Purpose: a) To build a functional rollercoaster. b) To gather rollercoaster performance data at key locations. c) To mathematically analyze the data. d) To interpret the trends in the data.

Procedure:

1. Use the given apparatus to build a working rollercoaster. After the first hill you must have at least one more hill and one loop. Your rollercoaster works when the car can make it all the way along the track without coming off of the track.

2. Collect data on your rollercoaster for each peak and valley and the side of one loop. Sketch the shape of your rollercoaster and letter each peak and valley and the side of one loop. Set up data table columns for lettered postion, height, average velocity (measured using a photogate), and track radius parameters "A" and "B" (using the T-shaped device). Attach the plastic prongs to the rollercoaster car and record the car mass. Measure heights to the center of mass of the cart while the photogate beam passes between the two prongs at the point marked with a silver line.

To determine the track radius, use the T-shaped device to measure the length of the semichord, A, and the distance from the chord to the curve, B. The radius of the curve can then be calculated by:

track radius = [((A^2-B^2)/(2B))^2 + A^2]^.5

If you would like to derive the radius equation presented above, I will be happy to give you extra credit.

3. Calculate corrected radius and velocity values. Because the track radius, cart's center of mass radius, and the photogate flag's radius are not the same, some corrections are needed.

cart path radius = track radius + 2.0 cm       (plus for hills; minus for valleys and loops)

corrected velocity = measured velocity x [cart path radius / (cart path radius + 2.5 cm)]       (plus for hills; minus for valleys and loops)

4. Mathematically analyze your rollercoaster data. For each lettered point on your rollercoaster, calculate the following values: gravitational energy, kinetic energy, dissipated energy, cart path radius, centripetal force, normal force, Fnormal/mass, and Fnormal/Fgravity. Show an example of each type of calculation in an organized manner and use units! Make a table that summarizes your calculated results and includes a quantitative force diagram for the car at each lettered point on your rollercoaster.

5. Assemble your written report: (Typed and double-spaced)

 a. (5pts) Make a title page with a photo of your rollercoaster. Pictures will be posted on the class website.

 b. (5pts) Describe the materials and procedures used to build the rollercoaster.

 c. (5pts) Explain your procedure for measuring height, velocity, and track radius.

 d. (8pts) Data table (with a sketch of the rollercoaster) including the measurements from section 2 and corrections from section 3. (This does not need to be typed.)

 e. (10pts) Your calculated values and force diagrams in a concise, well-labeled table, with an example of each calculation clearly shown as part of the column header, for all of the quantities listed in section 4. (This does not need to be typed.)

 f. (6pts) Explain why and where the gravitational energy increases and decreases. Also explain why and where the kinetic energy increases and decreases.

 g. (6pts) Describe the trend in the dissipated energy and state the reasons for the trend. Propose reasons for any discrepancies between what was expected and what was observed.

 h. (5pts) Explain why and where the normal force increases and decreases in terms of speed and track radius. Refer to your force diagrams in your explanation.

 i. (5pts) The ratio of Fnormal/Fgravity (also called force factor) along the head-to-toe axis increases and decreases just like the normal force does, but it is much more useful from the standpoint of finding the forces on the rider. Why? (Explain how you can use a measured value of Fnormal/Fgravity to find the normal force on any rider.)

 j. (5pts) For each lettered position, quantitatively describe what it would feel like to ride on your rollercoaster, assuming that you could shrink down and fit on it. Use the head-to-toe force factor (Fnormal/Fgravity) calculation to determine how many times "heavier" or "lighter" you would feel.

All pages must be neat, in order, stapled, and 3-hole punched.

Your report is worth 60 points.