# Train relativity question

1. Mar 23, 2005

### Jimmy Snyder

This is not original with me, and might be on the web somewhere, but I like it a lot:

Two trains travel nose to nose at the same speed along adjacent parallel gradeless tracks. The trains are identical in construction, maintainance, cargo distribution, fuel load, etc. When they approach the depot, the engineer on on one train applies the brakes gradually and comes to a slow stop. A while later, the engineer on the other train applies the brakes more abruptly and comes to a rapid stop, but nose to nose with the other train. Both trains take on cargo, and offload other cargo, and are refueled. They still have identical configurations. The engineers start up their engines. The train that stopped abruptly leaves, but the train that came to a gradual stop is unable. The engineer on that train then backs up the train for a while, stops, and is then able to go. What gives?

2. Mar 23, 2005

### 20questions

Maybe linkage between cars on the slow-stopped train are stretched, the quickly stopped train's links are compressed so the engine will not have to move all cars at the same time when it starts going.

3. Mar 23, 2005

### Jimmy Snyder

Bingo. Nice going 20questions.

4. Mar 23, 2005

### T@P

that is a good idea :) but it assumes the train cant pull (from rest) all the cars were they affixed by immovable steel atachemnets or what not. something i didnt know. well now i know :)

5. Mar 23, 2005

### BicycleTree

Why would the linkages ever be stretched?

6. Mar 23, 2005

### Jimmy Snyder

The term stretched here is used rather loosely.

I heard this one on the radio and I have no idea if that actually happens when a train stops. But the concept struck me as appealing even if it isn't true.

20questions' answer was correct. Here is an elaboration.

When the train is moving, the linkages are all snug. The engine is tugging on the first car, the first car is tugging on the second car, etc.

When the train stops abruptly, all of the linkages are loosened up as the train 'accordions'. When the engine starts, it is only pulling itself until the first linkage becomes snug. At that point in time, the engine will have a little inertia to help it out. As each linkage engages, the load becomes heavier, but the train is picking up inertia too.

When the train stops slowly, the linkages remain snug. The train can't move unless the engine can overcome the inertia of the entire train. When the train backs up, it loosens the linkages. Then it can go.

7. Mar 23, 2005

### BicycleTree

Slow braking would compress the linkages too. I don't see why it would compress them any less than fast braking. But if it compresses them significantly at all, then the situation is the same no matter how much it compresses them, because again the train starts moving one car at a time.

Last edited: Mar 23, 2005
8. Mar 23, 2005

### hedons

The engines were Diesel Electrics and when the one train stopped it did so with the electric drive engine on a dead spot on the forward direction winding on the motor armature. Backing up moved the armature off the dead spot eneabling it to stop and then continue in the forward direction.

That's my story and I'm sticking to it. ;-)

-Glenn

9. Mar 23, 2005

### Janitor

Train people use the expression "taking up the slack" to refer to pulling the couplers out to their maximum extension, by the way.

10. Mar 23, 2005

### BicycleTree

Sure, taking out the slack... that part makes sense. It's why you wouldn't have slack when you stop more slowly that does not make sense.

11. Mar 23, 2005

### T@P

if you think about it, decelerating slowly, ideally, is just like barely changing your speed at all. and because of friction, it would keep it from smoothly sliding the cars together (remember, the cars are pulled apart when you are just cruising). that way, when you finally stop, you would have it stretched out *more* than a sudden stop at the very least. and from experiance, it just makes sense.

12. Mar 23, 2005

### BicycleTree

It seems to me that a sudden stop could make the cars bounce against each other and end up farther separated. I don't think there is any common experience about this that you could say it "makes sense" from.

For the cars to decelerate at all, slowly or quickly, each must be pushed back by the car in front of it. If the train is slowing, no matter how rapidly or gradually, the cars must be in contact and the linkages must be fully slack.

13. Mar 24, 2005

### T@P

but if you go slow enough, the force that pushes them together may not be enough to overcome the frictional force between the cars. at least thats what i think. although it would require a *very* slow deceleration.

14. Mar 24, 2005

### hedons

If the train stops suddenly, the train will be compressed. To start moving the engine must just get the first car moving who's momentum helps get the second car get moving and so on...

If the train stops slowly, the train will be at maximum extension. To start moving forward, the engine would have to move the weight of the whole train all at once. Backing up first would set the train up at maximum compression in a state identical to the first train which has the ability to go forward.

-Glenn

15. Mar 24, 2005

### Bartholomew

T@P, for that to be true the train would have to be coasting and not braking. If it's stopping from the friction each car makes with the ground and not because of one car pushing against another, that's just like having no engine and no engine brakes at all. The train would gradually slow in that circumstance, and then the linkages could remain taut, but the problem said that the engineer does apply the brakes.

16. Mar 24, 2005

### 20questions

Sorry, stretched and compressed weren't clear. What I was picturing was more like a connecting chain pulled tight or hanging down with slack. Not unlike towing another car (automobile) behind yours with a chain, it's not that difficult to stop without having the pulled car rear end you.

17. Mar 24, 2005

### BicycleTree

I've never towed a car as you say, but in order to stop without being rear-ended you must decelerate slowly enough that the car behind you rolls to a stop on its own. And if you're doing that, you're decelerating gradually enough that your own car will roll to a stop on its own, so you don't need to brake.

18. Mar 24, 2005

### Jimmy Snyder

I think there might be some way to salvage the puzzle by having the trains go up a slope near the depot, but still manage to stop on the level in the depot. That way one train could glide to a stop losing most of its speed on the incline and losing the rest from friction on the level. The other train brakes. However, such a detailed description of the stopping process might give away the answer.

When a train brakes, do all of the wheels on all the cars brake too. If they do, then the slowly decelerating train might not accordion after all.

19. Mar 24, 2005

### T@P

im pretty sure a train is run by an engine and a bunch of cars that are just dead weight with wheels. and honestly i think theres too much fuss about the whole compression buisness. when you slow down, there is a force acting on the other cars that pushes them together, a force which if made small enough can be overcome by friction. thats my take. the puzzle is quite neat without the adjustments.

20. Mar 24, 2005

### BicycleTree

Do you have a clear idea of what it means for the force of compression to be "overcome by friction"? It means that the cars are just coasting and the engine is not braking.