The Conservation Of Energy Roller Coaster animation on this page explores the conservation of kinetic and potential energy. You can interact with the animation, and immediately see the effects on the roller coaster train. The animation is accompanied by a discussion.
A roller coaster train is carried uphill on the roller coaster lift hill, which gives the train a huge initial potential energy (height) and extremely small kinetic energy (speed). The train is released and then coasts through the rest of the track, giving up potential energy and gaining kinetic energy when traveling downhill, and giving up kinetic energy and gaining potential energy when traveling uphill.
In this animation, you can...
The energy curves can be "stacked" or "unstacked". When the energy curves are stacked, the kinetic energy curve is added to the potential energy curve, which helps to show how their total stays constant.
There are actually multiple types of potential energy, so it should be stated that the potential energy mentioned in this web page is "gravitational potential energy", which is the energy due to the train's height in a gravitational field. The gravitational potential energy is computed using PE = mass * gravity * height. When height increases, the potential energy also increases.
There are actually multiple types of kinetic energy, so it should be stated that the kinetic energy mentioned in this web page is "linear kinetic energy", which is the energy described by the train's speed. The linear kinetic energy is computed using KE = 1/2 * mass * speed2. When speed increases, the kinetic energy also increases.
Although the potential energy and kinetic energy change quite a bit, their total ideally stays constant (at 100%) starting at the top of the lift hill and while the train coasts around the roller coaster. In this ideal case, we say that the total energy is "conserved", and we can use the following equations:
TEa = TEb
KEa + PEa = KEb + PEb
where TE=train's total energy, KE=train's kinetic energy, PE=train's potential energy, and a and b are any two points between the top of the lift hill and the end of the roller coaster. In this simulation it is often useful to consider the top of the lift hill as point a.
In the real world, energy gets lost in various ways to the surrounding environment over time, so the total energy of the train slowly drops from its initial value of 100%. These unwanted energy losses reduce the train's kinetic energy, and the speed in turn. Energy is still conserved if we consider the train and the environment together, because the energy lost by the train equals the energy gained by the environment. In this real world case, we can use the following equations:
TEa = TEb + ELb
KEa + PEa = KEb + PEb + ELb
where EL=energy lost to the environment.
Of course, there is one energy loss that we want - brakes that slow the tr ain down at the end of the ride so we can get off.
Here are some questions that are answered in the text of this web page, including the equations, or by experimenting with the animation:
Here is a question that is not answered in this web page: