# What causes tension in a rope moving in a vertical circle?

Frigus
I don't get how ball moves in a vertical circle,we say tension provides centripetal force to the ball, i have posted a image in this post and in I which I have shown that their is a downward force mg and upward velocity,in this what will cause tension in the rope...from non inertial frame it is understandable that it is centrifugal force but I can't understand it from inertial frame of reference.

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• vertical circle02-26-11.20.17.jpg
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...upward velocity,in this what will cause tension in the rope...
The velocity is changing, which requires a force.

Frigus
The velocity is changing, which requires a force.
Okay,i understand that force is smoke of acceleration but I intuitively can't understand what has caused this tension in rope like if their is a person who is whirling it I understand that person is providing the force similarly if car is turning over a curved road person who is driving it will rotate tyres to generate friction as to get centripetal accelaration.

Homework Helper
Gold Member
With no rope, what would happen?
The ball should be slowing down while fighting gravity in its way up, but in order to deviate from a straight trajectory, something must make it do so.

Mentor
I intuitively can't understand what has caused this tension in rope
The rope is under tension because it is being stretched by the ball and whatever is holding the other end of the rope. If you model it closely, you can use Hooke's law. The rope has a resting length ##L##, at which length the tension is 0. If you stretch the rope a little ##L+\delta## then there is some tension in the rope related to how much you stretched it ##\delta##. If you stretch it a little more then the tension is a little higher.

Typically we consider the rope to be ideal meaning that ##\delta## is so small that we can ignore it and consider that its length is ##L##. That is a reasonable approximation for typical rope, but it might fail for bungee cords.

• gmax137 and Frigus
zoki85
I don't get how ball moves in a vertical circle,we say tension provides centripetal force to the ball, i have posted a image in this post and in I which I have shown that their is a downward force mg and upward velocity,in this what will cause tension in the rope...from non inertial frame it is understandable that it is centrifugal force but I can't understand it from inertial frame of reference.
Do you understand how it moves in a horizontal circle and without gravity?

Frigus
Do you understand how it moves in a horizontal circle and without gravity?
I think I should have posted for horizontal circle because it is simpler than this and also the problem for which I am confused is present in both.

Frigus
The rope is under tension because it is being stretched by the ball and whatever is holding the other end of the rope. If you model it closely, you can use Hooke's law. The rope has a resting length ##L##, at which length the tension is 0. If you stretch the rope a little ##L+\delta## then there is some tension in the rope related to how much you stretched it ##\delta##. If you stretch it a little more then the tension is a little higher.

Typically we consider the rope to be ideal meaning that ##\delta## is so small that we can ignore it and consider that its length is ##L##. That is a reasonable approximation for typical rope, but it might fail for bungee cords.
I understand that the streching of the rope is providing the centripetal force but the thing which I am unable to get is that how does the ball streches the rope.if we take example of horizontal circle how does the ball streches the rope and get centripetal acceleration like the cases I have mentioned in post no.3.
I am too much frustrated with the situations like loop da loop where their is present normal force because their can be made many situations like this and I have to think for each and every case that how does centripetal force is generated...it took so much time and sometimes I feel like I am wasting my time by doing this process,it would be like blessing if I can know how to think for situations like this.

Mentor
the thing which I am unable to get is that how does the ball streches the rope
Suppose you have a very stretchy rope. In fact, let's take the limit that the rope can stretch to any length with no force. Now, one end of the rope is fixed and the other end is attached to a moving ball which is initially moving at a right angle to the line from the fixed end to the ball.

The ball experiences no force, so what is its path?

What happens to the length of the rope?

• Frigus
Mentor
I understand that the streching of the rope is providing the centripetal force but the thing which I am unable to get is that how does the ball streches the rope.if we take example of horizontal circle how does the ball streches the rope and get centripetal acceleration like the cases I have mentioned in post no.3.
Let's try an even easier example: You have a ball hanging (motionless) from a rope. What are the forces applied to each end of the rope and why?

• 256bits, Frigus and Dale
Homework Helper
Gold Member
... ,it would be like blessing if I can know how to think for situations like this.
Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

• Frigus
Frigus
Suppose you have a very stretchy rope. In fact, let's take the limit that the rope can stretch to any length with no force. Now, one end of the rope is fixed and the other end is attached to a moving ball which is initially moving at a right angle to the line from the fixed end to the ball.

The ball experiences no force, so what is its path?

What happens to the length of the rope?
Thanks a lot,
If ball is going in direction perpendicular to the direction then after covering very small distance the rope will be stretched because the ball was trying to move perpendicularly to the rope and not in the circle so the rope will stretch and pull the ball approximately perpendicular to the direction of motion.

• Klystron, russ_watters, vanhees71 and 2 others
Mentor
Excellent. That is what I had hoped!

• Frigus
Frigus
Excellent. That is what I had hoped!
Thanks again!😊

Gold Member
I intuitively can't understand what has caused this tension in rope like if their is a person who is whirling it I understand that person is providing the force
Look at this way. Someone got it whirling, but afterwards, it should keep whirling in a circle. It would even be possible to reduce friction to the point that it's negligible, say if you had a ball bearing configuration at the center of the rotation, with the rope tied to it. It'll keep spinning, and tension in the rope will will also continue. Yes, the direction keeps changing, but the magnitude of the tension in the rope stays constant.

• Frigus and Lnewqban
Gold Member
In the original question, where the rope moves in a vertical plane, are you having a constant angular velocity or allowing the rope to slow down as it climbs. To keep it at a constant speed, you would need to drive it (and brake it) on the way round and it would have to be rigid. Too hard for starters!

• Frigus
Frigus
In the original question, where the rope moves in a vertical plane, are you having a constant angular velocity or allowing the rope to slow down as it climbs.
In this question the ball is tied to rope at one end and another end is fixed and in whole scenario only two forces are acting on the ball that are tension and the gravitational force,hence the rope is slowing down as it climbs.
Can you please clear my another doubt.
I understand that the rope will stretch when the ball will go in straight will and I also have posted photo of this situation so one can clearly understand what scenario is in my mind,but now the thing which I can't understand is that how does ball streches the rope as ball is going with constant velocity but some force is required to stretch the rope
And also I tried to magnify the streching of rope so I can clearly show what is in my mind.

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Homework Helper
is that how does ball streches the rope as ball is going with constant velocity but some force is required to stretch the rope
If I may try to state your conundrum.

"If the ball is going with constant velocity, it cannot be stretching the rope because it cannot be exerting any force on the rope."

The logic is impeccable. The above is a true statement. But let us proceed with the chain of logical inference.

"But the rope is tied to the ball. The ball cannot go straight at constant velocity without dragging the rope with it. If it did that, it would have to stretch the rope".

The conclusion we can draw from this is simple: "The ball does not go straight".

If one opens one's eyes and looks at the ball on the rope, this conclusion is manifestly true. The ball does not go straight.

• Frigus
Mentor
I can't understand is that how does ball streches the rope as ball is going with constant velocity
The ball is not going with constant velocity. It is going with constant speed.

• sophiecentaur
Frigus
The ball is not going with constant velocity. It is going with constant speed.
I was trying to explain the situation before it streches the rope so it was instantaneously at constant velocity.

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Homework Helper
I was trying to explain the situation before it streches the rope so it was instantaneously at rest.
So you have a stationary ball, with one end of a rope tied to it and the other end of the rope tied to a pivot. Where is the motion?

You do not get to cancel motion by muttering the words "instantaneously at rest".

Frigus
So you have a stationary ball, with one end of a rope tied to it and the other end of the rope tied to a pivot. Where is the motion?

You do not get to cancel motion by muttering the words "instantaneously at rest".
Sorry, I wrote it mistakenly but now I have corrected it.

Homework Helper
Sorry, I wrote it mistakenly but now I have corrected it.
I was trying to explain the situation before it streches the rope so it was instantaneously at constant velocity.
Edit: It occurs to me that the concept of "constant velocity" at an "instant" is meaningless. What does it mean for something to be constant at an instant? How could it be otherwise?

OK. So we have this ball moving at constant velocity. It has a rope tied to it. And the rope is tied to a pivot.

What happens next? Does the ball drag the rope? Or does the knot come untied?

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• Frigus
Mentor
I was trying to explain the situation before it streches the rope so it was instantaneously at constant velocity.
Then I am not sure what your concern is. We already covered that and you seemed to already understand. Can you be much more detailed about your remaining concern?

• Frigus
Gold Member
I was trying to explain the situation before it streches the rope so it was instantaneously at constant velocity.
At which point in the cycle did you decide that the ball's velocity is constant? It's 1. Moving and 2. Not in a straight line.
Where is the velocity constant, except before the experiment has started and it's laying on the ground?
This thread needs to be re-started, with a properly defined model. So far, the OP's ideas are as stretchy as the rope we're using. I think the answers he is getting are not really sinking in.

Frigus
At which point in the cycle did you decide that the ball's velocity is constant? It's 1. Moving and 2. Not in a straight line.
Where is the velocity constant, except before the experiment has started and it's laying on the ground?
This thread needs to be re-started, with a properly defined model. So far, the OP's ideas are as stretchy as the rope we're using. I think the answers he is getting are not really sinking in.
Now I am trying to explain the whole ramayana of this situation going on in my mind.
My first question was that how does rope provides centripetal acceleration and then after posting this question I came to know that the centripetal acceleration is provided by rope streching and then the second question which arose in mind was how does the ball streches the rope and then I tried to anwser this question and the answer I got is "suppose at a moment let's say at middle of circle(photo posted in post #1)it's velocity's direction is upward and then ball will move tiny bit in upward direction due to which rope will stretch(as I tried to show in post #17) and this streching will provide centripetal acceleration" and my last question was that how does ball streches the rope with constant velocity as force is required to stretch the rope.
Please tell me where I am wrong and also tell me where clarity is needed in this post.

Mentor
Please tell me where I am wrong and also tell me where clarity is needed in this post.
Ok, that is a good summary of the thread, but it seems that all of your questions were answered already. So what specifically remains and what is your reasoning that leaves you confused?

• Frigus
Frigus
Ok, that is a good summary of the thread, but it seems that all of your questions were answered already. So what specifically remains and what is your reasoning that leaves you confused?
Can you please tell whether it is written wrong or right in the post #26.

Mentor
Can you please tell whether it is written wrong or right in the post #26.
Post 26 is fine but gives me no understanding of what is causing your remaining confusion. Everything you mention there has already been answered.

Gold Member
the centripetal acceleration is provided by rope streching
The Force is provided however 'stiff' the rope is. It doesn't have to "stretch" more than a vanishingly small amount. But this is the same for all idealised mechanical structures and is really not relevant except on an almost philosophical level, imo.
We normally just use the word Tension.

• Frigus
Frigus
Post 26 is fine but gives me no understanding of what is causing your remaining confusion. Everything you mention there has already been answered.
The only part I can't understand is third question that is how does ball streches the rope with constant velocity.it was answered by jbriggs but the thing which i want to know is that does this concept of pulling with constant velocity has a specific name so I can read about it.

Homework Helper
The only part I can't understand is third question that is how does ball streches the rope with constant velocity.it was answered by jbriggs but the thing which i want to know is that does this concept of pulling with constant velocity has a specific name so I can read about it.
There is no concept of pulling with constant velocity.

Newton's laws apply. From the first law: If you have constant velocity, you are subject to zero net force. From the third law: If the net force on you from everything else is zero, the net force on everything else from you is zero. Conclusion: If you have constant velocity, you are not pulling anything.

However...

Suppose that you have complete details about the ball and rope's current configuration. You can use this to determine what stresses exist within the rope. That's Hooke's law.

If you know what stresses exist within the rope, then you know what net force exists on the ball and on every bit of rope.

If you also know the mass of the ball and the mass distribution of the rope than you know what accelerations exist everywhere.

If you know the current velocity of the ball and rope and (from above) the accelerations of all of the bits then you can predict how the rope will be positioned a moment from now.

That gives you information on the rope's configuration a moment from now.

You can repeat the process to predict how the rope will behave over time. This is the essence of doing physics with differential equations.

• Frigus
Gold Member
The only part I can't understand is third question that is how does ball streches the rope with constant velocity.it was answered by jbriggs but the thing which i want to know is that does this concept of pulling with constant velocity has a specific name so I can read about it.
The situation when you are "pulling with constant velocity" is when you are pulling in a straight line at a velocity at which the resistive forces balance the driving force. This is often referred to as Terminal Velocity. But this has no place in Circular Motion, where velocity is changing all the time.

This has already been stated in the thread. Have you just ignored it? Are you aware of the difference b between velocity and speed? (also stated earlier)

• Frigus
Gold Member
force is required to stretch the rope.

Yes, no doubt. The string exerts tension force on the ball (preventing that it flies away) and by Newton's third law the ball exerts tension force (same magnitude, opposite direction) on the string.

how does ball ... with constant velocity

Well, as you were told, the ball has not constant velocity because it is constantly changing direction due to the force exerted by the rope. But note that, in any case, this relates to what the ball *suffers*. To understand why the rope is stretched, you have to look at what the rope itself suffers: as I said, it suffers tension force exerted by the ball...

A different thing is: for this to work, can the ball have constant *speed* (modulus always the same)? Yes. In a vertical circle, speed would change, but in a horizontal circle where a ball held to a pivot by a rope is rolling on the ground, its speed could be constant, but it would still be suffering tension force exerted by the string (that is why it would be changing direction) and exerting a force (that is why, if the rope did not have enough cohesion, it could end up being torn apart).

Still any doubt?

• Frigus and sophiecentaur