Using Energy Conservation for Finding Speeds

Generally we have two ways of determining the motion of objects - Newton's laws (F = ma) and energy.  Newton's laws are useful for finding accelerations and forces, but this can also be trickier since these are vectors, and for non-constant forces, we need calculus.  When we need to find speeds, I strongly recommend that you try energy to solve the problem.

Energy has the advantage that it is a scalar, so there are no vectors or components to worry about. We can also avoid calculus for NON-constant forces, such as springs and gravity.  Here are two examples with springs and gravity, and how energy conservation provides an easier, quicker way to get the speed.  Our starting point is:  Uo + KEo  =  Uf + KEf + heat, where heat is the work done by friction.