Does a tennis ball stop a train if it hits it?

[DaveC426913]

Let's calculate how fast a tennis ball would have to move to stop a train

Why? That has nothing to do with the problem.

What you're doing is calculating how fast a tennis ball must be moving to bring the train to a stop, which has nothing to do the train's instantaneous velocity being zero.

 

[russ_watters]

Definition problem (the word vs the problem): an instant is a point in time, so there can always points between points. But if the acceleration happens in one point in time, there can be no other point inside that point.

Therefore, if there is no deformation, the turnaround is instantaneous - ie, taking zero time.

Now, that particular instant is the one point at which this scenario becomes physically impossible. So it can't really be said what happens there. You must treat it like an asymptote - a limit - and analyze what happens on either side. And what happens on either side is that the speed of the object is constant, no matter how arbitrarily close you get to that point. And that means, instant/infinite acceleration.

 

[Quaoar]

Why? That has nothing to do with the problem.

What you're doing is calculating how fast a tennis ball must be moving to bring the train to a stop, which has nothing to do the train's instantaneous velocity being zero.

It's not directly related, but I just thought it would be interesting.

 

[3trQN]

if the train were ever to come to rest it will surely be at the time when the ball comes to rest and changes direction.

This is correct, however:

if this happens , then at that instant of time the total energy of the system is zero . hence they will stick together and not move .

This is only correct for a non-deformable system, in real terms the energy is stored in the deformation of the ball and the train, at the next instant of time this energy will rebound back as the compression of the ball/train re-equillbriates and the energy is again transferred to the ball as its sent off in the opposite direction ( conservation of momentum sais that the train will also be affected though by a much smaller fraction due to its mass ).

I think russ is correct to point out the flaw is in the over simplification of the situation by assuming a perfectly rigid body, which to me is only possibly acheived by cooling the body to absolute 0, at which point you can't also have it moving. I know nothing about the bose-einstein condensate but maybe someone could say something about this with respect to this problem?

 

[daniel_i_l]

Lets say you're inside the train which is moveing at a constant velocity (relative to the ground). Now if you throw the ball at the back of train the ball will bounce back in exactly the same way that it would if the train was stationary (relative to the ground), if it wasn't the same then you'd be able to tell that you were moving relative to the ground which is impossible even according to pre-Einsteinian relativity. Now this case is exacly the same as what I've just described if you look at the speed of the ball relative to the train - so, like when you throw the ball inside the train, the ball stops relative to the train but not relative to the ground - so obviously the train doesn't stop.

 

[DaveC426913]

so, like when you throw the ball inside the train, the ball stops relative to the train but not relative to the ground - so obviously the train doesn't stop.

This doesn't address the original problem!

When the tennis ball hits the rear wall, it stops and changes direction. Somewhere in there, the ball's v is zero. If the ball's v is zero, and it is in contact with the train, one could conclude that the train's v is zero for a moment.

That's the issue that needs to be addressed.

 

[ObsessiveMathsFreak]

The ball stops the train.

But the train doesn't all stop at the same time.

 

[Cyrus]

Um....what?


So you mean to tell me that a x-hundred ton train comes to a stop in the split second of time it makes contact with the ball, and then speeds back up to its original speed an instant later, after all, we agree that the train will continue straight ahead after the collision. What, can this train withstand thousands upon thousands of g' forces to do that? Does any of this seem unreasonable to anyone else?

DaveC gave the correct anwser the first time. Whats the issue?

 

[DaveC426913]

The ball stops the train.

But the train doesn't all stop at the same time.

As Cyrus point out,

No.

 

[DaveC426913]

I'm just going to say this one last time, and then y'all can do whatever you want.

There is no such thing as a perfectly rigid body. If the tennis ball and train were both perfectly rigid, we would definitely have a problem. The energy required to reverse the direction of one perfectly rigid body by another perfectly rigid body would be infinite - as would the acceleration rates.

And with infinite energy kicking around, bringing the train to a halt would be the most trivial of concerns. Note that neither the train nor the ball would be able to vapourize, or do any other such thing that would require the transfer of energy between atoms - which they can't do since they are perfectly rigid. And, since we have things changing direction without loss or gain of energy, kinetic or otherwise, we've also eliminated inertia. But I digress...

You can see how this universe rapidly deteriorates into a fantasy.

Bodies interact (transfer kinetic energy) over a non-zero distance and a non-zero time.

 

[Farsight]

Well said Dave.

 

[DaveC426913]

Theng kew...

Now, LOCK THIS THREAD before some idiot comes up with another completely erroneous explanation!

 

[Doc Al]

Good idea!