1. The problem statement, all variables and given/known data Consider the following situation: A 2.0 kg block is placed against a compressed spring on a frictionless 30° incline. The spring of force constant 19.6 N/cm is compressed 20 cm and then released. How far up the incline will the block go before coming to rest? 2. Relevant equations 3. The attempt at a solution The suggested (but perhaps naive) solution to this problem is to calculate the potential energy stored in the spring when it is compressed and set this value equal to the change in gravitational potential energy (see, for instance, http://www.physics.udel.edu/~jim/PHYS207_10J/Homework%20Solutions/Hwk7sol.pdf [Broken]). However, I see two fundamental problems with this approach: First, suppose our system is composed of the block, spring, ramp, and Earth. Then at its highest point (as with its initial condition when it compresses the spring), the block has no kinetic energy. Let the release point be the reference point for gravitational potential energy (potential energy = 0) and the unstretched equilibrium length of the spring to be its potential energy reference point. What is to say that when the block reaches its highest point, the spring will be at its equilibrium position? If this is not the case, then it certainly can't be true that the entire spring potential energy may be converted to gravitational potential energy. What I see the problem to be is attributing the potential energy stored in the spring to the energy transfered to the ball. Is this not a problem, in general? This problem is from an elementary text and, as such, may not be written paying attention to such details. Nonetheless, I have devised a solution which is independent of the abovementioned approach, but still poses some questions: We may calculate the work done by the spring on the box as it is released (since we are given the force constant and initial compression of the spring) and set this value equal to the change in gravitational potential energy (in this case we take only the box, ramp, and Earth as our system). This equation holds since here an external force acts on our system. This approach also yields the *suggested solution. However, it doesn't seem obviously true that the spring stops acting (contacting) on the box as it passes through its equilibrium position (which is an underlying assumption of this method)?