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Roller Coaster Design: Gravitational Potential and Kinetic Energy

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Roller Coaster Design: Gravitational Potential and Kinetic Energy

Physical Science

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Kinetic and gravitational potential energy are introduced and modeled relative to each other using a roller coaster

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Define gravitational potential energy as the energy stored in an object as the result of the object’s vertical position.
  • Define kinetic energy as the energy of motion due to a moving object’s speed.
  • Describe the changes between gravitational potential energy and kinetic energy as an object moves up and down hills.

Everything You'll Have Covered

In the study of physics, energy can be transferred from one object or system to another. All objects and systems possess energy and energy can be transformed from one form of energy into another, or the energy can be transferred from one object to another, but the total energy will remain the same. This is expressed in the Law of Conservation of Energy, which states that energy can not be created, or destroyed; it simply exists, and is most readily observed when converted from one form to another, or transferred from one object to another. Einstein showed this law is not always accurate because, in certain situations such as nuclear reactions, mass can be conerted into energy according to the famous equation E=mc2. However, this is beyond the scope of this Activity Object.

There are several different forms of energy that include thermal, gravitational, acoustic, light, elastic, nuclear, and electromagnetic energy.

This Activity Object explores two types of mechanical energy: gravitational potential energy and kinetic energy. Gravitational potential energy is the energy stored in an object as a result of its vertical position, or height. In other words, the potential energy of an object is a function of its position. Kinetic energy is the energy of motion, or the function of an object's movement. The faster an object is moving, the more kinetic energy it possesses.

This Activity Object explores the relationship between potential and kinetic energy as a rollercoaster car goes up and down. In middle and high school physics, the affects of friction or air resistance are removed from problems and simulations to help illustrate concepts.

Both position and movement are relative to a frame of reference, which must be specified, such as the Earth, or a moving roller coaster car. For instance, the gravitational potential energy stored in a roller coaster car at the top of a hill, versus the bottom of a hill, depends on the gravitational pull, or force applied to the object, due to its proximity to the Earth. Likewise, a seated passenger in the moving roller coaster car has zero kinetic energy relative to the roller coaster car, but positive kinetic energy relative to Earth. This is why a person can walk around in an airplane under flight, or why a bug can fly around in a car while the car is being driven. The energy expended to move within either vehicle is only relative to the moving vehicle, rather than the Earth; thus, the same amount of energy would be spent by the person walking in the airplane as if they were walking on the ground.

Generally, one form of energy can be readily transformed into another form of energy by employing some device or mechanism. For instance, an electric motor moves a roller coaster car from its starting point to the top of the first hill on the track, and thus electric energy is transformed into gravitational potential energy as the car goes higher and higher. At the top of the hill, the roller coaster car has maximum gravitational potential energy. As it rolls down the hill, that energy is converted into kinetic energy. The farther down the hill the roller coaster car goes, the more gravitational potential energy is converted into kinetic energy.

Because this Activity Object is introductory in nature, the effects of friction are not part of the simulation. It should be noted, however, that in the real world, friction occurs when two objects move past one another, which results in the production of heat. Heat is the transfer of energy from one object or system to another. Therefore, rather than the perfect, one-to-one relationship between kinetic and potential energy that this Activity Object demonstrates without friction, a roller coaster car moving down a track would experience friction and produce heat, thus transferring energy from the roller coaster to the track or the air. The remaining kinetic energy of the car is therefore less than the original gravitational potential energy. More simply, the original gravitational potential energy would equal the kinetic energy produced through movement, whether stored in the coaster car or transferred to the atmosphere, plus the thermal energy produced through friction that is transferred to the track or the air.

Tutorial Details

Approximate Time 30 Minutes
Pre-requisite Concepts Energy, gravity, maximum, position, relative, speed, transfer, vertical
Course Physical Science
Type of Tutorial Concept Development
Key Vocabulary amusement park, build, design