\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Potential Energy

Gravitational potential energy and elastic potential energy may look different but they have these things in common.

1. Energy stored as potential energy can be released again, converted back into other forms of energy
2. The potential energy of a system depends on the relative position or configuration of the parts of that system, not on how it got there or how fast it is moving. Elastic potential energy depends on the position of the ends of the spring, while the gravitational potential energy of a ball depends on the relative position of the Earth and the ball.
3. If you start an object at rest and let it go, it will spontaneously move in the direction that will decrease its potential energy: balls fall down, springs snap back to their natural length.

There are other types of potential energy in nature, and they all have these three things in common.

This last quality is particularly interesting, and important enough that I want to put it in a little box of its own.

• KE increases
• PE decreases
• Total energy can stay constant.

• KE increases
• PE increases
• Total energy is not constant.
• Something must have done positive work on the ball.

Why is this true? If something starts to move, that means it has gained kinetic energy, and so there must be a source of that energy. Assuming that there are no other forces around doing work on the object, that kinetic energy must come from potential energy: kinetic energy increases, potential energy decreases. For the potential energy and kinetic energy to increase at the same time, there would have to be another source of energy, such as the work done by someone's hand, and the behavior would no longer be considered to be "spontaneous".

I like to think of it like this: when a system is doing what it "wants" to do, then its potential energy drops: balls "want" to fall down, springs "want" to relax. Decreasing potential energy means that the system is "relaxing" (like the spring), while increasing potential energy is like the system is "tensing" (also like a spring).