Compute the kinetic energy of a proton (mass 1.67 * 10-27 kg) using both the nonrelativistic and relativistic expressions, and compute the ratio of the two results (relativistic divided by nonrelativistic) for speeds of (a) 8.00 * 107 m/s and (b) 2.85 * 108 m/s.

Starting from rest, two skaters "push off" against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.0 m/s relative to the ice. The mass of the woman is 57 kg, and the mass of the man is 76 kg. Assuming that the speed of light is 3.5 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice. (Hint: This problem is similar to Example 6 in Chapter 7.) Number i Units

Starting from rest, two skaters "push off" against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.2 m/s relative to the ice. The mass of the woman is 57 kg, and the mass of the man is 88 kg. Assuming that the speed of light is 2.8 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice. (Hint: This problem is similar to Example 6 in Chapter 7.) Number i Units

In special relativity, we introduced the momentum of a particle in a given Lorentz frame as pu = (E, pi ), where E is the energy of the particle and pi is the relativistic 3-momentum. Explain why, in general relativity, the energy of a particle measured by an observer is given, irrespective of the coordinate system used, by −p · uobs, where pu is the momentum of the particle and uuobs is the velocity of the observer in those coordinates.