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In example c, the tractor’s force on the trailer accelerates it, increas- ing its kinetic energy. If frictional forces on the trailer are negligible, then the increase in the trailer’s kinetic energy can be found using the same algebra that was used on page 39 to nd the potential energy due to gravity. Just as in example b, we have W = Fd . Does this equation always give the right answer? Well, sor t of. In example d, there are two quantities of work you might want to calcul ate: the work don e by the tractor on the plow and the work done by the plow on the dirt. These two quantities can’t both equal F d. Mos t of the energ y tra nsmitted through the cable goes into fri cti ona l hea ting of the plow and the dirt. The work done by the plow on the dirt is less than the work done by the tractor on the plow, by an amount equal to the heat absorbed by the plow. It turns out that the equation W = Fd gives the work done by the tractor, not the work done by the plow. How are you supposed to know when the equation will work and when it won’t? The somewhat complex ans we r is post poned un til section 3.6. Un til then, we will restri ct ourselves to examples in which W = F d gives the right answer; essentially the reason the ambiguities come up is that when one surface is slipping past another, d may be hard to dene, because the two surfaces move dierent distances. e / The baseball pi tc her put ki - netic energy into the ball, so he did work on it. To do the greatest possible amount of work, he ap- plied the grea test possible force over the gre ate st possible dis- tance. We have also been using examples in which the force is in the same direc tion as the motion, and the force is constan t. (If the force was not constant, we would have to represent it with a function, not a symbol that stands for a number.) To summarize, we have: rule for calculating work (simplest version) The work done by a force can be calculated as W = Fd , if the force is constant and in the same direction as the motion. Some ambiguities are encountered in cases such as kinetic friction. Sect ion 3.1 Wo rk: the T ransfer of Mecha nical Ene rgy 51

Conservation Laws II

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