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## Investigating Kinetic and Potential Energy

Lesson Summary

### Overview

In this lesson, students use a variety of resources to explore the concepts of potential, kinetic, and total energy withindifferent types of systems. Students watch a video that explains the transfer of energy in a trebuchet’s release, use an interactive activityto determine the types of energy involved in different parts of a roller coaster ride, do an in-class investigation that demonstrates theeffect of mass and gravity on energy systems, explore the difference between gravitational and elastic potential energy, and finally, use theformulas for kinetic and potential energy to examine the path of a projectile.

### Objectives

• Understand the difference between kinetic and potential energy
• Identify the types of potential energy in a system
• Identify the areas in a system where potential and kinetic energy exist
• Apply the formulas for kinetic and potential energy to determine the amount of energy in a system

### Suggested Time

• Three to five class periods

### Materials

• Ramps or chutes
• Marbles

For each group of two students:

### Before the Lesson

• Acquire materials for each group—groups of two work best. If you prefer groups of three or four, students can take turns dropping or rolling, measuring, and recording.
• If possible, arrange computer access for all students to work individually or in pairs.
• Print and copy PDF documents for each group.

### Part I: Researching Energy

1. Introduce the concept of energy by showing students the Energy Transfer in a Trebuchet QuickTime Video. Ask students to identify the forces they see at work on the trebuchet as well as where the energy for the launch comes from. (See the Teacher Notes PDF Document.)

2. Tell students that they will be learning about the forms of energy that exist in a system, as well as the forces that act upon that system, affecting the energy.

3. Discuss with students the concepts of kinetic and potential energy and define each. Be sure to discuss the difference between mass and weight, and the magnitude of gravitational acceleration, as these are included in the formulas to be used in part two. (See the Teacher Notes PDF Document.)

4. Have students explore gravitational potential energy and kinetic energy, using a marble and a ramp or chute. As they release the marble and watch it roll down the ramp, have them identify where each type of energy occurs. Then discuss the total energy of the system as the sum of the two.

5. Have students read the What Is Energy? PDF Document. Tell them to begin with the introduction – “What Is Energy?" then read Part B, "Two Main Forms of Energy." When they have finished reading, allow students to askquestions.

6. Next, have students visit the Energy in a Roller Coaster Ride Flash Interactive. Before settingthe ride in motion, have students draw the path of the roller coaster in their journals and predict where the potential and kinetic energy are likely to be highest and lowest.

7. Students should then view the interactive activity, first at full speed, by clicking on the "play" button and focusing on the graph depicting how the forms of energy change as the coaster cars move along the track, and then in step form to view the motion in detail.

8. Discuss the interactive activity with students, reinforcing the concepts of kinetic and potential energy. How do the predictions they made in their journals compare with what the activity is showing them?

9. Have students draw a roller coaster track of their own design and label the areas of maximum and minimum potential and kinetic energy. This is also a good place to discuss the outside forces that affect the energy in the system, such as friction and air resistance, as well as the heat (thermal energy) produced by the movement in the system. (See the Teacher Notes PDF Document.)

### Part II: Assigning Value to Energy

10. Have students read the Kinetic and Potential Energy PDF Document. This handout introduces the idea ofelastic potential energy (as in a rubber band) and provides the formulas for calculating kinetic energy and gravitational potential energy,as well as sample problems for each.

11. After discussing the energy formulas, have the students do the activity below and complete the data sheet in order tocalculate gravitational potential energy. Be sure to review the fact that Weight = Mass (kg) × Gravitational Acceleration.

Activity: Energy in a Golf Ball

1. Provide each group of two students with one golf ball, one meter stick, one balance, and two copies of the Energy in a Golf Ball Activity Data Sheet PDF Document.
2. Have students determine the mass of the golf ball in grams, and then convert to kilograms. Tell them to recordthe data in the first two columns of the data sheet.
3. Have students calculate the weight of the golf ball in newtons and record it in the third column.
4. Have one student in each group hold the meter stick, while the other holds the golf ball one meter high. Recordthe height of the ball in the fourth column of the data sheet.
5. Have students then calculate the gravitational potential energy (GPE) of the ball using the following formula:GPE = Weight (N) × Height (m).
6. Tell the student holding the ball to drop it, and the other student to measure how high it bounces back up.Have them record the height of the bounce on the data sheet and use the new height to calculate the amount of GPE that remains after thefirst bounce. Tell them to record the new GPE on the data sheet. Do the results support the fact that the new GPE is less than the startingGPE? Discuss the fact that energy is absorbed by the floor, as well as the role that forces such as gravity and air resistance play when theball makes its journey upward. (See the Teacher Notes PDF Document.)
7. You can also mention the creation of thermal energy by the system. Does the temperature of the ballchange?
8. Have students repeat this activity, dropping the ball from different heights. Do the results match those of theoriginal test?
9. Have students also make note of how the bounce height changes if the ball is left to bounce until itstops.
10. Finally, students can time how long it takes a ball dropped from a particular height to stop bouncing and usethis data as a way to compare the time of bounce to the original amount of GPE. Does a ball dropped from a higher height have a longer bouncetime?

Discussion: Energy in a Golf Ball

• How does the GPE change as the height from which the ball is dropped changes?
• How does the GPE change as the ball continues to bounce?
• What forces besides gravity are acting on the ball as it bounces?
• How do you account for the change in GPE?

### Part III: Experimenting with Elastic Potential Energy, Thermal Energy, and Outside Forces

12. Direct students to the Masses and Springs Flash Interactive. Here, students canexperiment with elastic potential energy (EPE) under a variety of conditions, changing variables such as the size of the mass, friction,spring tension, and even the gravitational pull of the celestial body on which the experiment occurs. They can also view the experiment inslow motion and use the ruler to measure the distance that each weight causes the spring to stretch. As students work with the interactiveactivity, have them test individual variables by turning the other variables off. Then have them answer the questions below in theirnotebooks. Tell them to also record any of their own questions that arise while they are investigating.

1. What is the effect of friction on the motion of the masses, on the spring, and on the energy levels?
2. What is the effect of the stiffness of the spring on the motion of the masses and on the energy levels?
3. How does the initial stretch of the spring affect the motion of the masses and the energy levels?
4. What is the effect of gravity on the motion of the masses, on the spring, and on the energy levels?
5. Draw a diagram of one of the springs in motion. Indicate where the potential energy of the spring is highestand lowest and where there is increased kinetic energy.
6. What is thermal energy ("heat" on the energy graph) and how does it change as the spring continues tomove?

13. After examining the variables individually, students can experiment with combining variables and examine the variouschanges that occur within the system.

14. When students are finished experimenting with the interactive activity, have them answer these questions:

1. How does EPE differ from GPE? Give examples of other systems in which each type of energy exists and describe howthey change as the motion within the system progresses. Does GPE also exist in the spring system?
2. Which factors affect thermal energy? What do you notice about the makeup of the total energy of the system as thevariables are changed?
3. Is thermal energy change present in systems that have GPE? Give examples.

### Check for Understanding

1. In order to reflect on what they have learned, have students revisit the Energy Transfer in a Trebuchet QuickTime Video and indicate where the minimum and maximum GPE and KE (kinetic energy) of the system are found.
2. Ask students to give examples of other systems and describe how the PE (potential energy) and KE function in them. Then ask:
1. What are some of the factors that affect the amount of PE in a system?
2. How do outside factors, such as gravity, friction, and air resistance, affect the amount of PE that is transferred to KE ina system?

### Extensions and Challenges

• Direct students to the Projectile Motion Flash Interactive. This activity allowsstudents to change variables — such as mass and speed of a projectile, and angle of launch — while attempting to hit a target. In addition,the measuring tool allows them to determine the highest point the projectile has reached, and this height can be used to calculate the GPE ofthe object.
• After students have had an opportunity to explore the interactive activity, ask these questions:
• Where is the PE greatest? Smallest?
• Where is the KE greatest? Smallest?
• What happens to the PE as the KE increases?
• What difference do the mass and shape of the projectile make in the absence of air resistance?
• Compare the horizontal distance the object travels during the first and second seconds. Can you find evidence that thehorizontal velocity changes over time? What about the vertical velocity?
• Have students drop objects other than golf balls from varying heights onto different materials and measure the relativeamount of GPE. Are the results similar to the golf ball data? Does the type of surface on which the object lands make a difference? Why?
• Have students visit NOVA Medieval Siege for an interactive experience with the factors affecting how atrebuchet fires.
• Have students design and build model trebuchets like the one seen in the video and test them using different-size masses ascounterweights. The GPE can be determined by measuring the height to which the counterweight is raised. Examples of materials that can beused to build the trebuchets include LEGO’s® and balsa wood. (Examples of LEGO® trebuchets are available online.)

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