# 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

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#### Cyrus

:rofl: No.

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

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#### DaveC426913

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

#### Pengwuino

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

#### DaveC426913

Gold Member
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

DaveC426913 said:
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 explaination. And also why the tennis ball will explode if it happens. thx!

Hmmnnnn.

:grumpy:

#### NateTG

Homework Helper
tommyers said:
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

Mentor
Delzac said:
hmmm i still dun quite understand the reasoning behind why the train can't stop, can u give a clearer explaination.
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

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#### Gokul43201

Staff Emeritus
Gold Member
tommyers said:
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

Gold Member
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....)

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#### 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

Staff Emeritus
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?

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#### NateTG

Homework Helper
DaveC426913 said:
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

Staff Emeritus
Gold Member
Farsight said:
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

Gold Member
pervect said:
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

Staff Emeritus
DaveC426913 said:
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

Gold Member
pervect said:
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".

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

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