# Compound pulley tension question

• sailsinthesun
In summary: Ahh, just solved it. Thanks for all of your help. T1=T2=T3=Mg/2 and since T4=T1+T2+T3, T4=(3Mg)/2 and since F=T1, F=Mg/2
sailsinthesun
[SOLVED] Compound pulley tension question

## Homework Statement

An object of mass M is held in place by an applied force and a pulley system as shown in Figure P5.55. The pulleys are massless and frictionless.
http://img520.imageshack.us/img520/7840/p445fw5.th.gif
(a) Find the tension in each section of rope, T1, T2, T3, T4, andT5. (Answer in terms of M and g.)
(b) Find the magnitude of F.

## The Attempt at a Solution

The only thing I know is that T5=Mg. I'm trying to draw the a FBD for each pulley but I'm getting confused with relating T1, T2, T3, and T4 with Mg and F.

Last edited by a moderator:
sailsinthesun said:
The only thing I know is that T5=Mg. I'm trying to draw the a FBD for each pulley but I'm getting confused with relating T1, T2, T3, and T4 with Mg and F.
It's easier than it looks. The FBD for each pulley should be easy since the only forces on the pulleys are the string tensions.
Hint 1: The tension is the same throughout a continuous piece of rope (since the pulleys are massless and frictionless).
Hint 2: How does F relate to T1?

Doc Al said:
It's easier than it looks. The FBD for each pulley should be easy since the only forces on the pulleys are the string tensions.
Hint 1: The tension is the same throughout a continuous piece of rope (since the pulleys are massless and frictionless).
Hint 2: How does F relate to T1?

F-T1=0 so F=T1?

When I'm drawing the FBD for the top pulley, what would the downward force be? F?

sailsinthesun said:
F-T1=0 so F=T1?
Right!

When I'm drawing the FBD for the top pulley, what would the downward force be? F?
The downward force will equal the three tensions that pull on it.

Doc Al said:
Right!

The downward force will equal the three tensions that pull on it.

So the downward force would be T1+T2+T3? Meaning T4=T1+T2+T3? And how do I relate these tensions to M and g?

sailsinthesun said:
So the downward force would be T1+T2+T3? Meaning T4=T1+T2+T3?
Right.
And how do I relate these tensions to M and g?
By combining that with other equations you can come up with. What about the second pulley? And, especially, what about my hint #1?

Doc Al said:
Right.

By combining that with other equations you can come up with. What about the second pulley? And, especially, what about my hint #1?

Even if the rope goes through a pulley? So that means T1=T2=T3?

Ahh, just solved it. Thanks for all of your help. T1=T2=T3=Mg/2 and since T4=T1+T2+T3, T4=(3Mg)/2 and since F=T1, F=Mg/2

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Hey guys I have a problem I got wrong similar to this. The pulley set up is exactly the same, but the outside rope is pulled at an angle (60) and I was curious to see how the force changes with the angle. Don't get me wrong here, I know that to find the x component of the force it would be FCos(60) and the find the y component you would use FSin(60), but do you use 1/2MG as F even though its pulled at an angle? And furthermore, do you do you square Fx and Fy and then take the root of it to find the final F?

## 1. What is a compound pulley?

A compound pulley is a type of pulley system used to lift heavy objects by utilizing multiple pulleys in combination. It is made up of two or more pulleys, with the rope or cable passing through each one, allowing for a mechanical advantage to be gained.

## 2. How does a compound pulley work?

A compound pulley works by distributing the weight of the object being lifted across multiple pulleys, reducing the amount of force needed to lift it. As the rope or cable is pulled, the load is spread out and the weight is distributed equally among the pulleys.

## 3. What is the tension in a compound pulley system?

The tension in a compound pulley system refers to the amount of force being applied to the rope or cable used to lift the object. As the load is distributed across multiple pulleys, the tension in the rope or cable is reduced, making it easier to lift the object.

## 4. How is tension affected by the number of pulleys in a compound pulley system?

The number of pulleys in a compound pulley system affects the tension by reducing the amount of force needed to lift the object. As more pulleys are added, the tension in the rope or cable decreases, making it easier to lift heavier objects with less effort.

## 5. What is the mechanical advantage of a compound pulley system?

The mechanical advantage of a compound pulley system is the ratio of the output force (the weight being lifted) to the input force (the force applied to the rope or cable). In a compound pulley system, the mechanical advantage is equal to the number of pulleys used in the system.

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