Friction between pulley and rope

[avast2]

I have a question about friction between pulley and rope?
Does anyone know how to calculate friction between pulley and rope
I enclosed an example picture
Thank you!

 

[A.T.]

I have a question about friction between pulley and rope?
Does anyone know how to calculate friction between pulley and rope
I enclosed an example picture
Thank you!

If the tensions are the same on both sides, the net friction is zero.

 

[DrStupid]

If the tensions are the same on both sides, the net friction is zero.

You may assume zero friction in theory but in reality there is at least static friction. With equal tension all around the pulley I would expect it to be

$F_f \le \frac{\pi }{2} \cdot \mu \cdot F_0$

where $F_0$ is the total force acting on the pulley.

 

[A.T.]

You may assume zero friction in theory but in reality there is at least static friction. With equal tension all around the pulley I would expect it to be

$F_f \le \frac{\pi }{2} \cdot \mu \cdot F_0$

where $F_0$ is the total force acting on the pulley.

I was assuming a massless rope.

 

[Lnewqban]

I have a question about friction between pulley and rope?
Does anyone know how to calculate friction between pulley and rope

For a practical case, this may help you:
https://en.m.wikipedia.org/wiki/Capstan_equation

If the rope fits too tight inside the pulley's groove, friction should be greater than calculated by above equation due to wedge effect.

 

[DrStupid]

I was assuming a massless rope.

The mass of the rope is not the problem. It just changes the total force and can be neglected in the situation discussed. I started the derivation for the case that the tension can not assumed to be constant and already realized that the force increases exponentially. Thaks @Lnewqban's link to the Capstan equation I don't need to finish my calculation.

 

[tech99]

From school boy memories, I believe the frictional resistance for a rope wrapped round an object is the tension multiplied by e^(mu theta).

 

[A.T.]

I started the derivation for the case that the tension can not assumed to be constant and already realized that the force increases exponentially. Thaks @Lnewqban's link to the Capstan equation I don't need to finish my calculation.

I was referring to the situation as given in the OP's diagram, with equal forces on both rope ends. I agree that this is not realistic, but this assumption implies zero net effect of friction.

 

[DrStupid]

I was referring to the situation as given in the OP's diagram, with equal forces on both rope ends. I agree that this is not realistic, but this assumption implies zero net effect of friction.

Yes, the diagram shows equal tension on both sides and therefore no friction that needs to be considered. But that is just an example and it doesn't make much sense to limit the question to this special case. I referred to almost equal tension on both sides (because it is easy to calculate). The Capstan equation should always work.