Levers & Mechanical Advantage

A lever balances moments about its fulcrum: effort × effort arm = load × load arm. Rearranged, the mechanical advantage MA = load ÷ effort is simply the ratio of the arms. Make the effort arm four times the load arm and you lift four times what you push — that is why a long spanner, a tyre lever and a crowbar all work.

Nothing is free. The velocity ratio VR is the distance the effort moves divided by the distance the load moves, and for an ideal lever it equals the MA. Gain four times the force and the effort end must travel four times as far, so the work in equals the work out. Watch the two dimension arrows through a stroke: the long side sweeps a big arc, the short side barely moves. In a real machine friction makes the effort a little higher, and MA ÷ VR is then the efficiency.

The three classes differ only in the order of the three points along the bar. First class has the fulcrum in the middle (a see-saw, scissors, a control-column bellcrank) and can give MA above or below one. Second class has the load in the middle (a wheelbarrow, a nutcracker) and always gives MA above one. Third class has the effort in the middle (tweezers, your forearm) and always gives MA below one — it costs force to gain speed and range of movement.

• Try this: Lengthen the effort arm. What happens to the effort needed, and to the distance the effort end must move?
• Try this: Make the two arms equal. What is the MA then, and what has the lever actually gained you?
• Try this: Switch to a third-class lever. Why is the MA always below one, and what do you get in exchange?