# What force(s) make(s) change of direction in a pulley

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1. Jul 6, 2015

### juan gce

Hi guys .. Glad to be here in this forum of physcs fans.

This is the classical problem of cart HORIZONTALLY pulled by a rope that wraps around a pulley and it's pulled VERTICALLY by say, the same mass as the cart (yeah T1 = T2 horizontal and vertical tensions .. = in MAGNITUDE BUT NOT IN DIRECTION)

Question:
There is a change in direction .. is it there any set of mathematical equations that convert one force in one direction to another force in the other direction, using the classical physics?

Thanks a lot.

2. Jul 6, 2015

### insightful

To me, the equations that relate the vertical force to the horizontal force are those gotten from the free-body analysis of the pulley.

3. Jul 7, 2015

### juan gce

My guess is this: at the pulley at every point forces anule (first law).

Taking any angle from a horizontal line passing through the center of the pulley, as the rope is attached tangentially to the wheel, we may draw an inclined cartesian plane where each of the forces -horizontal and vertical- decompose and should coincide in direction and strength .. but there the question would be if there should also be a force from the center of the polley, acting at the point of tangency.

Another way to view it perhaps, would be to make an equivalence relation with a pendulum droped when the center and extreme point of it make a horizontal line.

Thank you Insightful, applying the free-body analysis, makes me ask: what makes me state that there is an horizontal force pulling the cart?
(yeah .. haha .. that is the obvious .. but I ask my self if there is a theoretical way to predict it)

4. Jul 7, 2015

### insightful

The fact that there is a horizontal tension in the rope from the pulley to the cart.

5. Jul 7, 2015

### juan gce

A way to predict that fact?

6. Jul 7, 2015

### brainpushups

If you are assuming the pulley and rope have no mass then the tension is the same throughout the rope.

It's pretty obvious isn't it? What's the old joke? To be a mechanical engineer (or was it civil engineer...) you need to know two things 1) F=ma and 2) you can't push with a rope. The change in direction comes from the constraints imposed upon the system. I think you just need to use some intuition.

Perhaps you might find the belt friction equation of interest...

7. Jul 7, 2015

### Staff: Mentor

The location of the cart (rolling on e.g. a tabletop) and the pulley (presumably fixed to the edge of the table) dictate the orientation of the rope as it runs between the cart and the pulley.

8. Jul 7, 2015

### juan gce

The problem might be posed through 90 degrees, where the vertical weight comes to change to a horizontal force .. how? and what does the weightless center of the pulley play there.

Is the obvius expresible in terms of equations based on classical physics? (what if the obvious results as the sun buzzing around our home?)

well .. what are the forces -magnitude and directions- nullifying at the point where the rope touching the wheel .. is at 3 degrees relative to the horizontal line that passes through the center of the pulley? and so on until it reaches the top, 90 degrees?

Last edited: Jul 7, 2015
9. Jul 7, 2015

### Staff: Mentor

Actually, it's not generally true that the forces exerted (or on) the two ends of the rope are equal in magnitude. They are equal only in an idealized situation which satisfies certain assumptions. Does your textbook (or other source) mention those assumptions?

10. Jul 7, 2015

### juan gce

Thanks jtbell
It ocurred to me, I have not seen it in any textbook. I just wonder if there is some way to treat "skewing" forces in the classical physics.

In a thought ideal situation with the usual conditions: no friction, no weight but to the two masses cart and the balance weight, having equal values .. I suppose it does not lose much touch from reality (taking ideal as an approximation where conditions uncounted become so little that are meaningless).

In this case, the rope turns -I ask my self- because there are forces turning it
(if the pulley were somehow taken apart, the rope would bend a the table corner and so on, to the cart attachment .. a movement that is analogous but harder to treat than the pulley)

If at this section only textbook problems are the subject of discussion .. I made a mistake .. and also if there is no interest in it wont insist.