Honors Research Topics in Physics

Here's a nice problem. Solve it tonight and bring it in tomorrow. By the way this is a requirement, not a suggestion.

Relativity problem 1-09

A train is 300 m long in and has a mass ( without fuel) of 1 million kg bothe as measured its own frame. It leaves a station and accelerates to and maintains a velocity of .6 c ( its an express train). It then enters a tunnel that is 400m long. The conductor on the train at the back of the train notes the time on his watch as noon or zero just as the back of the train enters the tunnel He also notices that the clock on the tunnel wall also says noon. The tunnel is exactly 300 m long in its own frame.


The usual “paradox” mentioned here is that the train sees the tunnel as shorter and therefore cannot fit entirely inside the tunnel. meanwhile the tunnel sees the train as shorter so it fits easily inside. Who is right?

For convenience assume that the tunnel frame and train frame are both lined with tape measures and clocks so we can always find t, t x, and x’. Assume the train tape =0 at back of train and tunnel tape = 0 at entrance to tunnel. To deal with this “paradox” we wiil answer the following. What is x at the front of the train ( x’ = 300m) when t’=0. What is t when t’=0 and x’=300m? What is x’ when x =300m and t =0 and more to the point , what is x when x’=300m and t=0? When you find all this, you’ll know who is right.

Also, how much fuel had to be converted to KE to get the train up to this speed?