# What if a train travelled at 3/5 c

1. Oct 4, 2004

### stunner5000pt

Using speical relativity

a train is moving along a track is v = (3/5) c. At the instant the train passes a construction worker standing right besides the track both the worker and the train driver set their watches to read the same time. A bridge collapses 200m furhter up ahead the track 2.0 e -7 seconds later, according to construction worker. At what time did the bridge explode according to the train driver? while setting her watch to 0 the consturction worker inadvertently sent a detonation signal to some dynamit loacted 200m at the foot of the bridge. Could the dynamite exploding have caused the bridge to collapse?

First of all what time did the bridge collapse according tothe train?

It's either one of two things, longer or shorter.
the worker will see the clock move slower on the train, and the train will see the workers clokc move faster. So the time seen by the train driver is 2.0 e -7 / gamma = 1.6 e -7 seconds

Could hte dynamite have caused the bridge to collapse?
not quite sure about this. it is as easy as common sense would say? But there must be something that makes this a second year physics class assignment worthy

2. Oct 4, 2004

### Staff: Mentor

Can't argue with that!
Careful. Both see each others clock as running slow. (Time dilation works both ways.)
Nope. Even if you got the direction of the time dilation correct (that moving clocks go slow), realize that the train driver will disagree that the worker is measuring the correct time. (Since the worker and his clock are not located at the site of the explosion.)

Instead of trying to take a shortcut, apply the Lorentz Transformations. You know the space-time coordinates of the explosion in the worker's frame; use the LT to calculate the coordinates in the train frame.

What does your common sense tell you? Try this: How fast must the signal travel to set off the explosion? Is that possible?

3. Oct 5, 2004

### stunner5000pt

according to what Doc Al said, then time contraction is a two way street

thus if the worker sees the train's clock move slower, the train will also see the worker's clock move slower?

thus the train driver would see the explosion a little longer after the worker say it?? Am i right in assuming this?

4. Oct 5, 2004

### Staff: Mentor

Yes, time dilation works the same for every inertial observer.

Observers on the train will say that the ground clocks are slow; workers on the ground will say that the train clocks are slow. All true, but that's not the full story.

If the problem was this "What time does the train observer's clock read when the ground observer's clock reads 2.0 e -7 seconds?", then you'd have a simple case of a moving clock. Then the time measured by the train observer would just be $\gamma t$. But that is not the problem! The problem is "What time did the train observer's clock read when the bridge collapsed?". According to the train observer, the collapse does not occur when the ground worker's clock reads 2.0 e -7 seconds. (In addition to time dilation, you must consider the relativity of simultaneity and length contraction--and the fact that the ground worker is 200m away from the bridge.)

No. As explained above, it is not a simple matter of a moving clock. Use the Lorentz transformations to convert the space time coordinates of the explosion from one frame to the other. (The LT automatically incorporates all the special relativity effects.)

5. Oct 5, 2004

### stunner5000pt

your suggestion of using the lorentz transformations leads me to use t' = gamma (t - vx / C^2)

but i am not sure waht calues of t, and x i would use
would the value of x be the contracted value as seen from the train??

in addition, would the value for t be the dilated value measurd by the construction worker??

i am not quite uncertain...

6. Oct 5, 2004

### stunner5000pt

if i use that method i get t = 1.52 x 10^-7s but i get it as a ngative number is that correct? Please help!!!!!!!!!!

7. Oct 5, 2004

### Gokul43201

Staff Emeritus
First ask yourelf how long after the bridge collapsed (according to an observer on the bridge itself), did the oberver 200 m away observe the collapse.

This will also answer the last question of whther the observer caused the bridge to fall.

8. Oct 5, 2004

### stunner5000pt

i understand the second part of the question but i need to know (or understand, rather) how much time later the train driver would see the explosion, but thanks for answering that anyway...

9. Oct 5, 2004

### stunner5000pt

10. Oct 6, 2004

### Staff: Mentor

Correct.

The prime coordinates (x' & t') are the position and time of the event (the bridge collapse) as measured by the train frame; the unprimed coordinates (x & t) are measured by the ground frame. You are given x and t.

11. Oct 6, 2004

### Staff: Mentor

What values did you use?