Conservation of Momentum & Energy

Conservation of Momentum & Energy

Potential Energy

Tibetan archer, 1938. WikipediaObjects can “store” energy. This can happen as a result of an object’s height in a gravitational field or its placement in an elastic material such as a spring, bow and arrow, slingshot, etc. This stored energy is called “potential energy”. It is the potential for movement, and you will remember, kinetic energy is energy from movement. In these cases, energy is stored as a result of position. A roller coaster awaiting passengers has no potential energy. It acquires potential energy as it is pulled to the top of the first crest and converts it into kinetic energy as it goes down. An arrow in a quiver has no potential energy, but acquires it as it and the string are pulled back. When the string is released, the potential energy of the bow and the arrow are converted into kinetic energy for the arrow, and the potential energy of the bow drops to zero.


Gravitational Potential Energy

The energy acquired by an object by virtue of its height in a gravitational field is called gravitational potential energy. It is dependent not only on the height of the object but also on its mass. Potential energy, PE, is expressed as:


gravitational potential energy = mass x gravity x height PE = mgh

Where m = mass, g = the acceleration due to gravity or gravitational field strength (9.8 m/s2 on Earth) and h = height.


To determine on object’s PE, we must first establish a zero height, typically the surface of the Earth. But imagine doing an experiment in a subterranean cave, or on a mountain top, table top, or Earth orbit! The zero height is purely arbitrary again, but it is often convenient to use the ground. From the above equation, you can see that doubling the height doubles the PE, and doubling the mass also doubles the PE. This is a simple linear relationship with no square or square root operators. This works well near the surface of the Earth. As we leave the Earth’s surface, moving outward toward space, the acceleration due to Earth’s gravity diminishes so that equation 3.3 becomes less accurate; on Earth it is fine.

Try It!


What is the potential energy of a 70 kg diver standing on the 10 meter high diving platform?




Answer: 6,860 J

PE = mgh = 70 kg * 9.8 m/s2 * 10 m = 6,860 J

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