## Introduction: Work, Power, and the Conservation of Energy Through Roller Coasters

This is a project that I wrote for my high school physics classes to apply the work, power, and energy formulas to an engineering design project. The project involved students constructing a roller coaster track for a marble out of high water pipe insulation. One they had constructed a working coast, they took measurements to calculate the energy loss of the coaster.

Students then redesigned their coaster to be more efficient and recalculated the energy loss to compare it to their first attempt. The overall question they were answering was what design changes would increase the energy lost of the marble as it traveled down the track. I designed this activity to address one specific performance expectation in the Next Generation Science Standards:

**HS-PS3-2**.Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative positions of particles (objects). [Clarification Statement: Examples of phenomena at the macroscopic scale could include the conversion of kinetic energy to thermal energy, the energy stored due to position of an object above the earth, and the energy stored between two electrically-charged plates. Examples of models could include diagrams, drawings, descriptions, and computer simulations.]

## Step 1: Resource Booklet for Students

The reference I provided the students to use during the project is a single page that is folded into the form of a mini book. I make these little books for each of the major topics that I teach, this one contains material about the conservation of energy and rotational mechanics including the formulas for several different moments of inertia.

I have attached the student instructions and the file to produce the little booklet of helpful information. If you need instructions on how to assemble the book see this instructable:

## Step 2: Roller Coaster Design, Construction, and Analysis

Here is the assignment information I provided to the students:

**Design Task**

Design and build a segment of roller coaster for a marble using foam track. Sketch a diagram of your roller coaster, label the dimensions of your coaster on the diagram. Based on your model calculate:

- the theoretical speed at which the marble reaches the bottom of your roller coaster track assuming no loss of mechanical energy. Be sure to include rotational kinetic energy in your calculation.
- the actual speed at which the marble reaches the bottom of your roller coaster track. The only tools you are permitted to use for this determination are one and two meter sticks.
- the total amount of energy lost to the environment during the roller coaster.

Write a detailed explanation of how you completed each of these three calculations.

## Step 3: Coaster Redesign for Increased Efficiency

**Redesign Task**

Redesign your segment of roller coaster to make a more efficient track. Sketch a diagram of your roller coaster, label the dimensions of your coaster on the diagram. Repeat the same three calculations you completed for your first roller coaster.

## Step 4: Student Product

After their investigation, students complete their calculations for the work and kinetic energy loss between the original design and their redesign. An example of student calculations is included in the photo. It is interesting to see how little energy is lost when students stabilize their tracks and loosen tight curves to reduce friction on the turns.

**Design Analysis Questions**

1. You calculated the amount of energy lost by your first design. In what forms was this energy lost? Be specific in analyzing the motion of your first roller coaster.

2. What percent improvement in energy loss were you able to make in your redesign?

3. How did you modify your roller coaster to improve its efficiency? What do you think was the most effective at reducing energy loss?

4. How much work was done on the marble in completing its run on your first roller coaster? Explain how you completed this calculation.

5. What force was doing this work on the marble?

6. How much work was done on the marble in completing its run on your second roller coaster?

7. How much power was developed as the marble completed the second roller coaster? Explain how you completed this calculation.

8. What percentage of the total energy of the marble at the bottom of your track was translational kinetic energy and what percentage was rotational kinetic energy?

9. How would the translational speed of the marble at the bottom of the track be affected if the mass of the marble were doubled?

10. How would the translational speed of the marble at the bottom of the track be affected if the marble had been a hollow sphere instead of a solid sphere? Give a numeric answer and show how you arrived at your result.