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TE Activity: Swinging Pendulum (for High School)

This activity shows students the engineering importance of understanding the laws of mechanical energy. More specifically, it demonstrates how potential energy can be converted to kinetic energy and back again. Given a pendulum height, students calculate and predict how fast the pendulum will swing by using the equations for potential and kinetic energy. The equations will be 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. Similar to the movement of a pendulum, an enormous wrecking ball when held at a height 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 flatten or take down the structure.

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

Grade Level: 10 (9-12)	Group Size: 3
Time Required: 45 minutes	Activity Dependency : None
Expendable Cost Per Group : US$ 1
Keywords: energy, gravity, kinetic energy, pendulum, potential energy, mass, mechanical 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 (PE) is due to its position (height), and an object's kinetic energy (KE) 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 hill or a book falling off a table). 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, as illustrated in Figure 1.

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.

Figure 1. 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. Students also compare the periods (the length of time it takes the pendulum to swing back and forth one time) of the pendulum by allowing it to swing from two different heights.

Four equations will be used in this activity:

PE = m∙g h

KE = ½ m∙Vt2

V_m = distance ÷ time

T = (2∙Π∙ ( l / g )½

where m is mass (kg), g is gravity (10 m/s2), h is height (meters), l is the length of the pendulum (m), Vt is the calculated velocity (m/s), and Vm is the measure velocity (also m/s), and T is the period of the pendulum(s). To make the calculations simpler, use the metric system for measurements and calculations.

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, leaving enough slack to reach the ground.

With the Students

Divide the class into groups of 3, and hand out the Swinging Pendulum Worksheet.

Have each group measure and record the mass of the weight.
Move each group to the designated test area and tie their weight to the line so that it barely misses the ground while hanging.
Place two pieces of tape on opposite sides of the hanging pendulum so that their distances are 50 cm apart. The pendulum should rest in the middle of the two pieces of tape.
Have students measure and record the height of the center of your weight when it is resting at equilibrium and again when it has swung to one of the pieces of tape.
Students should calculate the potential energy of the weight when it reaches (swings to) the piece of tape. Each team member should do this, as a way to verify the result.
Ask students to calculate the theoretical velocity, Vt, at the bottom of the swing by first calculating the kinetic energy of the weight at the bottom of the swing. (Note: Remind students to ignore wind resistance and other factors that would cause us to lose energy. Also, remind students to calculate the potential energy of the weight at equilibrium and factor this into their answer.)
Instruct one or two students to pull back the weight until it reaches the edge of one of the pieces of tape.
Have two students synchronize two stopwatches, each holding one, and start the stopwatches as soon as the weight is released.
The first student should stop her/his stopwatch when the pendulum reaches the first piece of tape, and the second student should stop her/his watch when it reaches the second piece of tape (the original piece).
Ask students to record the difference in times on their Swinging Pendulum Worksheet.
Students should repeat the experiment three times.
Repeat steps 4-12 but make set up the two pieces of tape so they are 80 cm apart.
Instruct students to calculate the theoretical period of the pendulum.
They should compare the theoretical period with their average measured period. (Note: The measured period is the time it takes for the weight to complete one full swing to one piece of tape and back to the other.)
Instruct students to complete the Swinging Pendulum Worksheet.

A light and dark blue drawing showing people riding on a rollercoaster.

click for copyright

If students are complaining that the weight is not reaching the pieces of tape, ask them if they think it should and if so, why it is not. Then tell them to stop the stopwatches when the weight reaches the furthest point of its swing (right as the weight is changing direction).

If students have not had much experience with pendulums, then be sure to give them the equation for finding the period and help them with Question 5 from Calculations and Results section of the Swinging Pendulum Worksheet.

Pre-Activity Assessment

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

Where will the pendulum have the greatest amount of energy? (Answer: It has the same amount of energy wherever it is.)

Prediction: Ask the students to predict:

Will a pendulum starting at a higher height go faster or slower than a pendulum that starts at a lower height? (Answer: It should go faster.)
Will a pendulum starting at higher heights have a greater period? (Answer: It should be the same as a lower-starting pendulum no matter the height.)

Activity Embedded Assessment

Complete the Swinging Pendulum Worksheet.

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: To create other amusement park rides besides roller coasters, in racing, or how to launch something, etc.)
Why did the pendulum have the same period even when the weight started from different heights? (Answer: The period of a pendulum is only dependent on the length of the pendulum, which is consistent no matter where the weight starts.)

Integrated Teaching and Learning Program and Laboratory, University of Colorado at Boulder Chris Yakacki, Malinda Schaefer Zarske, Denise Carlson, Janet Yowell © 2006 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: May 18, 2007