# Pulley with string attached to ground

• khkwang
In summary, this question is asking if the tension in a rope due to the weight of an object on one end is the same as the tension on the other end due to the same weight being supported by a different object. The answer is that the tension in the rope is the same along the entire length.
khkwang
Not exactly a homework question, but I need to know this before I can answer the question

## Homework Statement

There's a pulley suspended from a rope A. Hanging from the pulley from one side is a mass m. "Hanging" off the other side of a pulley is simply the same rope (which is attached to the mass) (rope B), attached to the ground.

Is the tension on rope A simply mg?

none

## The Attempt at a Solution

I know the tension on rope B would be mg. But I'm wondering about rope A. I don't know whether to count the side of rope B attached to the ground as a contributing factor in the tension of rope A.

The way I see it is that since rope B is attached to the ground, the only thing that moves if one were to pull on rope A would be mass m. Thus the only work done is on mass m, and the only force required to move mass m would be needed: mg.

So then the tension on both ropes would be mg?

The work done on mass m if rope B is pulled does not concern the rope A. The centre of the pulley where it is suspended remains stationary. The resultant of the forces acting at the pulley must cancel. The tension is the same along a rope. Rope B pulls the pulley at both sides.

ehild

I'm confused about your reply and I don't know if the confusion is on my side or yours... just to clarify by question, I attached a diagram.

I'm wondering if rope A were pulled not rope B

#### Attachments

• tension.png
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If you pull rope A you have to pull both the mass and the Earth. Rope B is fixed to Earth.
If you prefer thinking in terms of work, find out how much the mass will rise if you pull up the pulley by a certain length Δy. Turn the figure upside down. Is not it familiar from your textbook?

If you cut rope B and fix the free end to a peg on the pulley the mass will move to a stationary position hanging bellow the centre of the pulley. In that case, the tension would be mg in the rope A.

ehild

I'm feeling pretty dense right now... I don't get exactly what you're trying to imply (I do you know you want me to come to my own conclusion though, rather than spell it out for me).

I'm taking it as the peg attached to the end of the rope is equivalent to the rope attached to the ground in the sense that in both cases the Δy of the mass is equivalent to the Δy of the pulley. So in both cases the tension on rope A is mg.

khkwang said:
I'm taking it as the peg attached to the end of the rope is equivalent to the rope attached to the ground in the sense that in both cases the Δy of the mass is equivalent to the Δy of the pulley. So in both cases the tension on rope A is mg.

No, the displacement of the mass is not the same as the displacement of the pulley when the rope B is fixed to the ground.

See this place. http://simple.wikipedia.org/wiki/Pulley

Your system is similar to an upside down movable pulley.

I must not tell you the solution. I only can help you to find it.

ehild

Oh no, of course you can't tell me the answer; that would defeat the purpose. I hope you didn't take the statement in my last reply as resentment!

Okay, I'll try again.

Since the mass is at rest, the tension all along rope B is equal. So the tension to the left of the pulley and to the right of the pulley are the same. Since the tension on the right is mg, then the one on the left must also be mg.

Since rope A is holding both tensions up, it must then have a tension equal to the sum of the tensions acting against it. Therefore T_A = 2mg.

Is that right?

It is right now.

ehild

Thanks for your help and patience.

Cheers

## What is a pulley with a string attached to the ground?

A pulley with a string attached to the ground is a simple machine that is used to lift or move objects. It consists of a wheel with a groove around the edge and a string or rope wrapped around it.

## How does a pulley with a string attached to the ground work?

When one end of the string is attached to the ground and the other end is pulled, the pulley rotates and lifts the object. This is due to the principle of mechanical advantage, where the force required to lift the object is divided between the string and the person pulling it.

## What are the different types of pulleys with strings attached to the ground?

There are two main types of pulleys with strings attached to the ground: fixed and movable. A fixed pulley is attached to a stationary object, while a movable pulley is attached to the object being lifted. There are also compound pulleys, which combine multiple pulleys to increase the mechanical advantage.

## What are some common uses of pulleys with strings attached to the ground?

Pulleys with strings attached to the ground are commonly used in various industries, such as construction, manufacturing, and transportation. They are also used in everyday objects, such as window blinds, flagpoles, and exercise equipment.

## What are the benefits of using a pulley with a string attached to the ground?

Using a pulley with a string attached to the ground can make lifting and moving heavy objects easier and more efficient. It also reduces the risk of injury from lifting heavy objects manually. Additionally, the mechanical advantage provided by the pulley allows for a smaller force to be applied to lift the object, making it ideal for tasks that require precision and control.

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