# Tension on chain on pulley

## Homework Statement

A worker lifts a weight w by pulling down a rope with a force F. The upper pulley is attached to a ceiling by a chain, and the lower pulley is attached to the weight by another chain. The weight is lifted at constant speed. Assume the chain, rope, and pulley all have negligible weights. In terms of w, find the magnitude of force F if the weight is lifted at constant speed.

F=ma where a=0

## The Attempt at a Solution

Okay, so I made a fbd again. This time I'm confused about the tensions, I'm not sure if it is pointed up or down, for both of the chains. So far, I have the weight pointed down, F is down, and both tensions are up (I assume that tension is up...but I'm not sure). With that, my equation is

F = -w+2T where I substitute T with w.

Can someone pls explain to me about tension? Many thanks in advance.

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PhanthomJay
Homework Helper
Gold Member

## Homework Statement

A worker lifts a weight w by pulling down a rope with a force F. The upper pulley is attached to a ceiling by a chain, and the lower pulley is attached to the weight by another chain. The weight is lifted at constant speed. Assume the chain, rope, and pulley all have negligible weights. In terms of w, find the magnitude of force F if the weight is lifted at constant speed.

F=ma where a=0

## The Attempt at a Solution

Okay, so I made a fbd again. This time I'm confused about the tensions, I'm not sure if it is pointed up or down, for both of the chains. So far, I have the weight pointed down, F is down, and both tensions are up (I assume that tension is up...but I'm not sure). With that, my equation is

F = -w+2T where I substitute T with w.

Can someone pls explain to me about tension? Many thanks in advance.
I'm not sure how to visualize your problem, but in terms of tension forces, tension forces external to an object in a FBD always pull away from that object in your FBD, never towards its.

Sorry, I have the picture right here. I figured out that both of the tensions, in upper and lower chains are w, but putting the whole problem together to find the magnitude of the force, I'm bit stuck, keep getting the wrong answer. Is both tensions not pointed up?

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PhanthomJay
Homework Helper
Gold Member
Sorry, I have the picture right here. I figured out that both of the tensions, in upper and lower chains are w, but putting the whole problem together to find the magnitude of the force, I'm bit stuck, keep getting the wrong answer. Is both tensions not pointed up?
There are a few tension forces to deal with here, so be careful. You have the tension in each of the chains, and the tension in the rope. For massless, frictionless pulleys, the tension in the rope is always the same on each side of the pulley it is wrapped around.

Since the top pulley does not move, and the lower pulley moves at constant speed, there are no net external forces acting on the system. Newton 1 applies.

Draw an FBD of the weight first. That will give you the tension in the lower chain....w, acting up on the block, pulling away from it, which you have correctly identified. Now draw an FBD of the lower pulley....isolate it with a cloud around it. You have the tension in the chain, w, acting down away from the pulley. What can you now say about the tension in the rope and the force F??

There are a few tension forces to deal with here, so be careful. You have the tension in each of the chains, and the tension in the rope. For massless, frictionless pulleys, the tension in the rope is always the same on each side of the pulley it is wrapped around.

Since the top pulley does not move, and the lower pulley moves at constant speed, there are no net external forces acting on the system. Newton 1 applies.

Draw an FBD of the weight first. That will give you the tension in the lower chain....w, acting up on the block, pulling away from it, which you have correctly identified. Now draw an FBD of the lower pulley....isolate it with a cloud around it. You have the tension in the chain, w, acting down away from the pulley. What can you now say about the tension in the rope and the force F??
The tension is pointed downward right? So if the tension is the same on both side, then counting all the forces together, there's two tensions (in the chains) pointed up and two tensions in the ropes, pointing downward. Doesn't that cancel out all the tensions? Unless I'm wrong about the direction of the tensions...?

PhanthomJay
Homework Helper
Gold Member
The tension is pointed downward right? So if the tension is the same on both side, then counting all the forces together, there's two tensions (in the chains) pointed up and two tensions in the ropes, pointing downward. Doesn't that cancel out all the tensions? Unless I'm wrong about the direction of the tensions...?
I don't think you are taking your FBD's properly. Let me start one of them off for you, or else we'll be talking forever about what acts up and what acts down.

Draw a circle or cloud around the lower pulley. The circle will cut through the lower chain and through the 2 ropes immediately above that lower pulley. The tension in the chain acts down on the pulley, pulling away from it, and equals w. The tension , T, in 'each' of the ropes above the pulley act up on the pulley, pulling away from it . The tension in 'each' of the ropes are equal. (I put 'each' in quotes because really it's the same rope, you know). From Newton 1,
$$F_{net} = 0$$
$$T + T - w= 0$$
$$2T = w$$
$$T = w/2$$
NOW, try solving for F.
Solve

Yeah, I don't understand about the direction of the tension....I'm not sure if it goes up or down when attached to an object.

Um, since the tension of the rope is same on both side of the pulley it's wrapped around, does that mean that the force F = T = w/2?

PhanthomJay