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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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?
The star Alpha goes supernova. Ten years later and away, as measured by astronomers in the galaxy, star Beta explodes.
a. Is it possible that the explosion of Alpha is in any way responsible for the explosion of Beta? Explain.
b. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is. According to the aliens, what is the time between the explosions?
A modest supernova (the explosion of a massive star at the end of its life cycle) releases 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?
Particle A has half the mass and twice the speed of particle B. Is the momentum less than, greater than, or equal to ? Explain.
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′?
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