A machine, in the mechanical sense, is any arrangement that lets a small force do a job that would otherwise need a large one. Levers, pulleys, ramps and gears are the four you will meet, and they all work the same underlying trick — so it is worth seeing the pattern once rather than learning four separate devices.
Mechanical advantage
The useful measure is how much the machine multiplies your effort.
Mechanical advantage
- the force the machine moves, in newtons (N)
- the force you apply, in newtons (N)
- a bare ratio — a force divided by a force, so no units
A mechanical advantage of 4 means the machine lifts four times what you push with. Like the coefficient of friction, it has no units, because it is one force divided by another — which is a useful check that you have not accidentally divided a force by a distance.
Levers
A lever is the principle of moments put to work. Because balance depends on force multiplied by distance from the pivot, a long effort arm and a short load arm let a small effort raise a large load. Its mechanical advantage is simply the ratio of the two arm lengths, and a crowbar, a wheelbarrow and a pair of scissors are all this same arrangement with the pivot in different places.
Pulleys
A single fixed pulley changes the direction of your pull without reducing it: to lift 200 newtons you still pull with 200 newtons, which is useful because pulling down is easier than lifting up. The gain comes when the load hangs from a movable pulley, so that more than one strand of rope shares its weight. Count the strands supporting the load and that is the mechanical advantage.
Ramps
An inclined plane lets you raise a load by pushing it along a slope instead of lifting it vertically. The gentler the slope, the smaller the force needed — and the longer the distance you must push. A ramp four metres long that rises one metre gives a mechanical advantage of about four, which is why loading ramps are long and shallow rather than short and steep.
Gears
Gears are toothed wheels that mesh so that one turns the other. Because the teeth are the same size on both, a small gear driving a large one turns the large one more slowly — and with more turning force. The ratio of the tooth counts gives both effects at once: a 10-tooth gear driving a 40-tooth gear turns it at a quarter of the speed with four times the moment. A gear train also reverses the direction of rotation at every mesh, so two meshed gears turn opposite ways and three bring the last one back to the same sense as the first.
Nothing is free
Every one of these machines shows the same pattern: whatever you gain in force, you pay for in distance. Two pulley strands halve your pull and double the rope you haul. A four-metre ramp quarters the force and quadruples the distance pushed. A gear ratio that quadruples the moment quarters the rotation speed. Push with a quarter of the force through four times the distance and, in an ideal machine, the two exactly compensate — which is the observation that the energy module turns into a precise statement. In a real machine friction takes a share, so you always have to put in a little more than the ideal figure suggests.
Putting it to work
Two more machines worth recognising
Two arrangements you will meet are really inclined planes in disguise. A wedge — an axe head, a chisel, a doorstop — is a ramp that moves instead of staying still: driving it in a long way forces the surfaces apart a short way, which is the usual trade of distance for force. A screw is a ramp wrapped round a cylinder, and its thread is the slope. Turning the head through a large circular distance advances the screw a tiny way along its axis, which is why a screw grips so powerfully and why a fine thread, with its shallower slope, gives more force than a coarse one.
This is worth seeing because it collapses a long list of devices into one idea. Levers, pulleys, ramps, wedges, screws and gears are six names for the same bargain: a force multiplied, paid for with distance. If a question offers you an unfamiliar mechanism, identify which of the six it resembles and the trade will be the same.
Real machines fall short
The mechanical advantages calculated above are ideal figures, assuming nothing is lost. Real machines have friction in their bearings, ropes that stretch and stiffen, and parts with weight of their own that must also be lifted. So the effort actually needed is always somewhat larger than the ideal calculation predicts, and the difference shows up as warmth in the mechanism — which is the friction lesson's point about work against friction turning into heat. A pulley block that ought to need 100 newtons might need 115 in practice. Questions in this course use the ideal figures unless they explicitly mention friction, but it is worth knowing which way reality departs from them.
It is worth being precise about what a machine does not do. It does not create force out of nothing, and it does not reduce the total effort required — it redistributes it, spreading a smaller force over a longer distance. Nor does it make a job possible that was impossible: if you cannot supply the effort even with the mechanical advantage, the machine does not help. What it genuinely changes is the size of force you need at any one moment, and sometimes the direction you need to apply it in, which is why a single fixed pulley with a mechanical advantage of exactly one is still useful. Pulling downwards while standing on the ground is easier to arrange than lifting upwards, even when the force is identical.
Why it matters in aviation
Mechanical advantage is built into an aircraft wherever a modest force at a control has to manage a large one at a surface. In a mechanically signalled aeroplane, cable runs over pulleys carry the pilot's input from the control column and rudder pedals out to the elevator, ailerons and rudder, and the pulleys change the direction of the pull along the way exactly as the fixed pulley above does. Flaps and trimming surfaces are commonly driven by screw jacks, which are this lesson's ramp wrapped into a helix: many turns of a motor move the surface a short distance against a large aerodynamic load, and because the ramp is so shallow the load cannot easily drive the jack backwards, so the surface holds its setting without anything having to hold it.
Where the aerodynamic load on a surface exceeds what leverage alone could handle, the arrangement changes rather than the principle. Hydraulic actuators supply the force while the pilot's input becomes a command rather than a pull, which is why a large aircraft depends on its hydraulic systems to move its controls at all and a light one does not. The trade the lesson describes still applies: nothing gained in force comes free, and the energy has to be supplied from somewhere.
What the test asks
The commonest error is expecting a machine to reduce the force and the distance together, which would be something for nothing. With pulleys, the specific trap is counting every visible rope rather than only the strands actually supporting the load. With gears, expect a question about direction — two meshed gears turn opposite ways, and an odd number of gears in a train ends up matching the first while an even number opposes it.