# General Tension Forces

1. Jun 16, 2013

Hello everyone, I am puzzled by how the sum of the tension forces on a rope is calculated.

So lets say a climber (5kg) is dangling on a cliff, with a rope around his waist. That same rope is wrapped around a rock (10 kg) 50 meters left of the cliff. How would the tension force of that rope be measured when the rope goes in different directions.

What about a pulley? Is the tension force just the sum of the mass * gravity?

Also, what is the equation for tension forces. Is it just the sum of all forces that the rope is tugged by?

Help is much appreciated

2. Jun 16, 2013

### rock.freak667

There is no fixed formula for tension. You would normally get the tension based on equilibrium conditions.

So if the 5 kg climber (that is quite small btw) is just hanging there then the tension is balancing the weight vertically so T = (5*9.81) N.

If there are two ropes and he is stationary, then the components of the tensions in the x and y directions will need to be balanced.

3. Jun 16, 2013

### barryj

If a rope goes over a FRICTIONLESS pully, then the tension of the rope will be the same on both sides of the pully. It wouldn't matter what direction of the rope took.

4. Jun 16, 2013

### voko

Frictionless AND massless.

5. Jun 16, 2013

### Staff: Mentor

If the system is in static equilibrium, then the mass of the pulley is irrelevant.

6. Jun 16, 2013

### voko

This is an oversimplification. The weight of a pulley might be relevant even statically.

7. Jun 17, 2013

### Staff: Mentor

Please give an example of how this can be the case for a frictionless pulley.

Chet

8. Jun 17, 2013

### barryj

See attachment. Here T1 = T2 + mg

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9. Jun 17, 2013

### Staff: Mentor

This does not address the issue that Voko and I were discussing.

10. Jun 17, 2013

### barryj

I thought you were asking for an example of a static situation with a frictionless pulley where mass mattered. Sorry, I guess I misunderstood the question.

11. Jun 17, 2013

### barryj

Chester, what was "the issue that Voko and I were discussing." I should have said that..
T1 = T2 + mg + (mass of pulley)g

12. Jun 17, 2013

### voko

I am not sure what particular issue you have in mind. My comment was generic, the mass of a pulley may not always be neglected even in static equilibrium. I believe the diagram supplied by barryj illustrates that.

13. Jun 17, 2013

### Staff: Mentor

What I was saying was that, for a frictionless pulley situated within a system under static equilibrium conditions, the cord tension on one side of the pulley is the same as the cord tension on the other side of the pulley, irrespective of whether the pulley has mass. Maybe I should have been more precise in what I said.

Chet

14. Jun 17, 2013

### voko

Yes, that is true. If the tensions were different, the pulley would have a non-zero net torque acting on it.

15. Jun 17, 2013

### CWatters

The man creates a tension = Mmg in the rope. Where Mm is the mass of the man and g is the acceleration due to gravity. The tension in the rope the other side is the same.

Some of that tension (the horizontal component) is countered by friction between rock and ground.

Some of that tension (the vertical component) is countered by gravity acting on the rock.

What fraction of the total does what depends on the angle and you didn't specify "h" so we can't work out the angle.

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16. Jun 17, 2013

### haruspex

This is a little unfair. The original point under discussion was specifically whether the mass of a pulley can lead to a difference in tension in the sections of rope with which it makes contact:
In statics, it doesn't, though its weight may contribute to tension in other parts of the system, or increase the tension equally both sides of itself.

17. Jun 17, 2013

### voko

I am not exactly sure what the "original point" really is. The original post does not specifically restrict the discussion to statics, that may at best only be inferred from it. The initial post of Chestermiller had a statement in such a form ("mass is irrelevant") that I did not realize it was strictly about the equality of tensions.

Anyway, I think I have addressed both the generic and the static cases explicitly.

18. Jun 18, 2013

### haruspex

I was referring to the point made in post #3 and the discussion that engendered starting with your #4.