# Investigating Pulleys

## Student Laboratory Kit

### Materials Included In Kit

Double pulley, 2
Single pulley, 2
Pulley cord, 9 m

C-clamp or books
Hook weight, 500-g
Meter stick
Paper clips, 2
Spring scale, 5- to 10-Newtons
Structure for hanging pulleys (see Lab Hints)

### Disposal

All materials should be saved and stored for future use.

### Lab Hints

• Enough materials are provided in this kit for one student group of 2–4 students. The laboratory can be reasonably completed in one 50-minute class period.
• Any solid lattice mounting system can be used for this activity. If laboratory lattice rods and clamps are not available, support stands and clamps can be used. Be sure to use C-clamps to clamp the ring stand bases to the laboratory tabletops.
• If the ring clamp is too thick for the pulley hook, a large bent paper clip may be used to hang the pulley.
• A pulley that does not move with the load is call a fixed pulley and only changes the direction of the force. A pulley that moves with the load is called a moveable pulley and multiplies the input force, but does not change direction of the force.

### Teacher Tips

• The activity can be extended by testing different masses with the same pulley arrangements. How does the efficiency change as the mass is increased or decreased?

### Science & Engineering Practices

Using mathematics and computational thinking
Constructing explanations and designing solutions

### Disciplinary Core Ideas

MS-ETS1.A: Defining and Delimiting Engineering Problems
MS-ETS1.B: Developing Possible Solutions

### Crosscutting Concepts

Cause and effect
Structure and function
Scale, proportion, and quantity

### Performance Expectations

HS-PS1-5: Apply scientific principles and evidence to provide an explanation about the effects of changing the temperature or concentration of the reacting particles on the rate at which a reaction occurs.

### Sample Data

{13862_Data_Table_1}

1. Calculate the mechanical advantage (MA) for each pulley arrangement by using Equation 5 from the Background section. Record the mechanical advantage in the data table.

See Sample Data table.

2. Calculate the percent efficiency of each pulley arrangement by using Equation 4 from the Background section. Record each value in the data table.

See Sample Data table.

3. Examine the percent efficiency for each pulley arrangement.
1. Do any of the arrangements have an efficiency of 100%?

Although arrangement 1 comes close, none of the arrangements have 100% efficiency.

2. What are some possible reasons that the efficiency of a pulley arrangement may be less than 100%?

The friction on the axle and between the string and the pulley wheel reduces efficiency. In arrangements 2–5, the weight of the moveable pulley to which the load is attached also reduces the efficiency.

4. Consider the mechanical advantage of the different pulley arrangements.
1. What happens to the input force (F) as the mechanical advantage increases?

As the mechanical advantage increases, the input force required to lift the weight decreases.

2. What happens to the distance (d) the force moves as the mechanical advantage increases?

As the mechanical advantage increases, the distance over which the input force is applied increases.

5. Both pulley arrangements 1 and 2 use a single pulley.
1. Describe some differences between pulley arrangement 1 and arrangement 2.

In arrangement 1, the pulley is fastened at a fixed point and does not move. One strand directly supports the weight and the other strand is pulled in the opposite direction. In arrangement 2, the weight is attached to the pulley and the pulley moves upward with the weight. Both the weight and the spring scale are pulled upward.

2. What is the advantage of using pulley arrangement 1?

The input force is in the opposite direction that the weight is lifted. It is easier to lift up a load by pulling downward.

3. What is the advantage of using pulley arrangement 2?

Less input force is required (nearly half) to lift the load.

4. What is the advantage of using a combination of pulleys?

A combination of pulleys can reduce the force required to lift a load and change the direction of the force.

6. Remember that for an ideal pulley, the input work is equal to the output work..
1. What would be the efficiency of an ideal pulley system?

An ideal pulley system would have 100% efficiency.

2. What would be the relationship between the number of supporting strands and the mechanical advantage of an ideal pulley system?

The mechanical advantage of an ideal pulley system would be the same as the number of supporting strands.

7. Consider the following statement: A machine reduces the amount of work you have to do..
1. Is the above statement true or false?

The statement is false.

The amount of work (in joules) required to lift the weight with a pulley or any machine is actually greater than the work accomplished in lifting the weight. Even if 100% efficiency were possible, the input work and output work would be the same.

# Investigating Pulleys

### Introduction

A pulley is a simple machine consisting of a wheel turning on an axle. Pulleys can be arranged in various combinations to make work easier, allowing a single person to perform difficult tasks such as lifting a piano or dragging a ship onto the beach.

### Concepts

• Simple machines
• Efficiency
• Work
• Pulley

### Background

A pulley is a grooved wheel on an axle and has a string, rope, chain or other material in the groove that can be moved to turn the wheel. The use of pulleys dates back to ancient times. Records indicate that pulleys were used on Greek ships to hoist sails as far back as 600 B.C. Archimedes (c. 287–212 B.C.) is credited as being the inventor of multiple pulley systems. Archimedes reputedly used a pulley system to single-handedly drag a fully loaded ship onto dry land.

Pulleys 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. Pulleys do not change the amount of work done. If the required input force is reduced, the distance the load moves decreases in proportion to the distance the force moves.

A single pulley behaves like a first class lever. A first class lever has the pivot point, called the fulcrum, located between the input force and output force. Other examples include a seesaw, a crowbar and a trebuchet. In the case of the pulleys, the axle acts as the fulcrum, and both lever arms are equal in length, which is the radius (r) of the wheel (see Figure 1).

{13862_Background_Figure_1_Lever analysis of simple pulley}
The mechanical advantage of a simple machine is the ratio of the output force to the input force. Since the lever arms in a single pulley are of the same length (r) the input and output forces are equal (discounting any friction) and the ideal mechanical advantage is equal to 1. A single pulley only changes the direction of the force (pull down to move the load up).

When several pulleys are used (multiple lever systems) the analysis becomes more complex and the mechanical advantage can be increased. Since energy is conserved in any machine, 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) times the height it lifts it (h). The work that is put into the lift is the force exerted on the pulley string (F) times the distance the string is pulled (d). For an ideal pulley:
{13862_Background_Equation_1}
Of course, some friction is present in a real pulley, so we would expect that some of the work that is put into the machine will be dissipated by friction and lost as output work. For a real pulley:
{13862_Background_Equation_2}
so
{13862_Background_Equation_3}
The actual efficiency of a pulley is the ratio of useful work done by the pulley (W•h) to the work put in (F•d) and is usually expressed as a percent (Equation 4):
{13862_Background_Equation_4}
The mechanical advantage (MA) of a machine is the ratio of the output force compared to the input force (Equation 5).
{13862_Background_Equation_5}
In this activity, we will experiment with different pulley arrangements and study the mechanical advantage and efficiency of different arrangements.

### Experiment Overview

The purpose of this experiment is to investigate different pulley arrangements and study the mechanical advantage and efficiency of each arrangement.

### Materials

C-clamp or books
Double pulleys, 2
Hook weight, 500-g
Meter stick or metric ruler
Paper clips, 2
Pulley cord
Single pulleys, 2
Spring scale, 5- or 10-N
Support stand with ring clamp

### Safety Precautions

The materials in this activity are considered nonhazardous. Please follow all laboratory safety guidelines.

### Procedure

1. Use the diagrams in Figure 2 to assist in setting up various pulley arrangements. Note: It is important to set up a rigid and secure support system for testing pulleys. Use whatever support frame that is suggested by the instructor. If a support stand is employed, clamp it securely to the bench top with a C-clamp or place heavy books on the base
{13862_Procedure_Figure_2_Various pulley arrangements}
2. Tie a paper clip to each end of the pulley cord.
3. Select a 500-g mass and record its value in kg in the data table on the Investigating Pulleys Worksheet.
4. Find the weight (w) in Newtons by multiplying its mass (in kg) by the acceleration due to gravity (g). Record the weight. Note: Remember: w = m x g, where g = 9.8 m/sec2 and 1 Newton = 1 kgm/s2.
5. Set up the first pulley arrangement.
6. Zero the spring scale without any tension on the pulley cord.
7. Carefully raise the mass by pulling on the spring scale.
8. Measure the height (h) that the mass is lifted and the distance (d) the spring scale moves, in meters, and record in the data table. Note: When lifting the load with the spring scale, pull at a slow, steady pace, using the bare minimum to keep the weight in motion.
9. Calculate the work output and the work input and record these values in the data table.
10. Count and record the number of supporting strands in the first pulley arrangement. Note: The supporting strands are each section of the pulley cord that directly supports the load.
11. Repeat steps 1–10 for the other pulley arrangements shown in Figure 2. Note: Only one wheel of the double pulley will be used in arrangement 3.
12. Complete the worksheet by answering the questions following the data table.
13. Materials from this lab can be saved and stored for future use.

### Student Worksheet PDF

13862_Student1.pdf

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