1. HANDS-ON ACTIVITY: SWINGING PENDULUM CONTRIBUTED BY: INTEGRATED TEACHING AND LEARNING PROGRAM AND LABORATORY, UNIVERSITY OF COLORADO AT BOULDER

2. KEYWORDS energy, gravity, kinetic energy, pendulum, potential energy, mass, mechanical energy, roller coaster, velocity, work energygravitykinetic energypendulumpotential energymassmechanical energyroller coastervelocitywork

3. LEARNING OBJECTIVES Understand the concepts of potential and kinetic energy. Relate concepts of Kinetic and Potential Energy to real life examples, as well as to engineering examples.

4. Understand that a pendulum has a specific period, regardless of where the weight on the pendulum is started, or how much it weighs. Use the concepts of kinetic energy, potential energy, and conservation of energy to perform an experiment to determine an object's velocity

5. MATERIALS LIST 2 cell phones to use as stop watches Masking tape 10 feet of string 200 gram weight Calculator Each student needs a copy of the pendulum worksheet. 1 measuring tape/tape measure

6. PRE-ACTIVITY ASSESSMENT Where will the pendulum have the greatest potential energy? Where will it have the greatest kinetic energy? Will pendulums with higher heights go faster or slower?

7. INTRODUCTION 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).

8. 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.

9. Recall that energy may change its form, but there is no net change to the amount of energy. This is called conservation of energy.

11. EQUATIONS PE = m∙g∙h KE = ½ m∙V t 2

13. PROCEDURE Each group use an area that does not interfere with other groups. Tie the string to the ceiling and use enough string that it reaches all the way to the ground.

14. Class divided into 6 groups. The mass of the weight is 200 grams. Have each group pick an arbitrary height at which they will pull their weight back to and release their pendulums. This should range from 15-40 cm (.15-.4 m) from the floor.

15. Calculate the potential energy. The height in the PE equation will be the height of the weight when you pull it back minus the height when its hanging straight down toward the floor. Calculate the theoretical velocity, V t, at the bottom of the swing.

16. 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 floor on opposite sides of the hanging pendulum and record the distance between the two pieces.

17. 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.

18. 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.

19. 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?

20. Safety Issues Do not swing the weight and hit people.

21. POST-ACTIVITY ASSESSMENT 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)? For what might an engineer use this information?