Gravitational potential energy is acquired by an object when it has been moved against a gravitational field. For example, an object raised above the surface of the Earth will gain energy, which is released if the object is allowed to fall back to the ground. In order for an object to be lifted vertically upwards, work must be done against the downward pull of gravity. This work is then stored as gravitational potential energy. When the object is released and falls towards the Earth, the potential is converted into kinetic energy, or movement.
A pendulum is a good example of the relationship between gravitational potential and kinetic energy. At its highest point, the pendulum has only potential energy. As it descends, this is converted into kinetic energy, reaching a maximum at its lowest point, where it has no potential energy. As it swings up again, the kinetic is converted to potential energy.
The amount of potential energy that an object possesses depends on the object’s mass or weight, its height above the surface, and the strength of the gravitational field. If the other factors are the same, a heavy object will have more gravitational potential energy than a lighter object. An object 1 mile (1.6 km) up in the sky will have more energy than the same object 1 foot (30.48 cm) from the surface. On the Moon, which has a weaker field of gravity than the Earth, an object will have less potential energy than the same object at a similar height above the Earth.
Calculating Gravitational Potential Energy
The potential energy of an object can be calculated as the mass of the object, multiplied by the gravitational force, multiplied by the height of the object above a given point. That point could be the surface of the Earth or it could be the floor of a room. In fact, the potential can be calculated for any point below the object.
The gravitational force is usually expressed as the acceleration experienced by an object allowed to fall freely, disregarding the effects of air resistance or friction. Although the strength of the gravitational field at the Earth’s surface varies from place to place, the variations are so small as to be almost negligible. In physics, therefore, the acceleration due to gravity near the surface of the Earth in usually considered a constant, with a value of approximately 32 feet (9.8 meters) per second per second (feet/s2 or m/s2). A simple potential energy formula for an object lifted up from the surface of the earth could therefore be stated as follows:
or
potential energy = mass of object in kilograms × 9.8 × height of object in meters
This formula works well for objects close to the Earth’s surface. It can easily be adapted to cope with similar scenarios in other gravitational fields, for example on the Moon or on Mars, by changing the value of the gravitational force accordingly. Since the strength of any gravitational field diminishes with distance from its source, however, this formula will only work for objects relatively close to the surface of a source of gravity, where the reduction in the gravitational force is too slight to be important. For objects relatively distant from a surface, the mass of the source of gravity and the distance from its center to the object must be taken into account.
Uses
Probably the most important use for gravitational potential energy is in hydroelectric power. Here, the potential energy of water in a lake or reservoir located high above a power plant is exploited to generate electricity. Water is allowed to descend from the reservoir, converting potential into kinetic energy, and the movement of the water drives a turbine, which generates an electric current. During periods of low demand, the power plant may have an excess of electricity, which can be used to pump water back up to the reservoir, building up more potential energy.
Another application is in counterweights, which are used in a number of mechanical devices. For example, some types of elevator employ a counterweight in such a way that it is descending when the elevator car ascends, and vice-versa. When the car is going up, the potential energy of the counterweight is converted to kinetic energy as it goes down, so that it helps pull the car up, reducing the amount of work that has to be done by the motor that drives the device. As the elevator car descends — helped by gravity — the counterweight is pulled back up, gaining potential energy.