Converting Between Potential Energy and Kinetic Energy

Converting Between Potential Energy and Kinetic Energy

Gravitational potential energy may be converted to other forms of energy, such as kinetic energy. If we release the mass, gravitational force will do an amount of work equal to \(\text{mgh}\) on it, thereby increasing its kinetic energy by that same amount (by the work-energy theorem). We will find it more useful to consider just the conversion of \({\text{PE}}_{\text{g}}\) to \(\text{KE}\) without explicitly considering the intermediate step of work. We will look at an example of this in the next lesson. This shortcut makes it is easier to solve problems using energy (if possible) rather than explicitly using forces.

(a) The work done to lift the weight is stored in the mass-Earth system as gravitational potential energy. (b) As the weight moves downward, this gravitational potential energy is transferred to the cuckoo clock.

More precisely, we define the change in gravitational potential energy \(\text{Δ}{\text{PE}}_{\text{g}}\) to be

where, for simplicity, we denote the change in height by \(h\) rather than the usual \(\text{Δ}h\). Note that \(h\) is positive when the final height is greater than the initial height, and vice versa. For example, if a 0.500-kg mass hung from a cuckoo clock is raised 1.00 m, then its change in gravitational potential energy is

Note that the units of gravitational potential energy turn out to be joules, the same as for work and other forms of energy. As the clock runs, the mass is lowered. We can think of the mass as gradually giving up its 4.90 J of gravitational potential energy, without directly considering the force of gravity that does the work.