A laboratory experiment shoots an electron to the left at . What is the electron’s speed, as a fraction of c, relative to a proton moving to the right at ?
The electron's speed is .
We have given that a laboratory experiment shoots an electron to the left at .
We have to find the electron’s speed, as a fraction of , relative to a proton moving to the right at .
Frame of Earth :
Frame of Proton :
moves at. In the laboratory frame, the electron's velocity is .
Using, the Lorentz velocity transformation equation,
Therefore the electron's speed is .
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′?
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 “hot.”)
Firecrackers A and B are apart. You are standing exactly halfway between them. Your lab partner is on the other side of firecracker A. You see two flashes of light, from the two explosions, at exactly the same instant of time. Define event 1 to be “firecracker A explodes” and event 2 to be “firecracker B explodes.” According to your lab partner, based on measurements he or she makes, does event 1 occur before, after, or at the same time as event 2? Explain
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