Commons

2.5 WorkImagine a black box 8 , containing a gasoline-powered engine, whichis designed to reel in a steel cable of length d, exerting a certainforce F .If we use this black box was to lift a weight, then by the time ithas pulled in its whole cable, it will have lifted the weight througha height d. The force F is barely capable of lifting a weight m ifF = mg, and if it does this, then the upward force from the cableexactly cancels the downward force of gravity, so the weight willrise at constant speed, without changing its kinetic energy. Onlygravitational energy is transferred into the weight, and the amountof gravitational energy is mgd, which equals F d. By conservationof energy, this must also be the amount of energy lost from thechemical energy of the gasoline inside the box. 9Now what if we use the black box to pull a plow? The energy increasein the outside world is of a different type than before: mainlyheat created by friction between the dirt and the ploughshare. Thebox, however, only communicates with the outside world via thehole through which its cable passes. The amount of chemical energylost by the gasoline can therefore only depend on F and d, soagain the amount of energy transferred must equal F d.The same reasoning can in fact be applied no matter what thecable is being used to do. There must always be a transfer of energyfrom the box to the outside world that is equal to F d. In general,when energy is transferred, we refer to the amount of energy transferredas work, W . If, as in the example of the black box, the motionof the object to which the force is applied is in the same directionas the force, then W = F d.w / The black box does workby reeling in its cable.x / The baseball pitcher put kineticenergy into the ball, so hedid work on it. To do the greatestpossible amount of work, he appliedthe greatest possible forceover the greatest possible distance.If the motion is in the opposite direction compared to the force,then W = −F d; the negative work is to be interpreted as energyremoved from the object to which the force was applied. For ex-8 “Black box” is a traditional engineering term for a device whose inner workingswe don’t care about.9 For conceptual simplicity, we ignore the transfer of heat energy to the outsideworld via the exhaust and radiator. In reality, the sum of these energies plus theuseful kinetic energy transferred would equal W .Section 2.5 Work 59