potential energy - Gravitational potential energy

The energy stored by an object by virtue of its position in the region of influence of some force; symbol V, units J (joule). For example, an object acquires potential energy equal to the work done against the force of gravity in raising it above the Earth's surface; when released, the object falls to the ground, and its potential energy is converted into kinetic energy, the energy of motion. Work done in compressing a spring is stored as elastic potential energy in the spring. The potential energy of a positive electric charge may be increased by bringing it closer to another positive charge.

Energy Portal

Potential energy is energy that is "captured" in an object, with the potential to be released. Many of these – such as gravitational, elastic, or electrical potential energy – arise from the relative positions or configurations of objects. The potential energy may then be defined as the work that must be done against a particular force – in these examples, gravitational, electrical or elastic force – so as to achieve that configuration. Chemical potential energy is slightly different, at least in its macroscopic manifestation: it is the energy that is available for release from chemical reactions (for example, by burning a fuel).

Gravitational potential energy

Gravitational potential energy exists in any system in which masses are separated.

In its most familiar manifestation on earth, gravitational potential energy is the energy that would be released if an object was allowed to fall from its current position to a given reference level (such as the surface of the earth).

For example, a book lying on a table has greater gravitational potential energy than the same book on the floor, but less than if it were on top of a tall cupboard. (If the book is lifted by a person then this is provided by the chemical energy obtained from that person's food and then stored in the chemicals of the body.) Assuming perfect efficiency (no energy losses), the energy supplied to lift the book is exactly the same as the increase in the book's gravitational potential energy. As the book falls, its potential energy is converted to kinetic energy.

The factors that affect an object's gravitational potential energy are: the mass of the object, the height to which it is raised, and the strength of the gravitational field in which it is raised.

Uses

Gravitational potential energy has a number practical uses, notably the generation of hydroelectricity. At times when surplus electricity is not required (and so is cheap), water is pumped up to the higher lake, converting the electrical energy to gravitational potential energy. At times of peak demand for electricity, the water flows back down through turbines, converting the potential energy into kinetic energy and then back into electricity.

Simplified calculation

Assuming that the opposing gravitational force is constant, the work done in raising an object is equal to the force applied multiplied by the distance through which the object is raised. The gravitational force that must be overcome is equal to the object's mass multiplied by the acceleration due to gravity, so the object's gravitational potential energy, Ug, is given by

where

m is the mass of the object g is the acceleration due to gravity (approximately 9.8 m/s2 at the earth's surface) h is the height to which the object is raised, relative to a given reference level (such as the earth's surface).

The equation shows that gravitational potential energy is proportional to both mass and height. For example, raising two similar objects, or raising the same object twice as far, doubles the potential energy.

To calculate potential energy with varying g it is necessary to sum all the individual increments of potential energy as the masses are separated, taking account of the varying value of g as we go.

With this simplifying assumption, integrating force over distance leads to the following general expression for the gravitational potential energy, Ug, of a system of two masses:

where

m1 and m2 are the masses of the two objects G is the gravitational constant (not to be confused with the g used earlier) h1 is the reference level (the separation at which potential energy is considered to be zero) h2 is the actual distance between the objects.

For example, in the case of a small object above the surface of the earth, with reference level at the surface, m1 and m2 are respectively the masses of the earth and the object, h1 is the distance from the earth's centre to the earth's surface, and h2 is the distance from the earth's centre to the object.

If we try to calculate an "absolute" potential energy by setting the reference level at zero then the formula "blows up" with division by zero.

Using this convention, potential energy is zero when r is infinitely large, and negative at any finite r.

Ug as calculated above measures the potential energy of the whole system. The sum of the kinetic energy gained by the two objects is exactly equal to the decrease in the potential energy of the system. In some sense, therefore, we can say that almost all the potential energy of the system is embodied in the light object, and almost none in the very massive object.

Gravitational potential

Gravitational potential is the potential energy per unit mass of an object due to its position in a gravitational field.