Is Equilibrium Achievable in a Simple Pulley System?

[T@P]

Assume that a person is pulling himself up in a bucket attached to a simple pulley (no double pulleys or anything), and that it is in a state fof equilibrium. For this to be true, equal forces must be applied to both sides of the pulley. (if the person has a mass m, and the force on one side is f, then f = mg)

does it matter the force is applied by the person in the bucket or not? I have reason to believe that fromthe bucket one must pull with less force to maintain and equilibrium, but this is counter intuitive. Any thoughts on why either can be true?

 

[Doc Al]

For an ideal pulley and massless rope the tension will be the same throughout the rope. If one end of the rope is attached to the bucket, and the person pulls on the other end, then the amount of force the person must pull with is only half the weight of the "bucket + person". Think about it: how many ropes attach to the "bucket + person"?

If there was no pulley, just a single rope hanging down, the person would have to pull with twice as much force since they would have to support the entire weight. (The pulley provides a mechanical advantage.)

Does this help?

 

[T@P]

can you be more precise? i don't quite understand the "mechanical advantage" of the pulley

 

[5X5]

Forget about the man in the bucket and even the pulley. In the first case just look at it as a single mass (a brick say) held up by two ropes. Assuming the ropes are evenly spaced about the center of gravity, each will share the load equally. If you had three ropes attached to the same mass each would carry 1/3 the load and so on. In the second case, only one rope is attached to the same mass. It doesn't matter where the other end of the rope is as long as only one rope is attached to the mass and holding it in equilibrium. Since there is only one rope attached to the mass, it must provide all of the force on its own.

 

[Doc Al]

can you be more precise? i don't quite understand the "mechanical advantage" of the pulley

Think of it like I and 5X5 explained. If the "person + bucket" is supported by two ropes, then each rope need only support half the weight. (Note: It doesn't matter that the "two" ropes are just the two ends of the same rope!) But if there's only one rope attached, that single rope must support the entire weight.

That arrangement of a person pulling themselves up in a bucket (or chair!) attached to a pulley is called a Bosun's chair. Check out the cartoon of "harry the painter" at the bottom of this web page for an illustration: http://www.phy.ntnu.edu.tw/java/wheelAxle/pulley.html

 

[T@P]

thanks a lot for your help. I was wondering if any of you knew the equations of these forces? I understand it conceptually, but i would greatly appreciate the equations. thanks again for the wonderful site Doc Al.

 

[Doc Al]

I was wondering if any of you knew the equations of these forces? I understand it conceptually, but i would greatly appreciate the equations.

It's easy. Since the person is in equilibrium, the forces pulling him up (the tension in the ropes) must balance the force him down (his weight). In the case of the person pulling himself up in the bosun's chair there are two rope connections, thus: 2T = mg.

 

[T@P]

Thanks a lot for your advice. Everything makes sense now, thanks!

 

[saksham]

What if the person uses his muscles too, not only his weight?

 

[Doc Al]

What if the person uses his muscles too, not only his weight?

In the person exerts a force on the rope (thus creating tension in the rope) such that 2T > mg, then he will accelerate upwards.

 

[psyducks]

I'm a bit confused. I understand the concept. What happens if someone is trying to pull the man in the bucket from the ground? Would that be the same as pulling him up with one rope from someone above him? I have this homework question and the force required to keep the man in equilibrium is twice that of the man in bucket trying to keep himself at equilibrium.

[edit]
heres a picture
http://img337 . imageshack.us/i/physicsyp.png/
with no spaces