0.20 Phy1180: energy -- potential energy  (Page 4/7)

The higher the starting point for the rock,

• the faster it would be going right before it strikes your head,
• the more kinetic energy it would possess at that point in time, and
• the more damage it would do to your head.

Gravitational potential energy is proportional to the product of mass, height, and gravity

Thus, the gravitational potential energy of an object that is elevated above the surface of the earth is equal to the product of the mass of the object, theheight of the object, and the acceleration of gravity. Expressed as an equation, we can write:

PEg = mass*kg * gravity*m/s^2 * height*m

where

• PEg represents gravitational potential energy
• mass, gravity, and height represent their namesakes
• kg, m, and s represent kilogram, meter, and second

Units of gravitational potential energy

As you can see from above, the units of gravitational potential energy are

kg*m^2/s^2 = kg*(m/s^2)*(m) = N*m = joule

What is the zero height reference?

Because the determination of gravitational potential energy requires knowledge of the height of the object, you must determine the height of theobject above a zero-height reference level. Therefore, to determine the gravitational potential energy of an object, you must first decide what levelyou are going to consider to be zero height.

The ultimate reference

The ultimate zero-height reference is the point in the center of the earth to which all objects are attracted. Using that point, however, would lead to a lotof arithmetic accuracy problems. The radius of the earth is something like 6378100 meters, and that depends on where on the earth you are standing -- deathvalley, Mount Everest, or somewhere in between.

I will leave it as an exercise for the student to determine why the use of the center of the earth as the zero-height reference might lead to arithmetic accuracy problems when doingcalculations involving gravitational potential energy.

Doubling the height doubles the gravitational potential energy

The gravitational potential energy of an object is directly proportional to its height above the zero position. Therefore, doubling or tripling the heightof the object above the zero position will have a corresponding doubling or tripling effect on the gravitational potential energy.

Elastic potential energy

Elastic potential energy is the energy stored in an object as a result of deforming the object within its elastic limit, such as stretching a rubber band,stretching a coil spring in a fisherman's scale, or compressing a coil spring in the suspension of an automobile.

The elastic limit

Many materials are elastic up to a point, some more than others. This means that they can recover from a deformation up to a point.

However, most materials have an elastic limit. The elastic limit is the point beyond which the material cannot recover from a deformation.

A rubber band

For example, if you stretch a rubber band by an inch or two, it will usually recover when the load is removed. However, if you stretch it too far, it willbreak. In that case, the rubber band has clearly been deformed beyond its elastic limit.