I have a problem with my train of thought. I have narrowed it down to several premises, and I think that one of them must be wrong. Premise 1 Δ total energy (E) = Δ kinetic energy (K) + Δ potential energy (U) (assuming that there is no change in any of the other forms of energy in the system) Premise 2 Δ E = q + w Consider the system of a block. The block is initially traveling upwards (+y direction), away from the earth's surface. At t=0 it has a kinetic energy of 1/2mv2 (v is non zero). It initially also has gravitational potential energy of 0. The velocity eventually decreases to 0 (at t1). The whole time (from t=0 to t1), the earth's gravitational attraction is exerting a force of mg on the block. No other force is acting on the block, since it is already in motion at t=0. It appears that the work done by the gravitational force on the block is -mgh. But, ΔE = 0, because the kinetic energy has simply been transformed into potential energy. So, how can work be non zero (-mgh)? It seems that (looking at the block as the system) ΔE = 0 = W= -mgh (no heat transfer, so q=0, no friction, no other energy transfer) Since this is impossible, I know that I did something wrong. Thanks for your help!