rest?
At , a moving clock tick at half the rate of an identical clock at rest.
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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�?
FIGURE Q36.5 shows Peggy standing at the center of her railroad car as it passes Ryan on the ground. Firecrackers attached to the ends of the car explode. A short time later, the flashes from the two explosions arrive at Peggy at the same time.
a. Were the explosions simultaneous in Peggy鈥檚 reference frame? If not, which exploded first? Explain.
b. Were the explosions simultaneous in Ryan鈥檚 reference frame?
A cosmic ray travels through the earth鈥檚 atmosphere in as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?
A rocket travels in the -direction at speed with respect to the earth. An experimenter on the rocket observes a collision between two comets and determines that the spacetime coordinates of the collision are . What are the spacetime coordinates of the collision in earth鈥檚 reference frame?
One of the important ways in which the Higgs boson was detected at the Large Hadron Collider was by observing a type of decay in which the Higgs鈥攚hich decays too quickly to be observed directly鈥攊s immediately transformed into two photons emitted back to back. Two photons, with momenta , were detected. What is the mass of the Higgs boson? Give your answer as a multiple of the proton mass.
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