Homework Problem Set 5
Homework Due on Thursday April 25
Partial credit may be given even if the final answer is incorrect so please show all work!
Question 1 (1 point)
How is Einstein’s Principle of Relativity the same as Galileo’s? How is it different?
Question 2 (3 points)
At the Belle Experiment electrons moving in one direction around the accelerator ring are collided with
positrons (or anti-electrons) moving in the other direction around the ring. The rest mass of both the
electron and the positron are 511 keV/c2. The total energy of the electron in the frame of reference of the
laboratory is 8 GeV, and the total energy of the positron is 3.5 GeV. What is the speed of the electron in
the laboratory frame in terms of the speed of light? What is its gamma factor? What is the speed of the
positron in the laboratory frame in terms of the speed of light? What is its gamma factor?
Question 3 (3 points)
At the instant before a particle collision at the Belle Experiment, an electron is moving north with a total
energy of 8 GeV, and a positron is moving south with a total energy of 8 GeV. What is the speed of the
electron as seen by the positron?
Question 4 (3 points)
When the electron collides with the positron they annihilate each other, and the energy from the
annihilation forms into a muon and an antimuon. The rest mass of both the muon and the antimuon are
106 MeV/c2 and each gets exactly half of the energy from the annihilation. What is the speed of the muon
in the lab frame? If the muon’s lifetime is 2.20 μs in its own reference frame, what is its lifetime as seen
in the laboratory frame?