Poential Energy is represented by the symbol U.
U = mgh
Wby Gravity = -ΔU
ΔU = UFinal – UInitial = 0 – mgh = -mgh
ΔU = -mgh = Wby Gravity = ΔKE
What is important is the change in potential energy.
-ΔU = (UFinal – UInitial) = Wdone by Gravity = ΔKE = KEFinal – KEInitial
Lost Potential Energy = gained Kinetic Energy
KEFinal + UFinal = KEinitial + UInitial
Total Mechanical Energy is Conserved
Conservative Force Field: Total work done about a closed path sums to ZERO.
Friction Force is non-conservative (You do not get energy back in a closed path)
Imagine how force looks as a ball is dropped from the sky. think of dy as the many very small distances it travels over to fall to the ground. dW is the very small but of work
ΔU = -W = -F
dU = -dW = -Fy
dydU/dy = -Fy
Read this “The potential Energy with respect to height is equal to mass times gravity times height.
Now what about stretched springs? This story is a little different. The force exerted to do work grows as the spring stretch’s further.
If you draw a graph, the potential energy of the spring as it is compressed and stretched would form a parabola.
Now what about a child on a slide?
The component of gravity parallel to the slide is mg cos θ. It is doing work. θ is changing all the time, as the mass of the child moves along the slide.