1. The problem statement, all variables and given/known data Hi everyone, I am generalizing the following problem because I disagree with how the book solves the problem. A square mass 'm' is attached to two springs with identical constants 'k', in a configuration such that the springs mount to the left/right sides of the mass and extend outward and upward towards the ceiling in a 'V' shape. It starts from rest and moves upward a distance 'h', catapulted upward by the springs and opposed by gravity. What is the final velocity of the mass when the mass reaches the ceiling (and now the springs are horizontally aligned with the mass). 2. Relevant equations Conservation of Energy PEsprings,initial = KEfinal + PEgravity,final + PEsprings,final Initial KE, Initial PE gravity are both zero. There is a 'final' potential energy from the springs because the springs haven't returned to their initial free length. 3. The attempt at a solution My problem with the book solution is that, at the final state configuration, the mass is moving upward and the springs are perfectly horizontal to the mass. Why should there be any potential energy from the spring in the system if the force of the spring is doing no work at that instant? The force is perpendicular to the displacement, so I'm thinking the solution should have some kind of cos(theta) term. In the book solution, they simply add everything together. I believe that whoever wrote the solution to this problem is misunderstanding the statement that 'spring forces are conservative' and didn't pay attention to the fact that the force is not doing any work at the final state.