# Homework Help: Length Contraction Problem

1. Feb 16, 2012

### RichardT

1. The problem statement, all variables and given/known data
An electron travels in an accelerator tube at a speed of 0.997 c relative to the Earth. In the frame of the electron, the length of the tube is 1.20 m.
A. What is the length of the tube relative to Earth?

B. Relative to Earth, how long does it take for the electron to travel the full length of the tube?

C. In the frame of reference of the electron, What is the speed of the tube?

D. In the frame of reference of the electron, how long does it take for the full length of the tube to pass the electron?

2. Relevant equations
l = lo âˆš1-v^2/c^2
t = d/v
c = speed of light = 3.0 x10^8m/s

3. The attempt at a solution
For Part A. I did l = lo âˆš1-v^2/c^2 and plugged it in so 1.2 = loâˆš1-(0.997)^2 and solved for lo which became to be 15.5m

For Part B. i used t = d/v and plugged in t = 15.50m/0.997c = 5.18 x 10 ^-8 seconds

For Part C. I said that the speed is the same and is constant so speed of the tube in frame of reference of the electron = 0.997c

For Part D. t= d/v = 1.20m/0.997c = 4.012 x 10^-9 seconds.