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

[tommyers]

Hi,

If I were to throw a tennis ball at an oncoming train would the ball stop the train momentarily while the ball changes direction? Due to the conservation of energy!

Regards

Tom

 

[Cyrus]

No.

If that were to happen, the tennis ball would explode.

 

[DaveC426913]

A tennis ball is not a perfectly rigid object, neither is a locomotive, so no.

 

[Pengwuino]

I've heard this before... why exactly do you think they train would momentarily stop?

 

[DaveC426913]

The logic goes thus:
The tennis ball clearly must stop in order to change direction, even if only instantaneously.
If the tennis ball is stopped even for a moment, and is in contact with the locomotive, then one could conclude that the locomotive is stopped even for a moment.

...if one didn't know that tennis balls and locomotives can deform.

 

[Cyrus]

Not if it is stopped relative to the front of the locomotive. Then the locomotive never stops moving.

 

[Mallignamius]

Hmm. Of course some energies are absorbed/dispersed. Is the train's speed or momentum decreased, however tiny, at all?

 

[Delzac]

The logic goes thus:
The tennis ball clearly must stop in order to change direction, even if only instantaneously.
If the tennis ball is stopped even for a moment, and is in contact with the locomotive, then one could conclude that the locomotive is stopped even for a moment.

...if one didn't know that tennis balls and locomotives can deform.

hmmm i still dun quite understand the reasoning behind why the train can't stop, can u give a clearer explanation. And also why the tennis ball will explode if it happens. thx!

 

[Farsight]

Hmmnnnn.

 

[NateTG]

If I were to throw a tennis ball at an oncoming train would the ball stop the train momentarily while the ball changes direction? Due to the conservation of energy!

It could happen with the conservation of momentum, however ...

Let's say that we have a light train at 100,000 kg, and a heavy tennis ball at 1 kg. So, if the train is moving at 1 m/s (3.6 km/h) the tennis ball would have to be moving at at least 180,000 m/s (648,000 km/h), and, realistically twice that fast, in order to stop the train. That's roughly 16 times escape velocity.

 

[tommyers]

Could someone explain how the conservation of a momentum would apply in this case?

 

[russ_watters]

hmmm i still dun quite understand the reasoning behind why the train can't stop, can u give a clearer explanation.

Conservation of momentum dictates that the train must keep moving.

The scenario described isn't reality, so it is a little pointless to speculate about it, but the logic is wrong anyway: If a tennis ball and a train were perfectly rigid, the train would not stop as the ball changed direction, but rather, the tennis ball would change direction instantly (infinite acceleration).

The scenario can be approximated, however, using increasingly harder objects. Steel ball bearings, for example, undergo an extrordinarily high acceleration - hundreds (thousands?) of g's - when you bounce them on the floor.

 

[Delzac]

but all we need is the ball to change direction isn't ? the ball will surely change direction is collision occur, so they ball will momentarily stop to change direction.

Originally Posted by DaveC426913
The logic goes thus:
The tennis ball clearly must stop in order to change direction, even if only instantaneously.
If the tennis ball is stopped even for a moment, and is in contact with the locomotive, then one could conclude that the locomotive is stopped even for a moment.Thus after the collision, momentum is still conserved right? ( Momentum Before = Momentum After )

Edit 1: sry didn't saw the above post :P
Edit 2: Thx for the help

 

[Gokul43201]

Hi,

If I were to throw a tennis ball at an oncoming train would the ball stop the train momentarily while the ball changes direction?

No, it would merely slow it down by a very tiny bit.

Due to the conservation of energy!

That is not a complete argument - in fact, I see no possible way that you can arrive at this from energy conservation. Provide a complete argument, and we can point out the error.

You are asking us to guess what your reasoning is, and then find the error in it!

 

[Farsight]

I think there's a bit of Zeno's so-called "paradox" in here somewhere.

 

[DaveC426913]

The point is thus:

The tennis ball does not instantaneously decelerate and change direction. The deceleration occurs over a non-zero time and a non-zero distance (the distance being somerthing less than the diameter of the tennis ball as it deforms on impact).

During this brief (but non-zero) contact, the tennis ball transfers an amount of energy to the train, that energy is first put into deforming the steel surface of the head of the train. The steel surface rebounds, giving most of its energy back to the tennis ball, but some of the energy is transmitted down the length of the locomotive in the form of a shock wave (i.e. sound wave, i.e. WHAP!). This wave has the effect of very slightly (VERY slightly) decelerating the train. This deceleration also occurs over a non-zero time and a non-zero distance. Note that it occurs atom by atom too, as each steel atom shoves the one next to it.

Meanwhile, the tennis ball has the energy given back to it by the train (and some more by the train's movement). It rebounds, (over a non-zero time and non-zero distance), accelerating away from the train.

The key (if it isn't obvious enoguh by now) is the interaction (i.e. energy transfer) over a non-zero time and non-zero distance*.



*(Interestingly, this strikes at the very heart of our current lack of understanding of the universe: why GR and QM are irreconcilable. How can a theoretically zero-dimension GR particle transfer its energy to another zero-dimension particle over a zero time? That results in an energy transfer rate of infinity! But I digress...)

 

[actionintegral]

To correctly analyze this problem you must first specify the elasticity of the collision. As a first attack, try perfectly inelastic. Then try perfectly elastic.

 

[prabhakar_misra]

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

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. 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 . for this to happen the train and the tennis ball have to have equal momentum . how u manage it is your concern .

bottom line is -
if a body comes to instantaneous rest during a collision , then the body will either change its direction of motion or come to permanent rest .

 

[pervect]

Let's start with an easier question. If you threw a tennis ball at a train that was standing still, would the train move backwards?

Use common sense. Suppose a tennis ball hit an automobile - would the car go flying backwards, or would it stay put?

You might put a dent in the car (one reason not to try the experiment). Would you call a dent in the car "making the car move backwards"? Or would you call it a dent?

 

[NateTG]

The deceleration occurs over a non-zero time and a non-zero distance (the distance being somerthing less than the diameter of the tennis ball as it deforms on impact).

The parenthetical is really only true from a limited number of reference frames. It's very easy to see that there are inertial frames of reference where the ball travels an arbitrary distance. (Not to mention that, since it deforms the tennis ball's diameter isn't well-defined.)

 

[Gokul43201]

I think there's a bit of Zeno's so-called "paradox" in here somewhere.

Please don't stop there. Which bit is it, and where is this bit to be found?

 

[LURCH]

At the instant the ball is stationary relative to the train, the train is stationary relative to the ball.

 

[DaveC426913]

Let's start with an easier question. If you threw a tennis ball at a train that was standing still, would the train move backwards?

Use common sense. Suppose a tennis ball hit an automobile - would the car go flying backwards, or would it stay put?

I believe this actually confuses the issue becasue it's not the same thing at all as the original problem.

It could be argued that, yes, if you hit an automobile with a tennis ball, the car does move backwards a tiny bit (no, not flying backwards like you claim but "a bit"). This lead the OP away from correct answer to the question.

 

[pervect]

I believe this actually confuses the issue becasue it's not the same thing at all as the original problem.

It could be argued that, yes, if you hit an automobile with a tennis ball, the car does move backwards a tiny bit (no, not flying backwards like you claim but "a bit"). This lead the OP away from correct answer to the question.

Not really. In fact, the point is that it is the same problem!

When you know what happens to the train when it gets hit by a ball when the train is standing still, you also know what happens to the train when it is moving. The only thing that is important is the relative velocity of the ball with respect to the train.

This is an important principle of physics. (It's even got a name, but I'll leave it as a question - what is this principle of physics called?).

If the train is moving 50 mph an the ball 50 mph, or the train 100 mph and the ball standing still, or the train standing still and the ball 100mph, this principle of physics says that the change in velocity (if any) of the train will be the same.

We can also see that if the train is to stop, even instantaneously, from 50 mph, it must suddenly acquire a velocity of -50 miles/hour from being hit by the ball. This should be obviously totally unrealistic, I hope.

 

[DaveC426913]

Not really. In fact, the point is that it is the same problem!

Yes, in principal it is, but for someone struggling with how a ball does NOT stop a train, it can be confusing to show them how a ball CAN move a train.

It's not much of a stretch to conclude (erroneously) that "moving a train backward from rest, even if only slightly", is comparable to "stopping a train from moving forward, even if only momentarily".

 

[Farsight]

Gokul: it's in the bit where the tennis ball changes direction. If we forget deformation for a moment, at one instant the tennis ball is moving at 50mph, at another instant the tennis ball is moving at -100mph. Therefore at some instant between it's moving at 0mph. And because it's touching the train, the "Zeno" logic says the train is also moving at 0mph at that instant.

But it's contrived by arbitrarily slicing time intervals into smaller and smaller intervals. In the end you take an interval of zero length and supposedly see that the distance traveled during that interval is zero, so the speed must be zero.

But it ain't. The slicing tends towards a false limit. You do overtake the tortoise. The arrow plunges home. And the five hundred tonne train didn't stop.

 

[DaveC426913]

But it ain't. The slicing tends towards a false limit. You do overtake the tortoise. The arrow plunges home. And the five hundred tonne train didn't stop.

I respectfully disagree (meaning I don't think you're wrong so much as I think I've hit closer to the mark). I think it's not about Zeno's paradox at all, and that deformation is the key principle being neglected.

I can't think of one now, but I suspect that this class of thought experiments has examples that don't involve Zeno's paradox.

 

[Quaoar]

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

"The heaviest train was a BHP Iron Ore train weighing 79,577 tons. The 10
locmotives and 540 ore cars ran from Newman to Port Hedland, Western
Australia, a distance of 253.9 miles, on May 28, 1996."

This works out to 7.2e7 kg. A train traveling 60mph (27 m/s) has total momentum 1.94e9 kg m / s.

A tennis ball weighs 56.7 g (.0567 kg). Classically, this would mean the ball would have to be traveling at 3.4e10 m/s, faster than the speed of light. Therefore, we must use the relativistic equation. Working with the relativistic momentum equation:

gamma_train * m_train * v_train = gamma_tennis * m_tennis * v_tennis

Since the train is not moving relativistically, we can ignore gamma_train. Plugging in the definition of gamma, we find the following equation for the velocity of the tennis ball:

v = \\frac{A}{\\sqrt{m^2 + \\frac{A^2}{c^2}}}

Plugging in the numbers, we get a velocity of .99996c. We better get Federer to work a bit on his serve... :)

EDIT: Why isn't tex working? I have the same syntax as this thread demonstrates: https://www.physicsforums.com/showthread.php?t=8997

 

[arildno]

Gokul: it's in the bit where the tennis ball changes direction. If we forget deformation for a moment, at one instant the tennis ball is moving at 50mph, at another instant the tennis ball is moving at -100mph. Therefore at some instant between it's moving at 0mph. And because it's touching the train, the "Zeno" logic says the train is also moving at 0mph at that instant. .

Totally incorrect!
How could you say such a thing?

 

[DaveC426913]

Totally incorrect!
How could you say such a thing?

Well, he's not, you misread his post. He's defining and clarifying the logic in the problem - which is flawed - as is the logic in Zeno's paradox. He then goes on to refute that logic.

The key that unlocks the puzzle is "instantaneous speed", which had not been invented by Zeno's time.

 

[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!