l . [40 pts - short essay] Name two examples of converting energy to mass and two examples of converting mass to energy. Be sure to explain which is which. This is a short essay, so I will not accept just a list. A (brief, but well formed) discussion of each example you present is requested. [35 pts short essay] Describe a reference frame from which it appears that Alpha Centauri [a star 4 light years from Earth) is traveling faster than the speed of light, or explain why no such frame exists. This is a short essay (and remember what I write above: \"Short essay questions should be answered with the same care you would apply to a term paper\"), so you are asked to explain your answer, presenting arguments why it should be right. ['15 pts question] Estimate how much mass in kilograms would be needed to replace all the electric power supplied to Amherst for one day, assuming the mass could be completely converted to electrical power. You'll need to make an educated guess as to how much electrical power is used by Amherst. Show all your work and include references for any numbers you quote. This is not an essay, but I am asking that you write explicitly the arguments you used to compute the result. The numerical result alone, no matter how correct, will get 0 pts. [19 pts - question] Many of the particles we see in cosmic rays [and also create in particle accelerators] are unstable. They live only for a short period of time before they decay to other particles. One such unstable particle is called a muon, essentially a heavy version of an electron. Imagine that a muon created in the upper atmosphere is headed straight down towards the Earth at 99.99% the speed of light. This particular muon lives for exactly one millionth of a second as measured in the muon's rest frame, before decaying into other particles. How far does the muon travel as viewed by a person on the ground? {Show exactly how you set up the calculation, as well as the result.) If you don't want to use an equation editor, you are welcome to just use the nri'l'hmn'tir' nnarni'in: f4. - 1" fl and than an: Inn: rnn+ cnrt