Friction in Pulley System: Calculations?

[boredaxel]

If a string around a pulley is pulled without slipping, I am wondering if there is any frictional force acting on the string by the pulley. If there is, will it appear in calculations? Thanks in advance

 

[Doc Al]

If a string around a pulley is pulled without slipping, I am wondering if there is any frictional force acting on the string by the pulley.

Sure, otherwise the string couldn't turn the pulley.

If there is, will it appear in calculations?

Not usually. (It's static friction and does no work.)

 

[boredaxel]

but wouldn't the static friction appear in torque calculation? Also what if the string is assumed to be massless, doesn't that implies no friction and so the pulley shouldn't be able to turn?

 

[Doc Al]

but wouldn't the static friction appear in torque calculation?

No, it just transmits the string tension to the pulley.

Also what if the string is assumed to be massless, doesn't that implies no friction and so the pulley shouldn't be able to turn?

No.

Typical assumptions (in intro courses) are that strings are massless (and thus have the same tension throughout) and that pulleys are frictionless (not between string and pulley, but about the axle of the pulley).

 

[boredaxel]

No, it just transmits the string tension to the pulley.

Care to explain this? I can't really visualize it. Thanks

 

[russ_watters]

The pulley moves with the string because the pulley is on bearings and free to rotate. Thus it doesn't restrict the motion of the string except by its own inertia when accelerating. It is the static friction between the string and the pulley that makes the pulley rotate.

 

[tiny-tim]

but wouldn't the static friction appear in torque calculation?

Hi boredaxel!

If the pulley has mass, and if you need to calculate the energy or angular momentum of the pulley, then yes, the friction is an external force on the pulley, and will provide a torque to the pulley.

But exam questions usually (though not always ) say that pulleys are massless.

Also what if the string is assumed to be massless, doesn't that implies no friction and so the pulley shouldn't be able to turn?

Friction depends on the normal force on the pulley, and (if the string is bent round the pulley) there will always be a normal force, even if the string is massless.

Typical assumptions (in intro courses) are that strings are massless (and thus have the same tension throughout) …

Hi Doc Al! May I qualify that?

A massles string with no obstructions will have the same tension throughout (while a massive string hanging vertically will of course have more tension at the top) …

but a string touching anything (like a pulley) with friction will have different tension on either side, even if the string is massless.

 

[Doc Al]

If the pulley has mass, and if you need to calculate the energy or angular momentum of the pulley, then yes, the friction is an external force on the pulley, and will provide a torque to the pulley.

Absolutely, but you generally don't need to explicitly consider static friction. The forces exerted on the pulley are represented by the tensions in the string.

but a string touching anything (like a pulley) with friction will have different tension on either side, even if the string is massless.

But not if the pulley is massless, a common assumption as you point out. I was waiting for the OP to bring up the issue of a massive pulley so I could qualify my statement. (One step at a time.)

 

[tiny-tim]

I was waiting for the OP to bring up the issue of a massive pulley so I could qualify my statement. (One step at a time.)

ah … I guessed that's what you were thinking … but I noticed the OP had mentioned torque, so I assumed his pulley already had mass.