Lever calculator, spot the machine and the quiz
Try the numbers, then test yourself. Every answer comes with its source.
How to play. Pick an answer and the fact behind it appears, with a link to where it comes from. Without JavaScript, open “Show the answer” under each question.
The lever calculator
A seesaw with the fulcrum in the middle. Put a load on the left, choose where you push on the right, and see how hard you need to push. The marks along the bar are equal steps from the fulcrum.
Move a slider to see the result.
Our own arithmetic from the law of the lever Britannica: it balances when load × its distance = your push × your distance. Real seesaws have a little friction and a bar with weight of its own, so this is the ideal case.
Spot the machine
Twelve things from around the house. Which simple machine is each one? Some have two right answers.
1 Scissors
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Lever (the blades are wedges too). A pair of scissors is a double first-class lever, with the pivot screw as the fulcrum. Illinois State Univ. Scissors are a compound machine: the edges of the blades are wedges, joined to make a lever. Science Trek
2 A door handle
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Sources differ: the US Navy manual calls a doorknob a wheel and axle, Science Trek lists door handles as levers. Both count. A doorknob is a wheel and axle. Try turning the bare square shaft with your fingers once the knob is off: it is tough work. US Navy Levers are all around us: door handles, the claws of a hammer, crowbars, light switches, bottle openers and hinges. Science Trek
3 A bottle opener
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Lever. In a second-class lever the load is between the fulcrum and the effort: wheelbarrows, nutcrackers and some bottle openers. BBC Bitesize
4 A wheelchair ramp
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Inclined plane. Stairs, escalators, ladders, wheelchair ramps and even mail chutes are versions of the ramp. Science Trek
5 A zip
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Wedge (plus hooks). A zip uses two ancient tools, the wedge and the hook: the slide holds a set of wedges that push the teeth together or force them apart. Indiana Public Media
6 A jar lid
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Screw. Screws are in jar lids, drills, bolts, light bulbs, taps, bottle caps and ball-point pens, and a spiral staircase is a kind of screw. Science Trek
7 The rope that raises a flag
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Pulley. Pulling down on a flagpole rope to raise the flag is a single pulley at work: down here, up there. Science Trek
8 An axe
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Wedge. An axe is a wedge, and so are the teeth on a saw. Britannica
9 A well with a winding handle
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Wheel and axle. The old well windlass: an 8-inch crank turning a 2-inch drum gives a theoretical mechanical advantage of 4. US Navy
10 A doorstop
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Wedge. Wedges also hold things in place: staples, drawing pins, nails, doorstops and shims. Science Trek
11 Tweezers
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Lever (third class). In a third-class lever the effort is between the fulcrum and the load: tweezers, tongs and fishing rods. BBC Bitesize
12 A spiral staircase
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Screw (and so a kind of inclined plane). Screws are in jar lids, drills, bolts, light bulbs, taps, bottle caps and ball-point pens, and a spiral staircase is a kind of screw. Science Trek Stairs, escalators, ladders, wheelchair ramps and even mail chutes are versions of the ramp. Science Trek
The simple machines quiz
1 Which of these is NOT on Britannica’s list of six simple machines?
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Gear. Britannica lists six simple machines: the inclined plane, the lever, the wedge, the wheel and axle, the pulley and the screw. Britannica A US Navy training manual also counts six, but a different six: the lever, the block, the wheel and axle, the inclined plane, the screw and the gear. US Navy
2 What is the pivot of a lever called?
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The fulcrum. A lever is a bar or board that rests on a support called a fulcrum. Britannica
3 A wheelbarrow is which class of lever?
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Second class. In a second-class lever the load is between the fulcrum and the effort: wheelbarrows, nutcrackers and some bottle openers. BBC Bitesize
4 Tweezers are which class of lever?
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Third class. In a third-class lever the effort is between the fulcrum and the load: tweezers, tongs and fishing rods. BBC Bitesize
5 A pulley system has four rope sections holding up the load. Its mechanical advantage is about…
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4. For a pulley system, the mechanical advantage is roughly the number of rope sections holding up the load: 2, 3, 4 and so on. OpenStax
6 A ramp lets you push with less force. What do you give up?
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You push over a longer distance. It takes the same amount of work, but less force, to move an object up a ramp than to lift it straight up. Science Trek Machines multiply force at the expense of distance: you push with less force, but over a longer distance. OpenStax
7 A screw may be thought of as…
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A wedge wrapped round a cylinder. In terms of how it works, a screw may be thought of as a wedge wrapped around a cylinder. Britannica
8 Where does the famous line “Give me a place to stand and with a lever I will move the whole world” come from?
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John Tzetzes, 12th century AD. The famous wording, “Give me a place to stand and with a lever I will move the whole world”, is from John Tzetzes, writing in the 12th century AD. Rorres, NYU Britannica calls the story that he said “Give me a place to stand and I will move the Earth” apocryphal: not reliably recorded. Britannica
9 How many simple machines did Hero of Alexandria describe?
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Five. The Greek engineer Hero of Alexandria described five simple machines: the lever, the pulley, the wheel, the wedge and the screw. Univ. of Oklahoma
10 You hold a heavy bag perfectly still for a minute. How much work have you done, in physics?
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None. Holding a heavy object still, however tiring, does no work in the physics sense. Britannica
11 The shadoof, used in Egypt and India for lifting water, is a…
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Lever. The shadoof is a long lever with a water container on the short arm and counterweights on the long arm; it is said to have been used in Egypt and India as early as 1500 BCE. Britannica
12 In which year did Guidobaldo del Monte show that the classical machines all follow from the lever?
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1577. In 1577 Guidobaldo del Monte showed that all five of Hero’s machines could be worked out from the principle of the lever. Univ. of Oklahoma
Myth or fact?
Eight statements. Some are true, some are myths.
1 Archimedes definitely said “Give me a place to stand and I will move the Earth”.
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Myth. Britannica calls the story that he said “Give me a place to stand and I will move the Earth” apocryphal: not reliably recorded. Britannica The oldest version is in Plutarch (about AD 45–120), writing some 300 years later: if there were another earth, Archimedes said, by going into it he could move this one. Rorres, NYU
2 A machine can give you more work out than you put in.
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Myth. A machine cannot do more work than the energy put into it, so energy is still conserved. OpenStax
3 A ramp means less force, but a longer distance.
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Fact. It takes the same amount of work, but less force, to move an object up a ramp than to lift it straight up. Science Trek
4 Everyone agrees there are exactly six simple machines, and which six.
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Myth. Britannica’s own articles on the pulley and the wedge call each of them one of “the five simple machines”, a list without the inclined plane. Britannica A US Navy training manual also counts six, but a different six: the lever, the block, the wheel and axle, the inclined plane, the screw and the gear. US Navy
5 A single fixed pulley halves the force you need.
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Myth. A single fixed pulley has a mechanical advantage of 1: it doesn’t reduce the force, it changes its direction. OpenStax
6 A zip works with wedges.
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Fact. A zip uses two ancient tools, the wedge and the hook: the slide holds a set of wedges that push the teeth together or force them apart. Indiana Public Media
7 Holding a heavy suitcase perfectly still counts as work, in physics.
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Myth. Holding a heavy object still, however tiring, does no work in the physics sense. Britannica
8 Gears are a form of the wheel and axle.
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Fact. Gears are a form of the wheel and axle. Science Trek