An elevator cable pulls an elevator up with a force of (g+a)*m for t seconds where m is the mass of the elevator, accelerating it upwards. Then, for t seconds (just as many as the first time interval), it applies an upward force of (g-a)*m, decelerating it to a stop (the net force here is downwards because of g-a). Let's put the potential energy reference point at the beginning of the situation. The elevator moved up. The elevator thus gained potential energy. Now consider that the order had been reversed. First (g-a)*m then (g+a)*m, each for the same time intervals. The total force applied to the elevator would have been the same, yet the elevator would have lost potential energy in the latter case. Is that correct? Did I do something wrong? It seems odd to me that two situations with identical force applications but differing orders of those applications would result in differing total energy for each case. Note: this is not a homework question.