1. The problem statement, all variables and given/known data: I'm curious to know why and how one would account for the force of a falling object dropped from a height. If I apply Newton's 2nd Law, force is only dependent on acceleration. So in a straight vertical drop, this acceleration is only gravity. But is it not that a bowling ball dropped from a skyscraper will have more force crashing down into the ground than the same ball dropped from only half a meter of a height? Here is my problem: If I drop a ball into a spring from a given distance x, the spring will compress. Assume that the ball sticks to the spring. After impact, the spring will eventually have a restoring force to counteract that force. But how much is that force? It is not equal to the weight of the ball, is it? (In this case, the spring is massless. Only mass of the ball (m), spring constant (k), and distance of the ball from spring (x) is given.) 2. Relevant equations: F = m * a, F (spring) = -kx, W = KE2 - KE1, Conservation of Energy, W = Fd 3. The attempt at a solution: W = KE2 - KE1 KE2 = mgx by conservation of energy, x is the height KE1 = 0, because ball is being dropped W = KE2 = mgx and F = W/d Substituting, F = (mgx)/d d = x + n, n is the distance the spring is compressed due to the weight of the ball I am unsure how to solve for n. F = (mgx)/(x+n) = -kn I'm stuck here. It looks like a quadratic, but it looks incorrect. Once I solve for n, I would have -kn, which is the restoring force. Can someone help me? Thanks in advance!