A single person cannot lift a car, yet a mechanic with a jack does it with one hand. A child on a see-saw can lift a grown-up. None of these break the rules of physics. They all use a simple machine: a device that changes a force to make a hard job feel easy. In the lab above, pick a lever, a ramp, a pulley, or a wheel and axle, change its shape, and watch the mechanical advantage and the effort force update as you go. The blue effort arrow shrinks below the amber load arrow every time the machine multiplies your force.
What are simple machines?
A simple machine is a basic device, with few or no moving parts, that changes the size or the direction of a force. There are six of them, and they split neatly into two families:
- The lever family: the lever, the wheel and axle, and the pulley.
- The inclined-plane family: the inclined plane (ramp), the wedge, and the screw.
Every complicated machine, from a bicycle to a crane, is just a clever combination of these six. Four of them (the lever, the ramp, the pulley, and the wheel and axle) are built to multiply force, and those are the four you can change in the lab above.
Mechanical advantage: less force, more distance
Mechanical advantage, written MA, is the number of times a machine multiplies your effort. It is simply the load force divided by the effort force:
MA = load force / effort force | effort force = load / MA
If a machine has an MA of 3, then a 100 N push holds up a 300 N load. That sounds like something for nothing, but it is not. The price is distance: to raise the load a little, you must move your end a lot. A machine with MA greater than 1 multiplies your force; a machine with MA less than 1 (like a lever with a long load arm) multiplies distance and speed instead, which is why a broom or a fishing rod moves its far end quickly. Drag any slider in the lab and watch the effort force and the two arrow lengths respond.
The lever: effort arm versus load arm
A lever is a stiff bar that turns on a pivot called the fulcrum. The effort arm is the distance from the fulcrum to where you push; the load arm is the distance from the fulcrum to the load. For a lever:
lever MA = effort arm / load arm
Push far from the fulcrum and lift a load close to it, and your force is multiplied. A see-saw, a crowbar, a bottle opener, and a wheelbarrow are all levers. In the lab, the beam stays level so you can compare the two arms directly, and each arm grows or shrinks as you change its length while the fulcrum stays put.
The inclined plane, the wedge, and the screw
An inclined plane, or ramp, lets you raise a heavy load by pushing it up a slope instead of lifting it straight up. You use a smaller force, but you push it over a longer distance. For a ramp:
ramp MA = ramp length / height
A long, gentle ramp has a high MA and needs little effort; a short, steep ramp needs more. The wedge and the screw are the ramp’s two relatives. A wedge is like two inclined planes placed back to back that move to split or lift things, as in an axe, a knife, or a doorstop. A screw is an inclined plane wrapped around a cylinder, so a small turning effort drives a large forward force, as in a jar lid, a bolt, or a car jack. The lab models the ramp directly; the wedge and screw follow the very same length-over-height idea.
The pulley: count the supporting ropes
A pulley is a grooved wheel with a rope over it. A single fixed pulley (attached to the ceiling) only changes the direction of your pull: you pull down to lift a load up, but you pull just as hard as the load weighs, so its MA is 1. Add a movable pulley that rides on the rope with the load, and now two rope segments share the load, halving your effort. The rule is beautifully simple:
pulley MA = number of rope segments that support the load
Count the ropes running down to the load-carrying block, and that number is the mechanical advantage. In the lab you set the number of supporting segments from 1 to 5 and watch the effort force fall.
The wheel and axle
A wheel and axle is really a lever that spins. A large wheel is fixed to a smaller axle so they turn together. Apply a small effort to the rim of the big wheel, and the axle turns with a much larger force. Because it is a rotating lever, it uses the same formula, with the two radii playing the part of the two arms:
wheel and axle MA = wheel radius / axle radius
A doorknob, a steering wheel, a screwdriver, and a windlass (the crank that raises a bucket from a well) are all wheels and axles. In the lab the radii are drawing units rather than metres, so the wheel-and-axle tab shows the trade as a distance ratio: the wheel rim turns MA times as far as the load rises.
Work in equals work out: why there is no free lunch
Here is the idea that ties all four machines together. Work is force times the distance moved:
work = force x distance
A simple machine never reduces the work you must do. It only lets you swap a big force over a short distance for a small force over a long distance. Whatever you save in force, you pay back exactly in distance, so:
work in = work out (ideal machine)
The lab shows this with two cards, Work in and Work out, and they stay equal no matter how you change the geometry. Cut the effort to one third with a lever and you must push three times as far. That is why an MA of 100 does not give you free energy: it just means the effort travels 100 times farther than the load.
| Machine | Mechanical advantage | The trade |
|---|---|---|
| Lever | effort arm / load arm | Push farther from the fulcrum, lift a close load with less force |
| Inclined plane | length / height | Push a smaller force up a longer, gentler slope |
| Pulley | supporting rope segments | Pull more rope with less force |
| Wheel and axle | wheel radius / axle radius | Turn the rim farther to move the axle with more force |
Worked examples
Lever. A 300 N load sits 0.5 m from the fulcrum (load arm) and you push down 1.5 m from the fulcrum (effort arm). MA = 1.5 / 0.5 = 3, so effort = 300 / 3 = 100 N. To raise the load 0.2 m you must push your end down 0.6 m, and the work checks out: 100 N x 0.6 m = 60 J = 300 N x 0.2 m.
Inclined plane. To lift a 500 N box, a plank 4 m long is propped to a height of 1 m. MA = 4 / 1 = 4, so effort = 500 / 4 = 125 N. You push 125 N along all 4 m of the plank to raise the box just 1 m: 125 x 4 = 500 x 1 = 500 J.
Pulley. A block and tackle has 3 rope segments supporting a 600 N load. MA = 3, so effort = 600 / 3 = 200 N. Pulling 200 N through 3 m of rope raises the load 1 m: 200 x 3 = 600 x 1 = 600 J.
Wheel and axle. A windlass has a wheel of radius 4 and an axle of radius 1. Modeled as a rotating lever, MA = 4 / 1 = 4, so a 240 N load needs effort = 240 / 4 = 60 N at the wheel rim, while the rim turns 4 times the distance the load rises.
Friction, efficiency, and real machines
Everything above is the ideal, frictionless mechanical advantage. Real machines are not perfect. Moving parts rub, ropes bend, and some of your effort is lost to friction as heat. So the actual mechanical advantage is always a little lower than the ideal value, and the machine’s efficiency, which is work out divided by work in, is below 100 percent:
efficiency = work out / work in x 100%
A well oiled, smooth machine wastes less and comes closer to its ideal MA. This is why you oil a squeaky hinge or a bike chain: you are not adding energy, you are cutting the friction losses so more of your effort reaches the load.
Common misconceptions
- “A machine reduces the total work.” It does not. It trades force for distance. The Work in and Work out cards stay equal for every setting.
- “A single pulley cuts your effort.” A single fixed pulley has MA = 1. It changes only the direction you pull, not how hard. Set the segments to 1 and see effort equal the load.
- “A high MA means free energy.” A high MA means a smaller force, but over a proportionally longer distance. The distance line shows exactly how much farther the effort must travel.
- “The ideal MA is what you really get.” Friction always takes a cut, so the real machine needs a bit more effort and runs below 100 percent efficiency.
Keep exploring
See where force and motion begin in Newton’s laws of motion, put a force into a calculation with the F = ma calculator, and find out why real machines never quite reach their ideal mechanical advantage in the lesson on friction.