Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

1.
A train moves past a tower at a speed of 0.78c. The train has a rest length of L' = 450m. When the front of the train passes the tower, the clocks in the tower and in the front of the train are synchronized to t=t'=0s. The instant that the back of the train passes the tower, the tower sends a signal which is subsequently detected by the receiver in the front of the train.  Assume that the speed of the signal sent has the speed of light.

a) according to the clock on the train, when is the signal sent?
b) when according to the clock in the tower, is the signal received at the front of the train
c)when according to the clock on the train is the signal received?
d) according to an observer on the tower, how far away is the front of the train when the signal is received?

2. Relevant equations

Time dilation equations
Length Contraction
lorentz transformation


3. The attempt at a solution
for part a, I simply used length/speed which gave me the time.
here I used 450m/0.78c = 1.92x10^-6 s.

The biggest problem I have is part b and c.
I first applied length contraction to obtain the train's length in the tower's reference.  At this point, I am not sure at all on how to solve for the signal received.

for part c, I believe I would use time dilation equation to find the time in the train's frame

For part d, I think the only equation that's needed is:
change in x = v * change in t where change in t is the time between signal received and signal sent and x is the distance traveled during time t plus the initial length(after length contraction).

Please help I really want to understand this problem as thoroughly as possible. Thanks!

Last edited by jianxu (2008-08-30 04:19:13)