Examples:
Real machines lose some work to friction. Levers and well-oiled pulleys can be very efficient (often over 90%); a screw jack is often well under 50% efficient, which also stops it from unwinding.
Most real machines are several simple machines joined together. The output force of one part is the effort for the next, so the mechanical advantages multiply. Load a real example or build your own with up to three parts.
The diagram you label in a test: the six simple machines, plus the effort, load and fulcrum of a lever and the wheel and axle. Switch between the labeled diagram, a blank one to test your memory, and a quiz where you place each label yourself. You can also download both versions or print a label worksheet.
Tap a word, then tap the numbered box it belongs to (on the diagram or in the list below). Tap a filled box to take the word back. On a phone, swipe the diagram sideways to see every number.
Ten questions about machines, mechanical advantage and work.
Tap an everyday object, then tap the machine it uses. Check when all twelve are placed.
Where is the fulcrum, the load and the effort? Sort the nine levers.
The force you put in is the effort. The weight or force the machine moves is the load. The mechanical advantage (MA) tells you how many times the machine multiplies your force: MA = load ÷ effort. A machine with MA = 5 lets a 100 N push move a 500 N load.
The lever turns on a fulcrum; the wheel and axle is a lever that goes round and round; the pulley is a wheel with a rope. The inclined plane is a ramp; the wedge is a ramp that moves; the screw is a ramp wrapped around a cylinder. So really there are two families: levers and ramps.
The ideal mechanical advantage (IMA) comes from the shape of the machine (the lengths), assuming no friction: IMA = distance the effort moves ÷ distance the load moves. The actual mechanical advantage (AMA = load ÷ effort) is smaller because of friction. Efficiency = work out ÷ work in = AMA ÷ IMA. Archimedes worked out the law of the lever more than 2,200 years ago; Hero of Alexandria described five simple machines, and the inclined plane was added later.
Lever: slide the fulcrum towards the load and watch the effort fall and the effort distance grow. Pulley: go from 1 to 6 ropes. Ramp: keep the height, make the slope longer. Then set efficiency to 70% and see where the extra work goes. Finally, load the bicycle in the compound machine builder: why is its mechanical advantage less than 1?
| Machine | Ideal mechanical advantage | Trade-off | Everyday examples |
|---|---|---|---|
| Lever | effort arm ÷ load arm | smaller force, larger movement (or the other way round) | seesaw, crowbar, wheelbarrow, nutcracker, tweezers, broom |
| Wheel and axle | wheel radius ÷ axle radius | turn the big wheel further with less force | doorknob, steering wheel, screwdriver, tap, well winch |
| Pulley | number of rope sections holding up the load | pull more rope with less force; a fixed pulley changes direction | flagpole, blinds, crane, sailing boat, gym machine |
| Inclined plane | length of slope ÷ height | push a longer way with less force | ramp, mountain road, stairs, slide |
| Wedge | about length ÷ thickness | push it in a long way to split a little | axe, knife, chisel, nail point, doorstop, zip |
| Screw | 2π × handle radius ÷ pitch | many turns for a small movement | car jack, bolt, jar lid, light bulb, clamp |
| Class | In the middle | Mechanical advantage | Examples |
|---|---|---|---|
| First | fulcrum | more than, less than or equal to 1, depending on where the fulcrum is | seesaw, crowbar, scissors, pliers |
| Second | load | always more than 1 | wheelbarrow, nutcracker, bottle opener |
| Third | effort | always less than 1 (gains distance and speed) | tweezers, broom, fishing rod, your forearm |
| Formula | Unit | |
|---|---|---|
| Work | W = F × d (force × distance moved in the direction of the force) | joule (J) = N × m |
| Weight of a load | weight = mass × g (g ≈ 9.8 N/kg on Earth) | newton (N) |
| Actual mechanical advantage | AMA = load force ÷ effort force | no unit |
| Ideal mechanical advantage | IMA = effort distance ÷ load distance | no unit |
| Efficiency | work out ÷ work in × 100% = AMA ÷ IMA × 100% | % |
| Compound machine | total MA = MA1 × MA2 × … | no unit |
A 60 kg crate (weight 60 × 9.8 = 588 N) is pushed up a ramp 3 m long to a height of 1 m. IMA = 3 ÷ 1 = 3, so with no friction the push is 588 ÷ 3 = 196 N. Work along the ramp = 196 N × 3 m = 588 J, the same as lifting it straight up (588 N × 1 m). If the ramp is 75% efficient, the push is 196 ÷ 0.75 ≈ 261 N.
The lever, the wheel and axle, the pulley, the inclined plane, the wedge and the screw. Almost every machine, from scissors to cranes, is made by combining them.
Key takeaway: lever, wheel and axle, pulley, inclined plane, wedge, screw.They let you use a smaller force (or a force in a more convenient direction) by moving it through a longer distance. The work, force × distance, is not reduced: at best it stays the same.
Key takeaway: less force, more distance, same work.How many times a machine multiplies your force: mechanical advantage = load ÷ effort. An MA of 4 means a 50 N effort moves a 200 N load. The ideal MA comes from the machine’s dimensions; the actual MA is lower because of friction.
Key takeaway: MA = load ÷ effort.No. A machine cannot give out more work than you put in, because energy is conserved. Friction always turns a little of the work into heat, so the work in is a little more than the useful work out.
Key takeaway: machines change force, not energy.First class: the fulcrum is in the middle (seesaw, scissors). Second class: the load is in the middle (wheelbarrow, nutcracker). Third class: the effort is in the middle (tweezers, broom, your forearm).
Key takeaway: what is in the middle: fulcrum (1), load (2), effort (3).Each rope section that holds up the moving pulley carries part of the load. With 4 supporting sections each carries a quarter, so your pull is about a quarter of the load, but you must pull 4 m of rope to lift it 1 m. A single fixed pulley just changes the direction.
Key takeaway: more supporting ropes, less force, more rope to pull.Along a ramp you only push against part of the weight (weight × height ÷ length, without friction), but you push for the whole length of the slope. The longer and gentler the ramp, the smaller the push.
Key takeaway: smaller force over a longer path.For each full turn of the handle, the effort moves round a circle of 2π × handle radius, but the load rises only one pitch. With a 30 cm handle and a 5 mm pitch, IMA = 2π × 300 ÷ 5 ≈ 377. Friction is large, so the real MA is much lower, but that friction also stops the car from sinking back down.
Key takeaway: a long circle in, a tiny rise out.Efficiency = useful work out ÷ work in × 100%. Some work always goes into friction (heating the axle, rope or surfaces) or into bending and moving parts of the machine itself, so real efficiency is below 100%.
Key takeaway: friction makes efficiency less than 100%.Two or more simple machines working together, such as a bicycle, scissors (two levers with wedge blades), a can opener or a crane. The total mechanical advantage is the product of the parts’ mechanical advantages.
Key takeaway: simple machines combined; their MAs multiply.