1. How fast must an object travel for its total energy to be (a) 1% more than its rest energy and (b) 99% more than its rest energy.

2. A proton is moving with a constant speed has a total energy 3.5 times its rest energy. What are the proton's

a. Speed?

b. Kinetic energy?

c. Momentum?

3. The Sun's mass is and it radiates at a rate of kW.

a. Over time, must the Sun's mass increase, decrease, or remain the same?

b. Estimate the lifetime of the Sun from the data given, assuming it converts all of its mass into energy. Express your answer in years.

c. The actual lifetime of the Sun is predicted to be much less than the answer you calculated above. What does this tell you about the 100 % energy assumption?

d. Current theoretical calculations have the sun burning out in 5 billion years. During that time, what percentage of its mass will it lose?

4. Suppose two black holes meet and coalesce into one larger black hole. If the have the same mass M, and Schwarzschild radius R,

a. Express the new single black hole's Schwarzschild radius as a multiple of R.

b. Express the average density of the new single black hole in terms of the average density (ρ) of each of the original black holes.