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Chapter 36: Q. 9 (page 1058)
A long train is heading for an long tunnel. If the train moves sufficiently fast, is it possible, according to experimenters on the ground, for the entire train to be inside the tunnel at one instant of time? Explain.
Yes, due to length contraction.
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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?
Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of ?
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�?
The radioactive element radium (Ra) decays by a process known as alpha decay, in which the nucleus emits a helium nucleus. (These high-speed helium nuclei were named alpha particles when radioactivity was first discovered, long before the identity of the particles was established.) The reaction is , where Rn is the element radon. The accurately measured atomic masses of the three atoms are , , and . How much energy is released in each decay? (The energy released in radioactive decay is what makes nuclear waste 鈥渉ot.鈥�)
A firecracker explodes in reference frame S at . A second firecracker explodes at the same position at . In reference frame S鈥�, which moves in the x-direction at speed v, the first explosion is detected at and the second at .
a. What is the speed of frame S鈥� relative to frame S?
b. What is the position of the two explosions in frame S?
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