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

[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.

 

[jbriggs444]

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.

 

[sophiecentaur]

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)

 

[Saw]

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?

 

[sophiecentaur]

Just to add a bit of oil to this somewhat daft fire. No one seems to have considered the fact that a stretchy string with a mass on it will have a natural oscillation frequency and, if this frequency is related to the rotational frequency, there will be interaction between the two modes. The ball could follow many exotic paths. In fact, it's only if the modulus of the string is very high that there will be none. Someone (apart from the OP) tell me where this could go if the regular situation of a non-stretch string is not explained fully.

 

[Rolacycle]

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.

It has to be secure on both ends otherwise load stay on ground. If there isn’t tension across pulley then there’s no point of the pulley. Tension happens when the force is applied to both ends.

 

[sophiecentaur]

I intuitively can't understand

Those four words sum up the OP's problem. No one can rely on intuition to 'understand' anything in this life. Politicians and snake oil salesmen work on that, every day. He has to leave that behind and do some learning - or thinking through what he's been told on this thread. That's better 'tuition' than 'in-tuition'.

 

[jbriggs444]

To me, constraint forces did not make a lot of intuitive sense until I put an intuitive mental model under them.

By themselves, constraint forces are not about causation. They are about correlation. If you have such and such an acceleration, you must have this much force. If you have such and such a force, you must have this much acceleration. Shut up and calculate.

The mental model that I personally put under a constraint force (e.g an object on the end of a rope) is that it is all about a stable equilibrium. Instead of an ideal rope with infinite stiffness, give the rope just a tiny bit of springiness. Now, if the object on the rope strays a little bit beyond the rope limit, the tension force gets higher. The result is that the object accelerates inward. It moves back to the rope limit. Similarly, if the object on the rope strays a little bit inside the rope limit, the tension force gets lower. Left to its own device, the object coasts back out to the rope limit.

By itself, this just means that there is an equilibrium point. But not necessarily a stable one. From experience, we know that things do not bounce back as fast as they left. There is always a little friction. Or hysteresis. Or whatever you want to call it. The equilibrium is stable. For a hemp rope (as opposed to a rubber band), the equilibrium will be approached quite rapidly.

This intuitive model does not need to be very quantitative. Or even very correct. It just has to be good enough to keep the intuition happy while one shuts up and calculates.You might find that the concept of Operational Amplifiers is relevant. It's the same kind of mechanism. You have an underlying stable negative feedback loop that does not have to be very precise in order to yield a result which precisely follows a mathematical model.

 

[Frigus]

By themselves, constraint forces are not about causation. They are about correlation. If you have such and such an acceleration, you must have this much force. If you have such and such a force, you must have this much acceleration. Shut up and calculate.

I personally think that this is the key idea of Newtonian mechanics as there can be gazillions of situations in which some acceleration is there so if we keep finding how that mechanism happens for which we are solving then it can be quite painful and also will be out of context(I don't mean course here). For me acceleration is like smoke so if there is smoke then there should be fire somewhere which is force and we can find where the fire is just like what is the magnitude of force rather than try to understand about chemistry of fire.

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)

I was not talking about some finite distance but the distance it covers during the moments when rope is unstreched and streched.so it is obvious that ball's velocity will be change if their is some force which will be their when rope will be stretched.

 

[jbriggs444]

I was not talking about some finite distance but the distance it covers during the moments when rope is unstreched and streched.so it is obvious that ball's velocity will be change if their is some force which will be their when rope will be stretched.

Except for the first few moments while the system equilibriates, there is no dichotomy. The rope is not over-stretched or under-stretched. It is stretched just right.

We do not usually care about the initial bouncing about and do not have enough information to calculate it anyway. So we settle for figuring out the equilibrium force after things have settled down.

Once again, switching to the electronics arena for an analogy. Switch bounce:

 

[sophiecentaur]

Instead of an ideal rope with infinite stiffness, give the rope just a tiny bit of springiness.

In School, we 'did' the Virtual Work method for solving certain statics problems and allowing an infinitesimal stretch gave you an answer. That was along the same lines.

Except for the first few moments while the system equilibriates, there is no dichotomy.

The transition process in all sorts of physical problems is the worst possible thing to consider at first - but that often tends to be the intuitive way that people look at things. There is a feeling that the 'steady state' solution is somehow not valid, however well it works. Of course, if you don't consider the transition at all, you arrive at situations where Energy has paradoxically disappeared from the system (e.g. connecting Capacitors together ) but that loss can be dealt with later; once the steady state has been understood.