PHYS126 Spring 2011 Homework 4, Due March 4, beginning of lecture. 1a. In lecture, we proved 2 2 2 2 ) ( ) ( E mc pc = + from the space-time relation. Prove this relation using a different method, by directly substituting 2 2 1 c v v m p-= and 2 2 2 1 c v mc E-= into the right hand side. After some algebra, you will get the left hand side. 1b. The rest energy of a unknown particle is 2GeV, and its kinetic energy is 4GeV. What is the momentum(in GeV/c), and its speed? 2. A lambda particle decays into a proton and a pion, lambda b p + pi, and it is observed that the proton is left at rest. a) what is the energy of the pion? b) what was the energy of the original lamda? ( the masses involved are mass of lambda particle = 1116, mass of proton = 938, and mass of pi particle = 140, in MeV/c 2 . ) Hint: do it algebraically, then put in numbers) 3. If u is much less than c, the binomial approximation ( 2 1 2 β γ + = ) shows that the relativistic kinetic energy, 2 ) 1 ( mc K rel-= is about
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This note was uploaded on 03/31/2011 for the course PHY 126 taught by Professor Hobunchan during the Spring '11 term at HKUST.