Levers and Simple Machines
A lever does not give you free strength. It trades distance for force, and once you see what is being traded, every simple machine works the same way.
The three parts
A lever is a stiff bar that turns around a fixed point.
Every lever has the same three parts, and naming them correctly is most of what is assessed on this topic.
- The fulcrum is the fixed point it pivots on.
- The effort is the force you apply.
- The load is the thing you are trying to move.
A see-saw, a pair of scissors, a wheelbarrow, a bottle opener and your own forearm are all levers, which is a strange enough list that it is worth pausing on: what they share is not their shape but the fact that each one turns about a fixed point and moves something at the other end. So does a spoon prising the lid off a tin of paint, which is the example most children have actually done.
Where the fulcrum sits
The whole usefulness of a lever comes from one thing: how far the effort is from the fulcrum compared with the load.
The rule that decides it
A longer effort arm than load arm means less force is needed.
A shorter effort arm than load arm means more force is needed, and you get speed and distance instead.
A crowbar has its fulcrum 20 cm from the load and you push 80 cm from the fulcrum. A 400 N load. Roughly what effort is needed?
- The effort arm is 80 cm and the load arm is 20 cm.
- 80 divided by 20 is 4, so the effort arm is four times longer.
- That means the force needed is about a quarter.
- 400 divided by 4 = 100.
About 100 N
What you trade
This is the part that gets left out, and it is the part that makes a lever make sense rather than seem like magic.
You pushed with a quarter of the force, and in exchange your end of the bar had to travel four times as far, so lifting the load by five centimetres meant bringing your hand down twenty. Nothing was created anywhere. You did exactly the same total work, spread out over a longer distance so that less force was needed at any one moment, which is the only thing any machine has ever done for anybody.
Machines never give you something for nothing
Every simple machine makes a job easier in one way by making it harder in another. Usually less force in exchange for more distance. A ramp is the clearest example: pushing a barrel up a long gentle slope is easy, and you have to push it a very long way.
Other simple machines
Levers are one of a small family of simple machines, and although they look nothing like each other, every one of them is making the same trade of force against distance.
- A ramp lets you raise something with less force, over a longer distance.
- A pulley lets you pull down instead of lifting up, and with several wheels it also reduces the force, in exchange for pulling more rope.
- A wheel and axle turns a small force at the rim into a large one at the centre. A door handle is one.
- A screw is a ramp wrapped round a cylinder, which is worth pointing out because nobody sees it until they are told.
Common mistakes
1. Thinking a lever reduces the work
It reduces the force and increases the distance, and those cancel out. If a lever really did reduce the total work, you could build one that powered itself. The clue is always in what your hand has to do.
2. Assuming the fulcrum is always in the middle
Only on a see-saw, because a see-saw is meant to balance rather than to help. Move the fulcrum and the whole behaviour changes, which is the one variable this topic is about. In a wheelbarrow the fulcrum is at the far end, at the wheel.
3. Mixing up effort and load
The effort is what you provide and the load is what resists. In a pair of scissors your hand is the effort and the paper is the load, and the fulcrum is the little screw. Working out which is which comes before any calculation, and getting it backwards makes every later step wrong.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
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What to learn next
Machines trade force for distance without changing the total work, and work is energy being moved about. Energy is the idea that ties this whole cluster together.
For parents
Open a tin of paint with a spoon, or a bottle with an opener, and ask where the pivot is. Then ask what would happen if they held the spoon halfway down instead of at the end. They will predict it correctly, try it, and find they were right, which is a better lesson than any diagram.
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