Download Midterm Test 1 - Introduction to Relativity and Quantum Mechanics | PHYS 3740 and more Exams Physics in PDF only on Docsity! Introduction to Modern Physics PHYS3740 Midterm test 1 Wednesday 11th 2006 Note: the best possible score is 125/100 1) Draw a Space time diagram A and B are at rest with respect to each other and are separated by a distance d measured in the reference frame where they are at rest. The following sequence of events occurs: (1) A sends a light signal towards B . (2) As soon as the signal is received by B , B sends a signal back to A . (3) A receives the signal from B . a) (5 points) Draw a space time diagram ๎ct , x๎ showing these events from the point of view of the reference frame S in which A and B are at rest ( choose xB๎
xA ). Indicate all the relevant ct intervals on your diagram. b) (5 points) Draw a space time diagram from the point of view of a reference frame S ' moving at speed v=๎ธc in the direction from A to B . c) (5 points) From the point of view of S ' , what is the distance d ' separating A and B ? How is the relation between d and d ' usually referred to? d) (5 points) From the point of view of S ' , what is the ct ' interval between event (1) and event (3)? e) (5 points) What is the ct ' interval between (1) and (2)? and between (2) and (3)? (Hint: using Lorentz transform might be a good idea) 2) Here comes the muon again A muon ๎ with mass m๎=105.5 MeV /c 2 has a kinetic energy K ๎=211 MeV measured in the lab reference frame. a) (5 points) What is the total energy E of the muon ๎ ? b) (5 points) What is the momentum p of the muon ๎ ? c) (5 points) What is the speed u (in terms of the speed of light) of the muon ๎ ? We now consider the same muon ๎ but this time from the point of view of a reference frame moving in opposite direction a speed v=0.8c with respect to the lab. d) (5 points) What is the total energy E ' of the muon ๎ ? e) (5 points) What is the momentum p ' of the muon ๎ ? f) (5 points) What is the speed u ' (in terms of the speed of light) of the muon ๎ ?
