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# Tricky lorentz transformation question watch

1. Could someone help me out with this question?
Its from the most recent past paper so the solutions aren't up anywhere yet.
Usually I get these type of questions but this ones got me messed up.
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Could someone help me out with this question?
Its from the most recent past paper so the solutions aren't up anywhere yet.
Usually I get these type of questions but this ones got me messed up.
What part are you stuck on?
3. Yes we don't have time to answer the lot! What have you worked out so far and what equations do you intend to use?

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4. For the first question, I believe it is simply a substitution of the values given (the lengths of the tunnel and train are measured at rest) into the Lorentz transformations.

For event A determined by O,
t: take the Lorentz contracted length of the train and divide by the relative speed,
x: 0 since observer O is at the entrance of the tunnel

Similarly, for event B determined by O,
t: the rest length of the tunnel divided by the relative speed
x: the rest length of the tunnel

Then for the following part, use the Lorentz transformations you have written at the beginning to solve for t' and x' for both events. You should obtain for event A x'= -250m and event B x'= 0. (sorry can't be too sure about the t' as I'm doing this on my head)

Next, O' will measure the length of the tunnel to be contracted.
So event A has t'= rest length of the train divided by the relative speed
And event B has t'= Lorentz contracted length of the tunnel divided by the relative speed

The time difference between both events should be the same value as what you have obtained in the previous part where you used the Lorentz tranformations.

Finally, what is meant by 'completely inside' is that the front end of the train exits the tunnel simultaneously or after the rear end has entered, as observed by O since the times of event B minus event A gives a positive value, meaning to say event A happens before B. Similarly the events can no longer simultaneous in O', and B-A has a negative time difference, so O' will observe train exit the tunnel before its rear end enters.

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Updated: January 6, 2013
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