Why Does Pulley Require Less Work to Lift Mass?

[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.

 

[Nugatory]

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.

 

[Dale]

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.

 

[sophiecentaur]

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.

 

[jldibble]

Here's the setup

 

[russ_watters]

If you can't see it in the diagram, you should get yourself some string and measure it.

 

[Nugatory]

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.