# 2D pulley forces

## Homework Statement

The problem is a 2D one, regarded as seen from above (no gravitational forces are relevant). A pulley is attached to a cable and is pulled with the force "F" towards north. Through the pulley goes another cable and is firmly attached to the ground on one end and attached to a box with the mass "m". The cable is non-elastic and as the pulley is pulled towards north, the angle "theta" becomes larger. The two respective cable forces are "S1" on the firmly attached side, and "S2" on the side where the mass is being pulled.

The problem lies in trying to determine the x and y components of the cable force "S2", expressed by the force "F" and the angle "theta".

I am unsure how to start tackling this problem. I've had problems with pulleys before but never in this fashion where the pulley itself is being pulled. Can anyone shed a light on it for me so I can get started?

Helgi.

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Doc Al
Mentor
A diagram would help. It's not clear what angle theta represents. Can we assume the pulley is massless and frictionless?

tiny-tim
Homework Helper
Welcome to PF!

Hi helgi! Welcome to PF! Just write out the components as usual, in terms of theta, and apply Newton's second law.

The only difference is that the equations will depend on theta. (if you want more specific help, you'll have to describe the problem in more detail)

Hi Doc.
A diagram is here: http://picasaweb.google.com/helgi2000/Iceland2008/photo#5201292838334570434 [Broken]
And yes, the pulley can be considered massless and frictionfree.

(P.S. I had to put spaces in the URL 'cause I'm new at the forum and they won't allow me to post URL's yet)

Thank you.
H.

Last edited by a moderator:
Doc Al
Mentor
And yes, the pulley can be considered massless and frictionfree.
So what does that tell you about the relationship between F and S1 & S2? And between S1 and S2?

Hint: What's the net force on the pulley?

Initially, when the angle theta = 0, then the force F is obviously divided equally between S1 and S2, but as the angle theta becomes > 0 and the mass m has displaced from it's original position, I would assume that F divides differently between the two S Forces.

It is this division of F after the initial theta = 0 that confuses me.

Doc Al
Mentor
If theta = 0 (the cable is horizontal), then you will not be able to exert a vertical force F on the pulley. (Is there any reason to think that theta = 0 is part of this problem?)

In any case, please answer my questions regarding the relationship among the forces. (They are general and would apply to any problem where you have a cord around a massless and frictionless pulley.)

tiny-tim
Homework Helper
Initially, when the angle theta = 0, then the force F is obviously divided equally between S1 and S2, but as the angle theta becomes > 0 and the mass m has displaced from it's original position, I would assume that F divides differently between the two S Forces.

It is this division of F after the initial theta = 0 that confuses me.
Hi helgi! You've asked lots of questions, but you haven't done anything yet, except to make the obvious point that when the picture is symmetric the forces are the same … which isn't really physics, is it?

You say that you've had problems with pulleys before … so I assume you know what a force diagram is … or alternatively some other method of doing pulleys …

So just try one, show us what you've done, even if it comes out wrong, and we can put it right for you! 