Is this following correct? : When you push a crate along the floor at a constant velocity for a long time, you get tired which indicates that you are tranferring some of your energy to the object, i.e. you are doing "work" on the object. But according to the definition of work which equates work to a change in kinetic energy (change in velocity), there is no work done on the crate since its velocity is constant. This is because while you do in fact do work on the crate, the force of friction does equal work in the opposite direction of you, causing the net work done on the crate to be zero. In the other definition of work where work is a line integral, although you are exerting a force on the crate over a distance which results in a positive value of W, the force of friction is equal and opposite, resulting in two integrals that void eachother.  http://upload.wikimedia.org/math/b/f/2/bf240d906ff97b33fc3e60f2508ab671.png  http://upload.wikimedia.org/math/7/6/8/7680d79cfc1c61f21fe00e1089a9493b.png THANKS!!