# A Pulley as a Simple Machine

the data table

## Questions:

1. What is the efficiency of a pulley?
2. What is the mechanical advantage of a simple pulley?

## Discussion:

A pulley is a simple machine consisting of a wheel turning on an axle. Pulleys are often used singly and in combinations to do work.

If energy is conserved for a machine, then the work done by the machine must be equal to the work put into the machine:

Work out = Work in

The work done by a pulley equals the weight it lifts, W (= mg), times the height it lifts it, h. The work that you put into the machine equals the Force that you exert on the string, F, times the distance that you pull the string, d. So, for an ideal pulley:

Fd = Wh (= mgh)

Of course, there is some friction present in any real pulley, so we would expect that some of the work that we put into the machine would be dissipated by friction (as heat energy, mostly). So for a real pulley,

Fd = Wh + Work done against friction

so,

The ratio of useful work done by the pulley (Wh) to the work you put in (Fd) is the efficiency of the pulley, which is usually expressed as a percent:

The mechanical advantage of a machine is the ratio of the output force to the input force, or:

## 2 single pulleys string 0.5 kg & 1.0 kg masses spring scale ring-stand clamp c-clamp ring stand Procedure:

 Apparatus A - The pulley is tied to the support
1. Set up Apparatus A as shown in the diagram.
1. Clamp the ring stand to the table (using the c-clamp) so that it won't tip over.
2. Tie one end of the pulley to the ring stand using a short piece of string.
3. Make a loop in one end of another piece of string to hang the mass you will be lifting.
4. Thread the string through the top of the pulley.
5. Tie the end of the string to the spring scale.
2. Lift the mass. Measure and record:
1. the mass lifted, m
2. the vertical height the mass was lifted by the pulley,h
3. the force required, F, you read off the spring scale as you lift the mass
4. and the distance you pulled the spring scale as you lifted the mass, d.
3. Calculate:
1. the weight of the mass you lifted, mg
2. the work done in lifting the mass, Wh
3. the work done by the pulley, Fd
4. Repeat for Apparatus B.
1. Tie one end of a string to the ring stand.
2. Loop the string through the pulley and tie the other end of the string to the spring scale.
3. Hang the mass from the bottom of the pulley.
5. If you have time and interest, try Apparatus C.
 Apparatus B - The pulley is tied to the weight being lifted
 Apparatus C - 2 single pulleys

## Analysis and Conclusions:

Calculate the efficiency (work lifting the mass/work pulling the spring scale x 100%) and mechanical advantage (weight lifted/spring scale force) for one trial of apparatus A & B (and C if you did it). Answer the questions on the data table page.

last update January 20, 2010 by JL Stanbrough