# Homework Help: Relativity Help

1. Apr 27, 2005

### starlooney

Hi, I'm really hoping somebody can help me. basically i have an exam coming up very shortly and from my revision thought i was doing ok with the relativity section. When i have come to look at past exam question i have discovered that although i know my theory i haven't a clue how to actually apply it to any of the situations given. What i'm hoping is that someone might read this and might be able to provide the starting blocks to answer the questions.

Here are 2 examples from the past two years:
(1) Consider two stars, one with mass m 0 and velocity 0.8 c and another one with mass 3mo and at rest in the reference of a distant observer. Suppose that the two stars collide and merge into one star.
(a) What is the initial total linear momentum of the system?
(b) What is the initial total energy of the system?
(c) What is the velocity of the system after merging?
(d) What is the rest mass of the resulting star?

(2) A pion is produced by the collision of a cosmic ray particle with a nucleon in the upper atmosphere. The pion rapidly decays into a muon, and the muon then decays into an electron and a neutrino. The rest mass of a muon mu is about 106 MeV, and the muon-decay timeseale is 2.2 x 10 .6 s.
(a) If the muon is produced at a height of 18 km above the sea level with a total energy of 30 GeV and it travels downward vertically, what are the Lorentz factor and relativistic parameter of the muon?
(b) What is the expected time of flight that the muon takes to reach sea level?
(c) What is the probability that the muon can reach sea level?

I am obviously not asking anyone to answer the above questions i am really just hoping to find the starting blocks for each question so that i could apply my knowledge to other situations. Thank you very much for your help!

2. Apr 28, 2005

### OlderDan

You might want to look here for a refresher on relativistic momentum and energy. Problems like your collision problem are usually transformed into the center of mass frame of reference and then transformed back to express the results.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html

Your second problem is based on an actual experiment that was performed to verify the predictions of length contraction and time dilation. Imagine riding along on the muon. What would the 18 km distance an earth observer sees look like to you? The lifetime of the muon assumes the rest frame of the muon. How would the moun's "clock" appear to be running to an earth observer?