Work and Energy
Forces on a body do work IF
Work done by force F defined as
FPath Dx
Units of work = Newton*meter = Joules
Example:
Let F = 5 N, FPath = 4 N, FPerp = 3 N, N = 7 N, W = 10 N, k = 2 N, Dx = 6 m

F Dx = FPath Dx = 24 J N Dx = 0 Dx = 0 J W Dx = 0 Dx = 0 J k Dx = 2 Dx =12 J Total work = 12 J 
But why talk about doing work? What is the result of doing work?
First let's look at the Net work done on a body by the Net force.
From Newton's Law, the net force equals mass times acceleration.
Newton's Law of NonInertia
Multiply both sides by Dx to give total work.
To evaluate this we draw a graph of mv vs v (recall v vs t) since then the area under graph will give total work.
Conclusion:
Total Work = Change in Kinetic Energy
Now let's investigate a very important work done by gravity. Let's do that by raising a mass up a height h. We must exert an upward force = mg, and we do not do any work when we move the mass sideways since we won't be exerting any of our force "along the path" so work done by gravity depends only on the vertical distance we move. So work done by gravity equals mg h.
Wg =  mgh
Thus
W'Total + Wg = DKE where prime means we removed one work term.
W'Total mgh = DKE
W'Total = DKE + mgh
We then call mgh a change in Potential Energy due to gravity. i.e. we say that an object raised above the earth a distance h has Changed its Potential Energy. DPEg = mgh
Now let's apply our ideas
Interactive Physics
Pendulums
Conservation concepts in energy but doesn't some energy get "lost"?