A mass m hangs from a spring. You push up on the mass until the spring reaches its natural length. How far will the hanging mass stretch the spring? How much work do you do against gravity? Against the spring? When the mass comes to rest, -mg+kx=0 or x=mg/k The work done by you against the spring should be zero, because you act in the same direction as the spring? I don't get this part in particular. What does it mean, "work against a force?" The work done against gravity is just the force required to balance gravity integrated wrt x. kx-mg+F=0 or F=mg-kx. W=[inte](mg-kx)dx=mgx-.5kx2|x0=mgx-.5kx2 Alternatively, I wrote W=dK=0=.5kx2 + Wyou -mgx or Wyou=mgx-.5kx2=mg(mg/k) - .5k(mg/k)2 Is this ok? My main confusion is the idea of work against a force.