00:01
I'll start off with a few general comments about conservation of mechanical energy.
00:06
This occurs in closed systems where you have only conservative forces working.
00:17
So conservative forces.
00:19
There are a few examples of this.
00:22
And what conservative forces are forces that have a field for which the work done by that field just depends on the endpoints.
00:34
It does not depend what happens in between.
00:38
But examples include gravity, the hooks law for a spring, and electricity.
00:49
Examples that are not included are things like friction, which turns kinetic energy into thermal energy.
00:58
People and animals can get energy from their metabolism and, of course, convert that energy into motion.
01:08
So here i'll start off with an example of a conservative system, but what the conservation of mechanical energy says is that the sum of kinetic and potential energies at any point inside the system has to remain constant.
01:28
Conservation means constant.
01:31
So k is kinetic energy, one -half mv squared, mass times velocity squared, or speed squared, and potential energy in the case of gravity is mass times g, times y, where y is close to the surface of the earth and a coordinate that measures how high above the surface one is.
01:57
So let's take a look at a numerical example.
02:01
We'll put someone on a swing.
02:08
And i like to choose my reference for gravity.
02:13
Y equals zero.
02:14
You can always choose your reference point the way you see fit...