What does the gravitational potential energy of a roller coaster car depend on?
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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A roller coaster is a machine that uses gravity and inertia to send a train of cars along a winding track. The combination of gravity and inertia, along with g-forces and centripetal acceleration give the body certain sensations as the coaster moves up, down, and around the track.
As they race down the other side of the hill, the potential energy becomes kinetic energy, and gravity takes effect, speeding the cars along the track. Furthermore, while the cars are rolling along the track, the energy from the cars is transferred elsewhere because of friction.
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.
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.
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.
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.
At the top of a roller coaster, the car goes from moving upward to flat to moving downward. This change in direction is known as acceleration and the acceleration makes riders feel as if a force is acting on them, pulling them out of their seats.
The gravitational potential energy of an object depends on its mass and height above reference level, while the kinetic energy of an object depends on its mass and velocity.