Potential Energy
The potential energy of an object is generally defined as the energy an object has because of its position relative to other objects that it interacts with. There are different kinds of potential energy such as gravitational potential energy, chemical potential energy ...
Potential Energy
The potential energy of an object is generally defined as the energy an object has because of its position relative to other objects that it interacts with. There are different kinds of potential energy such as gravitational potential energy, chemical potential energy, electrical potential energy, to name a few. In this section we will be looking at gravitational potential energy.
Definition: Potential Energy
Potential energy is the energy an object has due to its position or state.
Definition: Gravitational Potential Energy
Gravitational potential energy is the energy an object has due to its position in a gravitational field relative to some reference point.
Quantity: Gravitational potential energy (\({E}_{P}\)) Unit name: Joule Unit symbol: J
In the case of Earth, gravitational potential energy is the energy of an object due to its position above the surface of the Earth. The symbol \({E}_{P}\) is used to refer to gravitational potential energy. You will often find that the words potential energy are used where gravitational potential energy is meant. We can define gravitational potential energy as:
\[{E}_{P}=mgh\]where \({E}_{P} =\) potential energy (measured in joules, \(\text{J}\))
\(m =\) mass of the object (measured in \(\text{kg}\))
\(g =\) gravitational acceleration (\(\text{9.8}\) \(\text{m·s$^{-2}$}\))
\(h =\) perpendicular height from the reference point (measured in \(\text{m}\))
Tip:
You may sometimes see potential energy written as PE. We will not use this notation in this book, but you may see it in other books.
You can treat the gravitational acceleration, \(g\), as a constant and you will learn more about it in Newton's laws.
Let's look at the case of a suitcase, with a mass of \(\text{1}\) \(\text{kg}\), which is placed at the top of a \(\text{2}\) \(\text{m}\) high cupboard. By lifting the suitcase against the force of gravity, we give the suitcase potential energy. We can calculate its gravitational potential energy using the equation defined above as:
\begin{align*} {E}_{P} & = mgh \\ & = \left(\text{1}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{2}\text{ m}\right) = \text{19.6}\text{ J} \end{align*}If the suitcase falls off the cupboard, it will lose its potential energy. Halfway down to the floor, the suitcase will have lost half its potential energy and will have only \(\text{9.8}\) \(\text{J}\) left.
\begin{align*} {E}_{P} & = mgh \\ & = \left(\text{1}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{1}\text{ m}\right) = \text{9.8}\text{ J} \end{align*}At the bottom of the cupboard the suitcase will have lost all its potential energy and its potential energy will be equal to zero.
\begin{align*} {E}_{P} & = mgh \\ & = \left(\text{1}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{0}\text{ m}\right) = \text{0}\text{ J} \end{align*}This example shows us that objects have maximum potential energy at a maximum height and will lose their potential energy as they fall.
This lesson is part of:
Work, Energy and Power