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Roller Coaster Physics

In the Go Figure video, the roller coaster, Batman, at Six Flags St. Louis, is featured. The following problems were developed by the St. Louis Area Physics Teachers Association for Physics Day at the theme park.

1.Average Acceleration
On a roller coaster, the angle of inclination of the first drop is 50 degrees. A car has a speed of 2 m/s at the top of the incline, which is 50 m long. If it takes 3.8 seconds for the car to travel down the incline, calculate the average acceleration of the car.

Answer: D = 1/2 at2 + vt

50 m = 1/2 a (3.8 s)2 + (2 m/s) (3.8 s)
50 m - 7.6 m = 1/2 a (3.8 s)2
a = 42.4 m (2) / (3.8 s)2
a = 5.9 m/s

2. Finding Your Potential Energy

Potential Energy Graph

PE = mgh

Your potential energy at B, the top of the first hill, is the total energy you will have throughout the ride. If we ignore friction, this total energy is the sum of your potential energy and kinetic energy at any given moment. Let potential energy be 0 on the ground and calculate your potential energy at B. This is now your total energy (TE) for the ride.

TE = __________

3.Getting to the Top: Work and Power
The potential energy at B is a combination of the work you did to get to A and work the coaster did to get your from A to B.

Work = mghA

3a. Find the work you did climbing the stairs, which have a height of 7.2 m.

Work on stairs = _______

3b. Subtract the work you did from the total energy to find the work the coaster did to pull you to the top.

Work AB = _______

Power = work/time

3c. Calculate the power the ride used to get you from A to B.

Power = _______

4. Energy and Speed Down at the Bottom

PE = mgh; TE = PE + KE

During the ride you must account for your total energy as the sum of the potential energy and kinetic energy. At D the potential energy is not 0. (At this point, h = 6.4 m). Fill in the chart below to find your kinetic energy at the bottom.

TE = ___________ PE = ___________ KE = ___________

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Last Updated: 02/16/03
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