# Friction between pulley and rope

• avast2
In summary: 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.
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!

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avast2 said:
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.

davenn
A.T. said:
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.

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DrStupid said:
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.

avast2 said:
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.

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jrmichler and DrStupid
A.T. said:
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.

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

DrStupid said:
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.

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A.T. said:
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.

A.T.

## 1. What is friction between pulley and rope?

Friction between pulley and rope is the force that resists the motion of the rope as it passes over the pulley. It is caused by the roughness of the pulley and the surface of the rope, and it can reduce the efficiency of the pulley system.

## 2. How does friction affect the performance of a pulley system?

Friction between pulley and rope can cause a decrease in the mechanical advantage of the pulley system, as some of the input force is used to overcome the friction. This can result in a decrease in the overall efficiency and effectiveness of the system.

## 3. What factors can affect the amount of friction between pulley and rope?

The amount of friction between pulley and rope can be affected by several factors, including the roughness of the pulley and rope surfaces, the weight and tension of the rope, and the speed and direction of the pulley's rotation.

## 4. How can friction between pulley and rope be reduced?

To reduce friction between pulley and rope, you can use lubricants to make the surfaces smoother, use pulleys with ball bearings to decrease contact between the rope and pulley, or use a lighter and less tensioned rope.

## 5. What are some real-life applications of friction between pulley and rope?

Friction between pulley and rope is a common phenomenon in various real-life applications, such as in elevators, cranes, and rock climbing equipment. It is also an important factor to consider in the design and efficiency of pulley systems used in industries like construction and transportation.

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