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

In summary: Then try something in between. If you're trying to get the ball to just touch the train and change direction it's very difficult to do. As the ball's center of mass moves from moving towards the train to moving away from the train, the ball has to go through a point where there is no relative motion between the ball and the train. That is, the point has to move from stationary to moving at the train's speed. That means the ball has to stop for an instant and then start moving in the opposite direction. That stopping and reversing is the point where the ball is in contact with the train and being deformed. The deformation is a heat engine that does work on the ball to change its direction. If you're
  • #1
tommyers
58
0
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
 
Physics news on Phys.org
  • #2
:rofl: No.

If that were to happen, the tennis ball would explode.
 
Last edited:
  • #3
A tennis ball is not a perfectly rigid object, neither is a locomotive, so no.
 
  • #4
I've heard this before... why exactly do you think they train would momentarily stop?
 
  • #5
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.
 
  • #6
Not if it is stopped relative to the front of the locomotive. Then the locomotive never stops moving. :wink:
 
  • #7
Hmm. Of course some energies are absorbed/dispersed. Is the train's speed or momentum decreased, however tiny, at all?
 
  • #8
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 explanation. And also why the tennis ball will explode if it happens. thx!
 
  • #9
Hmmnnnn.

:grumpy:
 
  • #10
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.
 
  • #11
Could someone explain how the conservation of a momentum would apply in this case?
 
  • #12
Delzac said:
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.
 
  • #13
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
 
Last edited:
  • #14
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!
 
  • #15
I think there's a bit of Zeno's so-called "paradox" in here somewhere.
 
  • #16
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...)
 
Last edited:
  • #17
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.
 
  • #18
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 .
 
  • #19
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?
 
Last edited:
  • #20
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.)
 
  • #21
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?
 
  • #22
At the instant the ball is stationary relative to the train, the train is stationary relative to the ball.
 
  • #23
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.
 
  • #24
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.
 
  • #25
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".
 
  • #26
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.
 
  • #27
Farsight said:
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.
 
Last edited:
  • #28
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:

[tex]v = \\frac{A}{\\sqrt{m^2 + \\frac{A^2}{c^2}}}[/tex]

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
 
Last edited:
  • #29
Farsight said:
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? :confused:
 
Last edited:
  • #30
arildno said:
Totally incorrect!
How could you say such a thing? :confused:
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.
 
Last edited:
  • #31
Guillochon said:
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.
 
  • #32
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.
 
  • #33
DaveC426913 said:
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.
 
  • #34
prabhakar_misra said:
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:

prabhakar_misra said:
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?
 
  • #35
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.
 
<h2>1. How can a small tennis ball stop a large train?</h2><p>The size of an object does not necessarily determine its ability to stop another object. The key factor in determining whether a tennis ball can stop a train is the force of impact.</p><h2>2. What is the force of impact of a tennis ball hitting a train?</h2><p>The force of impact depends on several factors such as the speed and weight of the train, the speed and weight of the tennis ball, and the angle at which the ball hits the train. A collision between a tennis ball and a train would likely result in a relatively small force of impact.</p><h2>3. Can a tennis ball cause damage to a train if it hits it?</h2><p>It is highly unlikely that a tennis ball would cause any significant damage to a train, even if it were to hit it at a high speed. Trains are designed to withstand collisions with larger and heavier objects.</p><h2>4. What would happen if a tennis ball hit a train while it was moving?</h2><p>If a tennis ball were to hit a moving train, the ball would likely bounce off or be crushed under the train's weight. The train would continue to move forward with little to no impact on its speed or direction.</p><h2>5. Is it safe to play tennis near train tracks?</h2><p>It is not recommended to play tennis near train tracks as it can be dangerous. Trains can travel at high speeds and may not be able to stop in time if a ball or player were to accidentally get in its way. It is important to always stay a safe distance away from train tracks and follow all safety regulations. </p>

1. How can a small tennis ball stop a large train?

The size of an object does not necessarily determine its ability to stop another object. The key factor in determining whether a tennis ball can stop a train is the force of impact.

2. What is the force of impact of a tennis ball hitting a train?

The force of impact depends on several factors such as the speed and weight of the train, the speed and weight of the tennis ball, and the angle at which the ball hits the train. A collision between a tennis ball and a train would likely result in a relatively small force of impact.

3. Can a tennis ball cause damage to a train if it hits it?

It is highly unlikely that a tennis ball would cause any significant damage to a train, even if it were to hit it at a high speed. Trains are designed to withstand collisions with larger and heavier objects.

4. What would happen if a tennis ball hit a train while it was moving?

If a tennis ball were to hit a moving train, the ball would likely bounce off or be crushed under the train's weight. The train would continue to move forward with little to no impact on its speed or direction.

5. Is it safe to play tennis near train tracks?

It is not recommended to play tennis near train tracks as it can be dangerous. Trains can travel at high speeds and may not be able to stop in time if a ball or player were to accidentally get in its way. It is important to always stay a safe distance away from train tracks and follow all safety regulations.

Similar threads

Replies
3
Views
612
Replies
18
Views
914
Replies
3
Views
2K
  • Mechanics
Replies
7
Views
2K
  • Introductory Physics Homework Help
2
Replies
68
Views
3K
Replies
14
Views
1K
Replies
25
Views
6K
Replies
18
Views
4K
Replies
1
Views
1K
Back
Top