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Cosmology and Quantum Introduction solutions

Cosmology and Quantum Introduction solutions - PHYSICS 6...

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PHYSICS 6 SPRING 2006 HOMEWORK 3 SOLUTIONS 1. The charged pion ( π + ) decays has an average decay time of 2.6x10 -8 sec. a. If a π + is travelling in a lab at 0.9999c what is its average decay time? b. How far does it travel before decaying (on the average)? d=vt = 3x10 8 × 1.8x10 -6 = 5.4x10 2 m c. The π + turns into three particles (usually muon and 2 neutrinos) when it decays. Suppose the muon is produced along the direction of the π + motion and has a velocity of 0.99c in the π + rest frame. What is the muon velocity in the lab? In π + rest frame (S ) muon has u = 0.99c, but π + is moving at V=0.9999c in lab frame (S). Then 2. Judy and Andy are twins. Judy gets on a rocket that goes to a star system 20 light years away from earth (as measured from earth, i.e. Andy's frame of reference). a. She travels at 0.8c. How many years does it take her to reach the star according to Andy? t= 20 c yr / 0.8 c = 25 yr b. What will Judy's clock read when she reaches the star? Judy's clock runs slow according to Andy, via t(Judy)= 25 × (1-0.8 2 )= 25 × (1-0.64) = 25 × (0.36)= 25 × 0.6 = 15 yr c.
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