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Simple Machines

Levers, pulleys and ramps don't give you free energy, but they make hard jobs feel easier.

How can one person lift a car with a jack, or roll a heavy box into a truck? On this page you'll learn what scientists mean by work, meet the six simple machines, find out how mechanical advantage trades force for distance, and see why no machine is perfectly efficient.

Try the lever balance Take the quiz
On the ground, a box rests on the slope of a wooden ramp, and next to it a long board on a triangle fulcrum has a rock under its short end and an arrow pushing down on its long end effort

Work: force times distance

In science, work is done when a force moves something. You find it with W = F × d: work (in joules, J) equals force (in newtons, N) times the distance moved in the direction of the force (in meters). Work is a way of moving energy, which you can read more about in the Energy unit.

Worked example (made-up numbers): you push a box with 50 N for 4 m. W = 50 N × 4 m = 200 J. If you push a wall and it doesn't move, d = 0, so you do no work on the wall, even though you get tired.

A machine can't make extra energy. What it can do is trade force for distance: push with less force over a longer distance, and you can do the same work. Ignoring friction, work in = work out.

The six simple machines

  • Lever: a stiff bar that turns on a pivot called the fulcrum. There are three classes:
    • First class: the fulcrum is in the middle, between the effort and the load. Examples: a seesaw, a crowbar.
    • Second class: the load is in the middle. Example: a wheelbarrow, where the wheel is the fulcrum and you lift the handles.
    • Third class: the effort is in the middle. Example: tweezers, or your own forearm. These need more force than the load, but the tips move farther and faster.
  • Wheel and axle: a big wheel fixed to a smaller rod, so they turn together. A small push on the big wheel makes a big turning force on the axle. Examples: a doorknob, a steering wheel, a screwdriver handle.
  • Pulley: a wheel with a rope over it.
    • A fixed pulley stays in place and only changes the direction of the force, like on a flagpole. You pull down to lift the flag up.
    • A movable pulley moves with the load. Two rope segments hold it up, so ideally you need half the force but pull twice as much rope.
    • A block and tackle combines fixed and movable pulleys. The ideal mechanical advantage equals the number of rope segments holding up the load.
  • Inclined plane: a ramp. Pushing a load up a long, gentle ramp takes less force than lifting it straight up, but you move it farther.
  • Wedge: two inclined planes back to back that push things apart. Examples: an axe, a knife, a doorstop.
  • Screw: an inclined plane wrapped around a rod. Each turn moves the screw a little way forward with lots of force. Examples: jar lids, bolts, a car jack.

Mechanical advantage

Mechanical advantage (MA) tells you how many times a machine multiplies your force. The ideal MA ignores friction:

  • Lever: ideal MA = effort arm ÷ load arm (the distances from the fulcrum to where you push and to the load).
  • Ramp: ideal MA = length of the ramp ÷ height.

Worked examples (made-up numbers)

  • A crowbar has an effort arm of 1.5 m and a load arm of 0.5 m. Ideal MA = 1.5 ÷ 0.5 = 3. To lift a 300 N rock, you'd ideally push with 300 ÷ 3 = 100 N, but your hand moves 3 times as far as the rock.
  • A ramp is 6 m long and 1.5 m high. Ideal MA = 6 ÷ 1.5 = 4. A 400 N box would ideally need only 100 N to push up the ramp. Check: work in = 100 N × 6 m = 600 J; work out = 400 N × 1.5 m = 600 J.
  • Tweezers are a third-class lever: an effort arm of 4 cm and a load arm of 8 cm give an ideal MA of 0.5. You push harder, but the tweezer tips move twice as far.

Try it: the lever balance

A 100 cm board has a load on the left end and your push (the effort) on the right end. Move the fulcrum, change the load, and see how hard you must push to balance it. This is an ideal model: the board has no weight and there's no friction.

Load arm 25 cm, effort arm 75 cm. Ideal MA = 3.00. Effort needed to balance = 20.0 N.

loadeffort

When the board is level, effort × effort arm = load × load arm. If you push harder than needed, your end tips down; if you push too little, the load end tips down. A push within 2% of the exact amount counts as almost balanced, and the tilt is capped at about 20° to keep the drawing in the frame.

Efficiency and friction

Real machines lose some energy to friction, which turns it into heat, so you always put in a bit more work than you get out. Efficiency = work out ÷ work in × 100%.

Worked example (made-up numbers): you do 250 J of work pushing a box up a ramp, and the box gains 200 J of energy. Efficiency = 200 ÷ 250 × 100% = 80%. The other 50 J warmed the ramp and the box. No machine is 100% efficient, so the actual MA is always less than the ideal MA. Oil, wheels and smooth surfaces reduce friction.

Compound machines

A compound machine is two or more simple machines working together.

  • Bicycle: the pedals and crank are a wheel and axle, the chain and gears pass the turning to the back wheel, and the brake handles are levers.
  • Scissors: two first-class levers joined at a fulcrum, with blades that are wedges.
  • Can opener: the handles are levers, the turning key is a wheel and axle, and the sharp cutting wheel is a wedge.

Archimedes and the lever

Archimedes was a Greek mathematician and engineer who lived in Syracuse, on the island of Sicily, more than 2,200 years ago. He studied the math of levers and balances. He is often quoted as saying, "Give me a place to stand, and I shall move the earth." This saying is attributed to him by later writers such as Pappus of Alexandria, who lived more than 500 years after him, so we can't be sure of his exact words. The idea is true, though: with a long enough lever and a fulcrum, a small force can move a huge load, but your end would have to move an enormous distance.

Experiments to try at home

Ask an adult before you start. Keep coins and other small parts away from little kids, because they're a choking hazard.

Quick quiz

1. You push a cart with 20 N for 3 m. How much work do you do?

2. What class of lever is a wheelbarrow?

3. A ramp is 10 m long and 2 m high. What is its ideal mechanical advantage?

4. What do simple machines really do?

5. What does a single fixed pulley do?

6. A screw is really...

Talk about it

  • Find three levers in your kitchen. Which class is each one?
  • Why do roads up steep mountains zigzag back and forth instead of going straight up?
  • If machines don't save work, why do people use them at all?

Sources

Credits: All illustrations on this page are original, hand-coded SVG by Galileo. The share image was drawn in code.