Hey all, I was feeling confident with the idea of work when dealing with vectors and using the dot product to find the work. However, recently we have begun to discuss work while considering the object experiencing the force as part of a system. I'm having trouble transitioning into this idea and I don't really know when to consider energies and apply the work energy theorem versus using vectors and dot products. An example that I'm having trouble with: The first thing I'm tempted to do is draw a free body diagram and begin plugging vectors into newton's second law. I was able to solve the problem using a hint from my instructor but I don't understand why the method works. It was as follows: Ki + Wg + Ws = Kf Where Ki is initial kinetic energy, Wg is the work done by the gravitational force, Ws is the work done by the spring force and Kf is the final kinetic energy. When you substitute and simplify all this down you can solve for the displacement (x) via a quadratic equation and arrive at 0.131 m. We have not learned about the conservation of energy yet. Any insight would be much appreciated. I really want to understand this concept!