# Why Does Pulley Require Less Work to Lift Mass?

• jldibble
In summary, pulleys can reduce the force needed to lift objects but require a greater distance. The number of pulleys increases, the force decreases. However, for all cases, the work required to lift an object to a given height will remain the same. When attaching a mass to the axel of a pulley and pulling on the rope, the pulley with the attached mass will rise, with each end of the rope feeling half the weight of the attached mass. In a setup with a 2x mechanical advantage pulley, the end of the rope must move 2 meters to lift the weight 1 meter. This is similar to a lever, where the force is increased but the distance is decreased. It is important to use
jldibble
As I understand it, pulleys will reduce the force needed to lift objects but require a greater distance. As the number of pulleys increase, the force decreases. But for all cases of pulleys, the work required to lift a given object to a given height will always remain the same.

When I attach mass directly to the axel of a pulley, and have one end of a rope attached to a support beam while I pull up on the other end of the rope, the pulley with the attached mass will rise. Each end of the rope should feel a force which is half that of the weight of the attached mass.

Say the attached mass has a weight of 10 Newtons and I want to actual mass to be lifted 1 meter above the ground. Work done against gravity is 10 joules. When I actually go to do this with the pulley setup I described above, I find that I am pulling up my end of the rope with 5 Newtons and I have to pull up a total of 1 meter of rope to get the mass 1 meter above the ground. The work I have done seems to be 5 joules...

Why is this? I thought I should be doing 10 joules of work. This seems to be requiring only half of the total work needed.

I am taking all of my measurements very accurately and I am sure there is no problems with them.

jldibble said:
AI have to pull up a total of 1 meter of rope to get the mass 1 meter above the ground.

Can you post a diagram of your setup with the length of the segments of rope on each side of the pulley marked, both before and after? In the setup that I'm imagining, moving the end of the rope up one meter should only lift the weight .5 meters.

Nugatory is correct. If you have a 2x mechanical advantage pulley then you have to pull 2 m to get 1 m of lift. It is just like a lever, the force is increased but the distance is decreased.

You should use the term Velocity Ratio when calculating the ratio of string lengths and other distances moved in machines. Mechanical Advantage is the overall ratio of force out / force in and includes friction, weight of the pulleys and stuff, when applicable.
Mechanical Advantage / Velocity ratio is Efficiency
Credit to Mr Scales, my A level Physics teacher who would beat us if we got that sort of thing wrong. (Not really but we were never sure)
Machine weight can be highly relevant for small loads.

Here's the setup

#### Attachments

• Pulley Problem Image.jpg
11.2 KB · Views: 702
If you can't see it in the diagram, you should get yourself some string and measure it.

jldibble said:
Here's the setup

As I said above... Mark the lengths of the segments of rope on each side of the pulley (between the pulley and the fixed point on one side; between the pulley and the end of the rope on the other side) before and after the lift. You'll see that the free end had to move 2 meters up to lift the pulley one meter.

## What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or belt that runs along the groove. It is used to lift or move heavy objects by changing the direction of the force needed to lift the object.

## How does a pulley work?

A pulley works by using the principle of mechanical advantage. By using a pulley, the force needed to lift an object is spread out over multiple strands of rope, which reduces the amount of force needed to lift the object. This makes it easier to lift heavy objects.

## Why does a pulley require less work to lift mass?

A pulley requires less work to lift mass because it allows for the distribution of force over multiple strands of rope. This reduces the amount of force needed to lift the object, making the work required to lift the object easier.

## What is mechanical advantage?

Mechanical advantage is a measure of the effectiveness of a machine in multiplying the force applied to it. In the case of a pulley, it is the ratio of the force needed to lift an object without a pulley to the force needed to lift the same object with a pulley. The higher the mechanical advantage, the easier it is to lift the object.

## How does the number of pulleys affect the amount of work required to lift an object?

The more pulleys that are used, the less work is required to lift an object. This is because each additional pulley increases the mechanical advantage and reduces the amount of force needed to lift the object. However, using too many pulleys can also decrease the efficiency of the system due to friction and the weight of the pulleys themselves.

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