Problem 7.20 Derive the fine structure formula (Equation 7.68) from the relativistic correction (Equation 7.58) and the spin-orbit coupling (Equation 7.67). Hint: Note that (except for , where only the plus sign occurs); treat the plus sign and the minus sign separately, and you’ll find that you get the same final answer either way.

Alarge cruise ship of mass 7.00 ✕ 107 kg has a speed of 11.6 m/s at some instant. (a) what is the ship's kinetic energy at this time? (b) how much work is required to stop it? (give the work done on the ship. include the sign of the value in your answer.) (c) what is the magnitude of the constant force required to stop it as it undergoes a displacement of 3.00 km?