Machines

A machine is a device that makes work easier or more convenient. It can do this in one of four ways: multiply a force (a crowbar lifts a rock), change the direction of a force (a flagpole pulley lets you pull down to raise a flag), gain speed (the small effort moves a long way, the load moves fast), or simply be applied at a convenient point. A machine never creates energy. At best, work you put in equals work you get out. In every real machine some energy is lost to friction, so work output is always a little less than work input.

Three numbers describe any machine. Mechanical advantage (M.A.) is load divided by effort, how many times the machine multiplies your push. Velocity ratio (V.R.) is the distance the effort moves divided by the distance the load moves, fixed by the machine's design. Efficiency is the useful work you get out divided by the work you put in, equal to M.A. divided by V.R. For an ideal frictionless machine M.A. equals V.R. and efficiency is 1 (or 100 percent). For a real machine friction wastes energy, so M.A. is always less than V.R. and efficiency is always less than 1.

A lever is a rigid bar free to turn about a fixed point called the fulcrum. The load and the effort act at other points. By the principle of moments, load times load-arm equals effort times effort-arm, so M.A. equals effort-arm divided by load-arm. Levers come in three classes by what sits in the middle. Class I has the fulcrum in the middle (seesaw, scissors, crowbar) and M.A. can be more than, equal to or less than one. Class II has the load in the middle (wheelbarrow, nutcracker, bottle opener) and M.A. is always more than one. Class III has the effort in the middle (forearm, sugar tongs, fishing rod) and M.A. is always less than one, so it gains speed instead.

A pulley is a wheel with a grooved rim over which a rope runs. A single fixed pulley only changes the direction of the effort, so its ideal M.A. is 1, but pulling down is more convenient than lifting up. A single movable pulley has the load attached to the moving wheel, giving an ideal M.A. of 2: the effort is half the load, but it must move twice as far. A block-and-tackle combines several pulleys in two blocks. Its velocity ratio equals the number of pulleys n, so a system of four pulleys lets one person lift four times their effort, which is why such systems raise engines and cargo.