1. The problem statement, all variables and given/known data A 700 g block is released from rest at height h0 above a ver- tical spring with spring constant k = 400 N/m and negligible mass. The block sticks to the spring and momentarily stops after com- pressing the spring 19.0 cm. What is the value of h0? 2. Relevant equations W = 1/2kx^2 where W is the work, k is the spring constant, and x is the distance spring is compressed. Potential Energy = mgh0 where h0 is the initial height, g is gravitational acceleration, and m is mass. U0 + KE0 = Uf + KEf , expressing that the kinetic and potential energy before must equal the kinetic and potential energy after. 3. The attempt at a solution I have the solution for this problem, but I don't really understand it. At height h0 before release, the block has potential energy and no kinetic energy: U0 = mgh0 At the contact point between block and spring, the block has some kinetic energy and some potential energy, which will be equal to mgh0. mgh0 = KE + U U = mgx, where x is the remaining distance to compress the spring KE = 1/2mv^2, where v is the velocity of the block upon contact. I know KE is normally expressed as 1/2mv^2, but the solution shows it as 1/2kx^2. They make mgh0 = 1/2kx^2 - mgx This then allows them to calculate the h0. However, I'm confused at how they arrived at that equation (specific questions below): Why is mgx negative? Why is 1/2kx^2 expressed as the Kinetic energy? I thought 1/2kx^2 is the work done by a spring, not the kinetic energy.