Purpose:  To find the mechanical advantage and the efficiency of several different pulley systems.

Concept and Skill Check:

Pulleys are simple machines that can be used to change the direction of a force, to reduce the force needed to move a load through a distance, or to increase the speed at which the load is moving, but that do not change the amount of work done.  However, if the required effort force is reduced, the distance the load moves is decreased in proportion to the distance the force moves.  Pulley systems may contain a single pulley or a combination of fixed and movable pulleys.

In an ideal machine, one lacking friction, all the energy is transferred, and the work input of the system equals the work output.  The work input equals the force times the distance that the force moves, Fede.  The work output equals the output force (load) times the distance it is moved, Frdr.  The ideal mechanical advantage, IMA, of the pulley system can be found by diving the distance the force moves by the distance the load moves.  Thus IMA= de/dr.  The ideal machine has a 100% efficiency.  In the real world, however, the measured efficiencies are less than 100%.  Efficiency is found by the following:  

Procedure:

1. Set up the single fixed pulley system, as shown in Figure 1a.

2. Select a mass that can be measured on your spring scale.  Record the value of its mass in Table 1.  Determine the weight, in Newtons, of the mass to be raised by multiplying its mass in kilograms by the acceleration due to gravity.  Recall that W=mg.

3. Carefully raise the mass by pulling on the spring scale.  Measure the height, in meters, that the mass is lifted.  Record this value in table 1.  Calculate the work output of the mass by multiplying its weight by the height it was raised.  Record this value in Table 2.

4. Using the spring scale, raise the mass to the same height it was raised in Step 3.  Ask your lab partner to read, directly from the spring scale, the force, in newtons, required to lift the mass.  Record this value in Table 1 as the force of spring scale.  As you are lifting the load with the spring scale, pull upward at a slow, steady rate, using the minimum amount of force necessary to move the load.  Any excess force will accelerate the mass and cause an error in your calculations.

5. Measure the distance, in meters, through which the force acted to lift the load to the height it was raised.  Record this value in table 1 as the distance, d, through which the force acts.  Determine the work input in raising the mass by multiplying the force reading from the spring scale by the distance through which the force acted.  Record the value for the work input in Table 2.  

6. Repeat steps 2 through 5 for a different load.

7. Repeat steps 2 through 6 for each of the different pulley arrangements in Figures 1b, 1c, and 1d.  Be sure to include the mass of the lower pulleys as part of the mass raised.

8. Count the number of lifting strands of string used to support the weight or load for each arrangement, (a) through (d).  Record these values in Table 2.

Helpful Hints for the Tables:

Use the abbreviations/equations in red to help with the calculations in table 1 and 2.