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TE Activity: Swinging Pendulum

This activity demonstrates how potential energy (PE) can be converted to kinetic energy (KE) and back again. Given a pendulum height, students calculate and predict how fast the pendulum will swing by understanding conservation of energy and using the equations for PE and KE. The equations are justified as students experimentally measure the speed of the pendulum and compare theory with reality.

Mechanical engineers design a wide range of consumer and industry devices — transportation vehicles, home appliances, computer hardware, factory equipment — that use mechanical motion. The design of equipment for demolition purposes is another example. Like the movement of a pendulum, when an enormous wrecking ball is held at a height, it possesses potential energy, and as it falls, its potential energy is converted to kinetic energy. As the wrecking ball makes contact with the structure to be destroyed, it transfers that energy to take down the structure.

Learning Objectives
Materials
Introduction/Motivation
Procedure
Attachments
Safety Issues
Troubleshooting Tips
Assessment
Extensions
Activity Scaling

Grade Level: 7 (6-8)	Group Size: 4
Time Required: 45 minutes	Activity Dependency : None
Expendable Cost Per Group : US$ 1
Keywords: energy, gravity, kinetic, pendulum, potential, mass, mechanical energy, conservation of energy, roller coaster, velocity, work

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Colorado Math
- 1. represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation; (Grades 5 - 8) [2005]
- 1. read and construct displays of data using appropriate techniques (for example, line graphs, circle graphs, scatter plots, box plots, stem-and-leaf plots) and appropriate technology; (Grades 5 - 8) [2005]
- 1. demonstrate meanings for integers, rational numbers, percents, exponents, square roots, and pi (π) use physical materials and technology in problem-solving situations; (Grades 5 - 8) [2005]
- 1. estimate, use, and describe measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison; (Grades 5 - 8) [2005]
- 2. construct, use, and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers; (Grades 5 - 8) [2005]
Colorado Science
- Standard 1: Students understand the processes of scientific investigation and design, conduct, communicate about, and evaluate such investigations. (Grades 0 - 12) [1995]
- 2.1 Students know that matter has characteristic properties, which are related to its composition and structure. (Grades 0 - 12) [1995]
- 2.2 Students know that energy appears in different forms, and can move (be transferred) and change (be transformed). (Grades 0 - 12) [1995]
- 2.3 Students understand that interactions can produce changes in a system, although the total quantities of matter and energy remain unchanged. (Grades 0 - 12) [1995]

Remember that an object's potential energy is due to its position (height) and an object's kinetic energy is due to its motion (velocity). Potential energy can be converted to kinetic energy by allowing the object to fall (for example, a roller coaster going down a big hill or a book falling off a shelf). This energy transformation also holds true for a pendulum, as illustrated in the diagram. As a pendulum swings, its potential energy converts to kinetic and back to potential. Recall that energy may change its form, but there is no net change to the amount of energy. This is called conservation of energy.

A diagram of a swinging pendulum illustrates that the pendulum's potential energy, when at its highest point at the left, is converted into kinetic energy as it drops to its lowest point, and converted back to potential energy as it reaches its highest point to the right.

This diagram shows a swinging pendulum whose potential energy is converted into kinetic energy and back during the course of a swing from left to right.
click for copyright

In this activity, students prove that the transformation of energy occurs by calculating the theoretical value of velocity at which a pendulum should swing and comparing it to a measured value.

Three equations will be used in this activity:

PE = m∙g∙h

KE = ½ m∙V_t²

V_m = distance ÷ time

where m is mass (kg), g is gravity (10 m/s²), h is height (meters), V_t is the calculated velocity (m/s), and V_m is the measure velocity (also m/s). To make the calculations simpler, use the metric system for measurements and calculations. This way, we can approximate gravity as 10 m/s² and not worry about the English system's wacky units of mass.

Before the Activity

Gather materials.
Designate several areas, depending on the size of your class, for pendulums to swing.
Tie the string(s) or line(s) to the ceiling about 2 inches from a wall, leaving enough slack to reach the ground.

With the Students

Divide the class into groups of 4 and hand out the worksheet.
Have each group measure and record the mass of their object or weight.
Have each group pick an arbitrary height at which they will release their pendulums. This should range from 15-40 cm (.15-.4 m) from the floor.
Calculate the potential energy. Each team member should do this, as a way to verify the result.
Calculate the theoretical velocity, V_t, at the bottom of the swing.

Remember, KE at the bottom of the swing will equal PE at the top of the swing.
If your students do not know algebra yet, derive Vt for them (see the Troubleshooting Tips section).

Have each group move to a designated area and tie their weight to the string/line so that it barely misses the ground while hanging.
Place two pieces of tape on the wall on opposite sides of the hanging pendulum and record the distance between the two pieces.

The distance should range from 30-50 cm (.3-.5m). Choose a larger distance for a higher height (i.e., h = 40 cm → distance = 50 cm).
The pendulum should rest in the middle of the two pieces of tape.

One or two students pull back the weight until it reaches one of the pieces of tape.
Two students synchronize two stopwatches, each holding one, and start timing when the pendulum is released.
The first student stops his/her stopwatch when the pendulum passes over the opposite piece of tape and the second student stops his/her watch when it returns back to the initial piece of tape.
Record both times and calculate the difference in time.
Repeat the experiment four times so students can exchange roles.
Complete the worksheet.
How close were the values for the theoretical velocity and the measured velocity?

Pre-Activity Assessment

A drawing showing people having fun riding on a rollercoaster.

click for copyright

Question/Answer: Ask the students and discuss as a class:

Where will the pendulum have the greatest potential energy? (Answer: When it is pulled back.)
Where will it have the greatest kinetic energy? (Answer: At the bottom/middle of the swing.)

Prediction: Ask the students to predict:

Will pendulums with higher heights go faster or slower? (Answer: They should go faster.)

Activity Embedded Assessment

Question/Answer: Ask the students and discuss as a class:

What happens to the potential energy as the pendulum swings down? (Answer: It turns into kinetic energy.)
When the pendulum swings to the other side, what happens to the kinetic energy? (Answer: It turns back into potential energy.)

Post-Activity Assessment

Question/Answer: Ask the students and discuss as a class:

If engineers can use potential energy (height) of an object to calculate how fast it will travel when falling, can they do the reverse and calculate how high something will rise if they know its kinetic energy (velocity)? (Answer: Yes, as long as you know either height or velocity, you can calculate the other.)
For what might an engineer use this information? (Answer: Other amusement park rides besides roller coasters, or determining how high to build the next hill on a roller coaster, or how to launch something, etc.)

Integrated Teaching and Learning Program, College of Engineering, University of Colorado at Boulder Chris Yakacki, Malinda Schaefer Zarske, Denise Carlson © 2004 by Regents of the University of Colorado.
The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0226322. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last Modified: April 23, 2007