Mechanisms: MA, VR and efficiency

The hard step is the effort distance. Wound round once, the effort travels a circle: distance = circumference = 2 x pi x radius, not the radius. Using the radius alone gives a VR six times too small. For a screw jack, VR = (2 x pi x handle) / pitch; the 2 x pi is often dropped. In a wheel and axle it cancels to radius / radius.

In a compound train (small and large gear on one shaft) the overall ratio is the product of the stage ratios -- 3:1 then 2:1 gives 6:1 -- applied to the input speed; candidates do one stage, or add the ratios. Second, an idler does not change the ratio (it depends only on driver and final driven gear); it only reverses direction.

Efficiency can never exceed 100 per cent, because friction always wastes effort. Yet candidates hand in 110 or 133 per cent -- a sign the fraction was inverted, dividing VR by MA instead of MA by VR. The correct order is efficiency = (MA / VR) x 100, and since MA is smaller than VR the answer must be below 100. Treat 100 or more as an error.

For a block and tackle the velocity ratio is simply the number of pulleys (the rope sections supporting the movable block). Candidates measure pulley diameters off the drawing when they should count the pulleys. The diagram is not to scale; figures needed are given. Count rope sections for VR, take load and effort for MA = load / effort.

Asked how to raise a lever's MA, candidates say push harder or use a stronger bar -- neither changes MA. It is geometry: lengthen the effort arm (effort further from the fulcrum) or move the load closer to the fulcrum. Likewise a longer screw-jack handle or larger wheel raises the VR and so the MA. Distances, not force, set the advantage.

The definition trap. Mechanical advantage is a force ratio, load / effort; velocity ratio is a movement ratio, effort distance / load distance. Candidates state MA loosely instead of load / effort, and swap or invert them, so a VR of 5 becomes 1:5 or MA as effort / load. Keep MA as forces, VR as distances, each the right way up.

A testable error: that two gears whose teeth mesh turn the same way. In fact gears meshing on the outside always turn in opposite directions -- a clockwise driver gives an anticlockwise driven. Direction stays the same only with the drive carried differently: gears on the same shaft, an idler between them, or an uncrossed belt or chain.