Assignment:
Problem
1. A rocket (in frame S') is moving at a speed v = 4c/5 relative to the moon (frame S). At t 0 = 2×10-7 s a UFO appears at a point x' = 10m traveling in the x' direction with constant velocity u' = -c/2. It suddenly dissappears at t' = 2.5×10-7 s. As measured by someone on the moons surface,
(a) What was the velocity of the UFO?
(b) How far did it travel?
2. Three identical radio transmitters A, B and C each transmitting at the frequency νo in its own rest frame are in motion as shown
(a) What is the frequency of B's signals as measured by C?
(b) What is the frequency of A's signals as measured by C?
3. Consider three galaxies A, B and C. An observer in A measures the velocities of C and B and finds they are moving in opposite directions each with a speed of 0.7c relative to him. Thus according to measurements in his frame the distance between them is increasing at the rate 1.4c.
(a) What is the speed of A observed in B?
(b) What is the speed of C observed in B?
4. A Ko-meson (elementary particle) at rest decays into a π+ and π- meson each having a speed of 0.85c. If a Ko meson travelling at a speed of 0.9c decays
(a) What is the greatest speed that one of the π mesons can have?
(b) What is the least speed?
5. Show that the relativistic expression for kinetic energy reduces to the classical result when v << c.
6. (a) What is the speed of an electron whose kinetic energy equals its rest energy? Does the result depend on the rest mass?
(b) What is the energy equivalent of 1 gram of material?
(c) What is the "effective mass" of a photon of wavelength 500nm?
7. Show that for a particle of zero rest mass, mo = 0;
(a) Its velocity v = c 1
(b) its kinetic energy K = E
(c) momentum p = E/c
8. Compute the speed of (a) electrons mo = 9.1×10-31kg, (b) protons mo = 1.67×10-27kg, which fall through an electrostatic potential difference of ten million volts. (c) What is the ratio of relativistic mass to rest mass in each case?
Use electron charge e = 1.6×10-19C
9. (a) What potential difference will accelerate electrons to the speed of light according to classical physics? mo = 9.1×10-31kg, e = 1.6×10-19C and c = 3×108m/s
(b) With this potential difference what speed would an electron acquire relativistically?
(c) What would its mass be at this speed?
(d) What would its kinetic energy be at this speed?