Gravitational Potential Energy

We have been doing a lot of formal analysis. Let's backtrack a little and try to understand better what we have done. Let's look at the conservative piece a little more closely and examine potential energy in more detail. Let's consider the simplest conservative force, namely the weight force where W = mg which is a constant. Let's work out W_C and ΔU in 1-dimension.

The gravitational force due to weight is

giving

which gives -U_f = -mgy_f , i.e. U_f = mgy_f and U_i = mgy_i. Thus we can simply write

which is our expression for gravitational potential energy. If an object is raised to a large height y then it has a large potential energy. If we do work in lifting an object, then we give that object potential energy, just as we can give an object kinetic energy by doing work. Similarly if an object has potential energy or kinetic energy then the object can do work by releasing that energy. This is the principle of hydro-electric power generators. A large amount of water is stored in a dam at a large height y with a large potential energy. When the water falls and reduces it potential energy (smaller y) the energy is converted into work to drive electric generators.