When looking at potential energy you have to consider a force field. The potential energy occurs when an object is situated within the force field.

Force Field

For there to be potential energy there have to be forces that acts on a body in a way that only depends on the position of the body in space. These kinds of forces can be represented by a vector at every point in space. This representation forms a vector field of forces that is rather known as a force field.

An example of a force field is the earth’s gravitational field. At college level, we learnt during our physics tuition classes, that the gravitation potential energy of an object can be mathematically be expressed as: U = – GMm/r

Where U is potential energy measured in Joules, M is the mass of Earth while m is the mass of the object being considered, measured in kilograms, G is the gravitational constant and r is the distance between the C.G. of Earth and C.G. of the object.

Common Types of Potential Energy

Potential energy can be classified into different types which include:

1. Gravitational potential energy: As discussed above, this energy is as a result of the position of an object in relation to its height from the earth’s surface.

2. Elastic potential energy: This type of potential energy is as a result of the stretching of a solid substance/object like the spring. The potential energy for a spring is mathematically represented as: E.P.E = 1/2 kx^{2}

3. Electric potential energy: This potential energy is associated with the electric charges that are present within an electric field. The work required to move q from point to any point in an electrostatic force field is given by a function that represents the electric potential energy:

Potential Energy near Earth’s Surface

Gravitational potential energy near Earth’s surface can be mathematically represented as: G.P.E. = mgh

Gravity exerts a constant force *F*= (0, 0, *F** _{z}*) that acts downwards on the center of mass of a body moving near the surface of the Earth. From the potential energy for the near earth gravity, the work done on a body moving along a trajectory

*r*(t) = (

*x*(t),

*y*(t),

*z*(t)), is calculated using its velocity,

*v*= (

*v*

_{x},

*v*

_{y},

*v*

_{z}). With this the following equation is obtained and used:

The integral of the vertical component of velocity is the vertical distance (height).