# Activity Guide: Conservation of Energy

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The aerial acrobatics of the Russian Barre routine require exquisite balance, timing, and years of training. That's not enough though; conservation of energy plays a big role as well. At the top of the jump, Anna's energy is entirely potential but as she falls, her energy turns kinetic. Landing on the bar the energy changes form once more, stored as elastic energy in the bending bar. In this unit, students can learn the basics of these three common forms of energy.

## How to Incorporate the Video Into Instruction

This video can be used to motivate the study of kinetic, potential, and elastic energy, and their conservation. It can also serve as extra illustration to reinforce previous lessons on these topics. If you watch the video in class, ask students to pause the video at different points in the routine and compare the jumper's kinetic, potential, and elastic energy.

### Questions to Ask Students Before Watching the Video

1. What forms of energy do you see?
2. Where is the jumper's kinetic energy the greatest?
3. Where is her potential energy greatest?
4. How is she able to launch so high?
5. Where does the needed energy come from?
6. How high can a high-jumper jump?

## Watch the Video

### Questions to Kick-Start Class Discussion After the Video

1. How is the jumper able to go so high? How does the bar help?
The bar serves as a reservoir for elastic energy, allowing Anna to add some of the energy of her previous jump to her next.
2. How is the jumper's speed at the bottom related to her height at the top?
By setting P and K equal to each other, v= √(2gh).
3. What is energy? What is a Joule?
Energy is the ability to perform work. A Joule is the unit of energy.
4. How high a mountain could you climb with the energy in just one candy bar?
A typical candy bar has about one mega-joule of energy. Since most food in the US is labeled with calories instead, it's instructive to work through the conversion with the class first. Alternatively, you could look for a candy bar from another country. By setting this equal to potential energy, mgh, and using a reasonable value for m (about 80 kg for a large student), you can solve for h, which will be the max height climbable on the energy in one candy bar.
5. What are some forms that energy can take?
Kinetic, potential, elastic, chemical, heat, light, electrical...
6. Where does kinetic energy go when you stop a car? It goes into heating the brakes.
You might show a diagram similar to this...

...to illustrate how kinetic energy, the energy to be dissipated in brakes, scales quadratically, not linearly.

### Connections to Everyday Life

Driving illustrates energy concepts well. At the top of a hill, what determines the speed a car in neutral can reach? Braking distance...why is it harder to brake at higher speeds than lower? Traditional rollercoaster's use the potential energy present after the first large climb to power the cars throughout the entire track, loops, and all.

## Suggested Classroom Activities

### Activity 1: Rubber-band Machines

Give students popsicle sticks, tape, and a rubber band. Ask teams to build a machine that can launch a marshmallow the highest. The only energy in the system must come from rubber band. Ask students to find the amount of energy they are getting from their rubber band by measuring the max height and the mass of the marshmallow. The Russian Barre routine setup—a single elastic launcher suspended between two posts—can serve as design inspiration if students need an idea on how to get started.

### Activity 2: Dynamo

If you have access to an electromechanical generator, or dynamo, you can show the conversion of gravitational potential energy first into electrical energy, then into light. Attach a weight to a strong string wound around the axle of the generator. Connect the generator to a light bulb. Letting go of the weight will turn the axle, driving the dynamo, in turn lighting the light bulb. This demonstrates conservation of energy across two transformations. Ask students to think of places where some energy might be lost as heat, etc.

### Activity 3: Conservation of Energy Video Analysis

To do this activity you will need to download the video "Video Analysis: Conservation of Energy (QT)". Use VideoPoint or similar software for graphing and analysis.

Students will love watching Anna go through her routine transferring the elastic energy of the beam into her kinetic energy while she does work against gravity. The following figure shows a screen capture of a particular moment of her jump.

You can see from the red line that there is little drift in her horizontal position. The blue line shows the classic parabolic trajectory of an object only under the influence of gravity. Have students calculate the total energy of the jump using the position and velocity (from the slope) of Anna. Make sure to mark the origin. As a scale, consider the men holding the bar to be about two meters high.