I'm pretty sure I understand everything my book says about force and mechanical energy for point particles. I'm slightly confused about how this applies to systems of particles. For particles: The line integral of force over a path is the change in KE. For conservative fields you can set a zero to create a PE function. Therefore, in conservative fields, mechanical energy is constant. For systems: All of the above applies to the center of mass of the system with respect to external forces. In light of this, a lot of the problem I used to do just blindly by conservation of energy seem confusing. For example (Kleppner 4.4), imagine a square. Remove every part of the square that is a distance R or less from the top right corner. Allow a small block of slide on the track formed by the missing 1/4 circle. Release the block from the top of the track. How fast is it going at the bottom? All surfaces are frictionless. In the past, I set the zero of PE at the bottom of the track. Momentum is conserved. Then conserve mechanical energy. The initial PE of the block equals the final KE of the block + final KE of the square. Two equations, two unknowns. This method equates the mechanical energy of the individual elements of the system at two points in time. However, I no longer see why this is right. (1) Why is mechanical energy necessarily conserved for anything in this system at all? For the block: the normal force between the block and square is nonconservative. For the system: The normal force between the floor and the square is external and nonconservative. (2) If mechanical energy is conserved for a system, shouldn't it be the energy of the center of mass that matters, not the energy of the individual parts? Why do the parts in this system have to conserve? I'm also having trouble writing down all my thoughts clearly all at once, so there may be more in reply to any answers. Thanks in advance.