What is an example of gravitational potential energy in a roller coaster?

For most roller coasters, the gravitational potential energy of the cars at the peak of the first hill determines the total amount of energy that is available for the rest of the ride. Traditionally, the coaster cars are pulled up the first hill by a chain; as the cars climb, they gain potential energy.



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Gravitational potential energy is the energy that an object has because of its height and is equal to the object's mass multiplied by its height multiplied by the gravitational constant (PE = mgh). Gravitational potential energy is greatest at the highest point of a roller coaster and least at the lowest point.

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At the highest point on the roller coaster (assuming it has no velocity), the object has a maximum quantity of gravitational potential energy and no kinetic energy. As the object begins moving down to the bottom, its gravitational potential energy begins to decrease and the kinetic energy begins to increase.

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According to Kevin Hickerson, a physicist at the California Institute of Technology, “All the energy a roller coaster gets comes from the initial point it's cranked up to, and from there it just gains more and more kinetic energy.” The height of this first drop also determines the speed of the coaster cars.

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Most roller coasters run by the Law of Inertia. Since an object at rest stays at rest, all roller coasters have to be pushed or pulled to get started.

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Gravity always pulls downward with the same strength, and, in the case of a roller coaster, it pulls downward on the cars wherever they are on the track. Near the bottom of a loop, gravity pulls in a direction away from the center of the loop circle.

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The coaster will roll on indefinitely, or until of course the end of the track, where unbalanced forces like friction between the track and the wheels slow the coaster ultimately to a stop. The riders, which have inertia, are also acted on by unbalanced forces throughout the ride, causing them to change their motion.

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Basic mathematical subjects such as calculus help determine the height needed to allow the car to get up the next hill, the maximum speed, and the angles of ascent and descent. These calculations also help make sure that the roller coaster is safe. No doubt about it--math keeps you on track.

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