# Pulley ,String and tension

1. Jun 11, 2013

### Tanya Sharma

I am having few doubts regarding pulley,strings and tensions .

The doubts are

1)Can a massless pulley rotate ?

My reasoning - Yes .Just like a massless string can accelerate with zero net force .The same way a massless pulley can rotate with zero net torque.

2)Is tension in a massless string always same when it moves over a pulley .The string may be slipping(not sufficient friction) ,not slipping(sufficient friction,so moving along with the rotating pulley).

3)If the pulley is massless and the string is not massless,what are the tensions on the two sides?

My thoughts-Since the pulley is massless,the tensions at the end points of segment of string over the pulley should be same.But the tension in a string having mass is not same at any two points .

4)How does friction between string and the pulley affect the tension on the two sides of the string?

Kindly help me in clearing the concepts.

Last edited: Jun 11, 2013
2. Jun 11, 2013

### Staff: Mentor

Sure. Realize that a massless pulley is just an idealization, of course. Real pulleys have mass.

When discussing friction in a pulley, usually they mean the friction about the axle not the surface of the pulley where it touches the string. So, if the pulley has friction, the strings must exert unequal tensions to overcome that friction.

Interesting question! Since the segment of the string over the pulley has mass, I'd say that the tensions must be unequal at the endpoints.

For a massless string over a massless pulley, the tension will be the same. (Friction would be irrelevant.)

I'm not sure I've addressed your concerns. If not, try again. Is there a particular sort of problem that you want to solve?

3. Jun 11, 2013

### Tanya Sharma

Hi Doc Al

Thank you very much for the response .But things are still not clear to me.

I understand what happens when the pulley is considered massless .If the pulley has mass,then we need to consider its inertia as well as rotational inertia.

But the role of friction between pulley and string and how it affects the tension in the string is not clear.

Again role of mass of string in affecting the tensions on the two sides of the string is not clear.

I would be grateful if you could elaborate on these issues .Thanks :)

Does that mean,in the problems we encounter the pulley always rotates along with the string ,irrespective of whether the pulley is massless or has mass ?

Here you mean friction at the axle ?

Are tensions unequal due to string having mass or because static friction is present between string and pulley ?

Again,the tensions are same due to massless string or massless pulley ?

No. There isnt specific problem in my mind

4. Jun 12, 2013

### Buckleymanor

Would that not depend on the length of string over the pulley.Same length over each side, same tensions at the end points.

5. Jun 12, 2013

### jbriggs444

Negative.

Possibly you are thinking of an arrangement where the string is hanging over the top of a pulley and is either stationary or moving at a fixed speed. Or, similarly, of an arrangement where a pulley is hanging from a loop of string that is either stationary or moving at a fixed speed.

However, if the pulley is being pulled horizontally then gravity can cause a change in tension over the length of the string where it is adjacent to the pulley. Tension at the top will exceed tension at the bottom.

If the string is accelerating then that acceleration will be associated with a change in tension over the length where it is adjacent to the pulley. Otherwise it would not be accelerating.

6. Jun 15, 2013

### Tanya Sharma

I think I have figured out most of the things.But i am still unclear about one thing . When the pulley has mass,with massless string around,having sufficient friction present(i.e no slipping between string and the pulley),the tension on the two sides is unequal .

How is that the net force on the massless string is zero ?

7. Jun 15, 2013

### jbriggs444

There are four forces on a massless string wrapped around part of a pulley.

1. The tension on the one end.
2. The tension on the other end.
3. The normal force from the pulley applied throughout the arc.
4. The tangential force from the pulley applied throughout the arc.

Number 3 does not contribute to tension.

Number 4 is the interesting one. If the pulley has mass and is accelerating, there must be an unbalanced tangential force between the string and the pulley.

Newton's second law applied to the string says f = ma. But if m is zero, the net force on the string must be zero. If there is unbalanced tangential force contributed by the pulley, that must be balanced by a difference in the tension at the two ends of the string.

If you are a bicycle rider, one way to think about it is to consider the chain leading to your back wheel as if it were a string going to a pulley. The top of the chain is under a great deal of tension. The bottom, not so much.

8. Jun 15, 2013

### Tanya Sharma

Hi jbriggs444

Thanks for the response...Isnt tension in the string throughout the arc ,apart from being at the ends?

9. Jun 15, 2013

### Staff: Mentor

Yes, thanks for that excellent response. (I have been too busy to respond for the last few days.)

The tension will vary along the arc, but any section will have a net force of zero.

10. Jun 15, 2013

### Tanya Sharma

Hi Doc Al
Okay... And the tension remains same when the string is out of the arc .Is that so?

11. Jun 15, 2013

### Staff: Mentor

Right.

12. Jun 15, 2013

### Tanya Sharma

So the difference between a massless string and a string having mass can be stated as -

Massless string -The tension varies along the arc,remains constant out of the arc .

String having mass -The tension varies throughout the length i.e varies along the arc and also varies out of the arc .

Is that so?

13. Jun 15, 2013

### Staff: Mentor

Yes, for a massless string over a massive pulley.

Yes. I think you've got it.

14. Jun 15, 2013

### Tanya Sharma

Thanks Doc Al

Now considering the massive pulley,the net tangential force on the pulley is the frictional force which will be equal to the difference in tensions at the two ends of the arc .

Am I right ?

15. Jun 15, 2013

### Staff: Mentor

Yes, that makes sense to me.

16. Jun 15, 2013

### Buckleymanor

No mention of movement and no mention of orientation or speed.
So I reckon that it is too much for any one to presume it's just a pulley with a stationary peice of string hanging over it with both ends dangling down towards the ground with both ends the same length.
Which I reckon you understood first time round but did not like it's implication or lack of for some reason.

17. Jun 16, 2013

### Tanya Sharma

Thanks jbriggs444 and Doc Al

18. Jun 17, 2013

### Tanya Sharma

I didnt quite understand it.

If the pulley is massless ,it requires zero torque to rotate it.This means the tensions at the two ends of the string over the arc are same .But,if there is friction present between string and the pulley,in order to overcome that friction,the tensions need to be unequal.

How would tension be the same and friction becoming irrelevant ?

19. Jun 17, 2013

### Staff: Mentor

How much friction is required to turn a massless pulley?

20. Jun 17, 2013

### Tanya Sharma

To turn a massless pulley,zero torque is required.This in turn means,no friction is required.The friction required is equal to the difference in the tensions on the end points of the arc.Hence tension on the two sides is same.

Am I correct ?

If I am correct , does that mean even though sufficient static friction is present ,it doesn't come into picture due to pulley being massless ?

Strangely,I am finding it difficult to comprehend the situation.

Last edited: Jun 17, 2013
21. Jun 17, 2013

### Staff: Mentor

Right.

The static friction force is zero. The surfaces may support friction, if needed, but no friction force is needed.

22. Jun 17, 2013

### Tanya Sharma

Thanks Doc Al

Even though I have done quite a few problems with pulleys ,I am managing to confuse myself very nicely :shy: .

Why dont we take static friction into account while drawing FBD of a massive pulley in intro physics problems ?

It doesnt do any work,but why dont we consider it while writing force equations?

23. Jun 17, 2013

### Staff: Mentor

Since the difference in string tension will equal the required friction, that's all you need to worry about.

24. Jun 17, 2013

### Tanya Sharma

Thanks Doc...You are beautifully clearing my doubts :)

If the string has mass ,pulley is massless and frictionless,then the tensions at the end points of the arc are unequal.How is mass of the string creating a difference in the tensions,even though the pulley is massless and frictionless ?

25. Jun 17, 2013

### Staff: Mentor

The string segments have mass and thus require a net force to accelerate.