Kinematics

A ball bearing is flying through space (vacuum and no overall gravitational field). It heads towards a doughnut, through it's centre and out the other side. Draw the graph of speed versus time.

So first of all according to newtons law, it will continue to move with constant speed until just before it enters the doughnut (it will also continue at a lowers constant speed after leaving). Now I want to know if the acceleration is constant as i showed in my graph or not? and is my graph correct like this?
Why does it have a slower speed after leaving?
Original post by Stonebridge
Why does it have a slower speed after leaving?

Wouldn't it decelerate inside the doughnut?

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Original post by Stonebridge
Why does it have a slower speed after leaving?

Gonna add another question. is it because of the donut causing a small gravitational force on the ball bearing:?
Original post by Daniel Atieh
Wouldn't it decelerate inside the doughnut?

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Yes, but if so why can it not also accelerate?
Original post by AwesomeSauce#1
Gonna add another question. is it because of the donut causing a small gravitational force on the ball bearing:?

As there is no background provided with this question one can only guess that this is what you have to take into account.
Original post by Stonebridge
Yes, but if so why can it not also accelerate?

Aha right. So it will accelerate due to the gravitational attraction between them?

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Original post by Daniel Atieh
Aha right. So it will accelerate due to the gravitational attraction between them?

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Assuming this is what the question is expecting (where has it come from?) then the ball bearing is attracted to the doughnut as it approaches and also as it moves away. So how do you think this force will affect its speed
A. As it approaches
B. as it moves away?
Original post by Stonebridge
Assuming this is what the question is expecting (where has it come from?) then the ball bearing is attracted to the doughnut as it approaches and also as it moves away. So how do you think this force will affect its speed
A. As it approaches
B. as it moves away?

As it approaches, it will accelerate towards it increasing its velocity and the opposite happens when it leaves. So speed stays the same then?

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Original post by Daniel Atieh
As it approaches, it will accelerate towards it increasing its velocity and the opposite happens when it leaves. So speed stays the same then?

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Correct.
But what does the graph look like, then?
Original post by Stonebridge
Correct.
But what does the graph look like, then?

---/\--- right?

And it's very clear to me in terms of gravitational attraction, but i am still confused about why the donut won't cause an oppose force to motion just like air resistance? I dunno how to exactly phrase my question tho :/

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Original post by Stonebridge
Correct.
But what does the graph look like, then?

Let me just try one more time.

So I did understand the the gravitational attraction between them will cause an increase in speed as it approaches and the opposite as it leaves so the speed will be the same as before entering. And the graph might look like this:

Now till this part it's okay with me.

Now if I want to think about it further.
As the all approaches the donut particles, why there won't be any force that oppose the motion like friction force when a car moves on a road with a certain "mu" value.
I don't mean the force is due to friction here but just shooting an example.
This is what i mean
^ The bold arrows shows the gravitational attraction and the other dotted arrow is the force when they hit (?)

Sorry for confusing it, but I hope you'll be able to clarify my problem.
Original post by Daniel Atieh
Let me just try one more time.

So I did understand the the gravitational attraction between them will cause an increase in speed as it approaches and the opposite as it leaves so the speed will be the same as before entering. And the graph might look like this:

Now till this part it's okay with me.

Now if I want to think about it further.
As the all approaches the donut particles, why there won't be any force that oppose the motion like friction force when a car moves on a road with a certain "mu" value.
I don't mean the force is due to friction here but just shooting an example.
This is what i mean
^ The bold arrows shows the gravitational attraction and the other dotted arrow is the force when they hit (?)

Sorry for confusing it, but I hope you'll be able to clarify my problem.

There is only one force here - gravitation. This happens in space so no air resistance. No viscosity. There is no physical contact between the ball and the ring. I have to assume the question is talking about a ring doughnut and the ball goes through it without touching. The question is poorly written as it gives no background, or this was not the complete question. Or it is open ended and not an exam style question. If you post questions like this you will not get a straight answer in most cases.

The whole process is symmetrical, the ball could have gone from left to right or right to left. The attractive force on approach varies in an identical way to the force as the ball moves away.The accelerating force at any point on the left of the doughnut is exactly equal to the decelerating force at the equivalent point on the right.
The graph is symmetrical.

In reality, the gravitational force of a ball bearing on a doughnut is incredibly small, so I can't imagine how the writer of this question is expecting anyone to take it that seriously, because you would never be able to measure the change in the velocity as it goes through. However, taking the spirit of the question to be that it wants you to talk about this incredibly small change in velocity, then your red line needs to be
a) symmetrical, not lop sided
b) smooth and without a sharp discontinuity, rising, levelling out, then falling back to the original value.

You didn't say where you found this question.
Original post by Stonebridge
There is only one force here - gravitation. This happens in space so no air resistance. No viscosity. There is no physical contact between the ball and the ring. I have to assume the question is talking about a ring doughnut and the ball goes through it without touching. The question is poorly written as it gives no background, or this was not the complete question. Or it is open ended and not an exam style question. If you post questions like this you will not get a straight answer in most cases.

The whole process is symmetrical, the ball could have gone from left to right or right to left. The attractive force on approach varies in an identical way to the force as the ball moves away.The accelerating force at any point on the left of the doughnut is exactly equal to the decelerating force at the equivalent point on the right.
The graph is symmetrical.

In reality, the gravitational force of a ball bearing on a doughnut is incredibly small, so I can't imagine how the writer of this question is expecting anyone to take it that seriously, because you would never be able to measure the change in the velocity as it goes through. However, taking the spirit of the question to be that it wants you to talk about this incredibly small change in velocity, then your red line needs to be
a) symmetrical, not lop sided
b) smooth and without a sharp discontinuity, rising, levelling out, then falling back to the original value.

You didn't say where you found this question.

Wow! That's beyond brilliant! Thanks a ton
You made everything clear.

oh sorry, I didn't know that you asked me.
I found it here: https://sites.google.com/site/oxbridgeinterviewquestions/why-is-water-so-important-to-life
Check the first question. I think this was asked in an interview or something :/
Original post by Daniel Atieh
Wow! That's beyond brilliant! Thanks a ton
You made everything clear.

oh sorry, I didn't know that you asked me.
I found it here: https://sites.google.com/site/oxbridgeinterviewquestions/why-is-water-so-important-to-life
Check the first question. I think this was asked in an interview or something :/

Yes, well interview questions require a different approach. They are usually starters for some sort of discussion and/or designed to see how you think. The last one is a good example.

"What happens if I drop an ant?"

If you asked this on here with no background you would get a number of different replies depending on how the reader has interpreted it. Your reply to this is more about the way you interact with the interviewer, and demonstrate your thinking process, than coming up with the "correct" answer.
Original post by Stonebridge
Yes, well interview questions require a different approach. They are usually starters for some sort of discussion and/or designed to see how you think. The last one is a good example.

"What happens if I drop an ant?"

If you asked this on here with no background you would get a number of different replies depending on how the reader has interpreted it. Your reply to this is more about the way you interact with the interviewer, and demonstrate your thinking process, than coming up with the "correct" answer.

Yeah, I utterly agree with you.
Original post by Stonebridge
There is only one force here - gravitation. This happens in space so no air resistance. No viscosity. There is no physical contact between the ball and the ring. I have to assume the question is talking about a ring doughnut and the ball goes through it without touching. The question is poorly written as it gives no background, or this was not the complete question. Or it is open ended and not an exam style question. If you post questions like this you will not get a straight answer in most cases.

The whole process is symmetrical, the ball could have gone from left to right or right to left. The attractive force on approach varies in an identical way to the force as the ball moves away.The accelerating force at any point on the left of the doughnut is exactly equal to the decelerating force at the equivalent point on the right.
The graph is symmetrical.

In reality, the gravitational force of a ball bearing on a doughnut is incredibly small, so I can't imagine how the writer of this question is expecting anyone to take it that seriously, because you would never be able to measure the change in the velocity as it goes through. However, taking the spirit of the question to be that it wants you to talk about this incredibly small change in velocity, then your red line needs to be
a) symmetrical, not lop sided
b) smooth and without a sharp discontinuity, rising, levelling out, then falling back to the original value.

You didn't say where you found this question.

Lol this was 9 years ago, But was wondering that surely if the ball has an initial velocity with respect to the donut - the time that the ball bearing would experience a force would be less as it leaves the donut because it was has accelerated untill it reached the centre of the donut then it decelerates once it has gone past the donut. Would there not suggest a disparty in the momentum lost as it leaves vs the momentum gained travelling in? If we take this we would surely find that the velocity of the ball bearing should be greater at very far distances

This would need to be in a system in which the donut has gained velocity - then it had previously, since if the ball bearning has gained velocity, the donut must have (in the negative direction) in order for momentum to be conserved.

An arguement to be constructed against this is, there would be an increase in energy of the system as both the ball bearing and the donut has increased in speed, and so increase in kinetic energy. But one could argue that the masses of the ball bearning and the donut decreases to account for the energy.

All this said, could you consider the interaction of the donut and the ball bearing as some sort of elastic momentum collision, where the donut imparts a force on the donut and so the momentum of the donut increases and the momentum of the ball bearing decreases. This is system could be consistent with both the conservation of energy and momentum. And so why would this model of whats going on be necessarily wrong.

Finally, a reason to potential support the first model as you have described could be that the time the force IS in fact experienced over as it travels in and out of the donut being equal because it is in the gravitational field of the donut and so the time it experiences relative to another person would be "Slower / faster" depending upon its motion through spacetime determined by the shape and mass of the donut. Supporting the idea that the momentum gained before reaching the centre of the donut would be equibalent to the momentum lost leaving the centre of the donut.

Just wondering if anyone would like to weigh in on what I have said. This is not really an answer per se, but Just considering other models ( gave two others) that may be consistent with at least my current knowledge of physics. It's a very interesting question!
(edited 4 months ago)
Original post by abeatboxer17
Lol this was 9 years ago, But was wondering that surely if the ball has an initial velocity with respect to the donut - the time that the ball bearing would experience a force would be less as it leaves the donut because it was has accelerated untill it reached the centre of the donut then it decelerates once it has gone past the donut. Would there not suggest a disparty in the momentum lost as it leaves vs the momentum gained travelling in? If we take this we would surely find that the velocity of the ball bearing should be greater at very far distances

This would need to be in a system in which the donut has gained velocity - then it had previously, since if the ball bearning has gained velocity, the donut must have (in the negative direction) in order for momentum to be conserved.

An arguement to be constructed against this is, there would be an increase in energy of the system as both the ball bearing and the donut has increased in speed, and so increase in kinetic energy. But one could argue that the masses of the ball bearning and the donut decreases to account for the energy.

All this said, could you consider the interaction of the donut and the ball bearing as some sort of elastic momentum collision, where the donut imparts a force on the donut and so the momentum of the donut increases and the momentum of the ball bearing decreases. This is system could be consistent with both the conservation of energy and momentum. And so why would this model of whats going on be necessarily wrong.

Finally, a reason to potential support the first model as you have described could be that the time the force IS in fact experienced over as it travels in and out of the donut being equal because it is in the gravitational field of the donut and so the time it experiences relative to another person would be "Slower / faster" depending upon its motion through spacetime determined by the shape and mass of the donut. Supporting the idea that the momentum gained before reaching the centre of the donut would be equibalent to the momentum lost leaving the centre of the donut.

Just wondering if anyone would like to weigh in on what I have said. This is not really an answer per se, but Just considering other models ( gave two others) that may be consistent with at least my current knowledge of physics. It's a very interesting question!

As for your first model, I'm not sure what your reasoning is but the increase in kinetic energy isn't plausible if we take the conservation of KE + GPE and let's say the ball bearing is moving at speed v and donut is stationary initially, both separated by an arbitrarily large (infinite) distance, so we can say EPE is 0 initially, so total energy of the system is equal to initial KE of ball. If you want to think about the work done on the ball, we can say that the integral of force wrt distance =0 as the ball moves from -infinity, meets donut at 0 and travels towards +infinity, and we can assume that the force on ball is symmetrical about the origin (where they meet). Because the integral =0, we can say the work done to accelerate the ball = work done to decelerate the ball, so final velocity must be v. Equally, we could consider the motion of the donut. If the ball is travelling left to right, the donut will initially accelerate to the left until they meet, then accelerate to the right. Because the separation of the particles goes from -infinity to 0 to + infinity, I think we can make the same integral argument as before and say that the final KE of the donut is 0.

I also like a time-symmetry argument but not really sure how to explain it or justify. Try to imagine a video of the motion happening, ball travelling from infinity, meeting etc and then play it backwards in your head. There's nothing to distinguish the 2 videos from each other, except the direction the ball is travelling in, but that is irrelevant, so I think we can make the argument that initial conditions = final conditions.

As for your elastic collision argument, yes the donut exerts a force on the ball and vice versa but the force varies w time and in order to calculate the impulse (change in momentum) we would need to integrate force wrt time and maybe some DE's to find a function for force vs time, which would be pretty disgusting I'd imagine, but probably doable for someone good enough at this stuff.

And with the relativity argument, I'd imagine you're right in some way but its too late for me to think about relativity rn!

Also how old are you because you sound pretty interested in physics?

edit: I have a feeling momentum gets a bit difficult to talk about with varying forces, unless you have some pretty simple F-t functions. I think doing DE's with a, v and x wrt time is probably more doable, but just speculating! Starting DE's in January half-term so we'll see!
(edited 4 months ago)