Energy transfers · Quantitative
Simple machines
A paving slab weighing 600 N will not budge. Slide a crowbar underneath and a push of 100 N lifts it. The bar has no motor and no battery. Where did the extra 500 N come from?
Start here
Six times the force. No extra effort.
A paving slab weighing 600 N will not budge when you pull on it. Slide a crowbar underneath, and a push of 100 N lifts it easily. The bar has no motor, no battery and no moving parts.
Commit. Where did the extra 500 N come from?
Nowhere. Force is not conserved and there is nothing strange about multiplying it — you get six times the force and you move your end six times as far. Multiply force by distance on each side and the two products match. The energy is what cannot be multiplied, and that is what the bench below measures.
A simple machine is any device that trades force against distance: levers, ramps, pulleys, gears, screws. None of them creates energy, none of them reduces the energy needed for a job, and every one of them makes a job possible that your muscles could not do directly. This lesson measures the trade rather than asserting it.
The lever bench · move the fulcrum and measure
Read both ends, then multiply.
A 600 N load on a 2.4 m bar. Slide the fulcrum, lift the load by 5 cm, and record what the force meter and the two rulers say.
Commit first. A lever lets you lift a load with a quarter of the force. What happens to the energy you have to supply?
Your force
Your distance
Energy in
Energy out
| Your force | Your distance | Energy in | Energy out |
|---|
Every row has nearly the same number in the last two columns, whatever you did with the fulcrum — and the input column is always a little the larger, never the smaller. That is friction at the fulcrum taking its cut into a thermal store. A machine changes the shape of a job; it never changes the size of it, and it never does it for less.
Writing it down · the shape of this relationship
force on one side × distance on that side = force on the other side × distance on that side
force is measured in newtons (N)
distance is measured in metres (m)
their product, the energy, is in joules (J)
One side at a time
Which quantity are you solving for?
Energy is alone at the top. Cover it and the other two sit side by side — multiply.
Force sits underneath with energy above it. Cover F and you are left with E over d — divide.
Distance sits underneath with energy above it. Cover d and you are left with E over F — divide.
Two things side by side means multiply. One thing over another means divide. This triangle is for ONE side of the lever rule: the rule itself has four quantities and an equals sign, not three quantities and a bar, so read that off the beam above.
Five lines, every time · CFIFA
You push a lever with 250 N and your end moves 0.12 m. How much energy do you transfer?
Step 0 of 5
Convert
250 N stays 250 N · 0.12 m stays 0.12 m
The force is already in newtons and the distance already in metres, so there is nothing to convert. The step still gets written down — that is how you notice the times there IS something.
Formula
E = F × d
Cover E on the triangle: F sits beside d, so you multiply.
Insert
E = 250 N × 0.12 m
The distance is how far YOUR end moved, not how far the load rose. Those are different numbers and this is where they get swapped.
Fine-tune
250 × 0.12 = 30
Newtons times metres gives joules.
Answer
E = 30 J
Thirty joules in at your end — and the load end can never get more than that.
The same five lines · when the units do not match
You push a crate up a ramp with 80 N and it moves 250 cm along the slope.
Step 0 of 5
Convert
250 cm ÷ 100 = 2.50 m
A joule is a newton times a metre, and a centimetre is a hundredth of one, so divide by 100.
Formula
E = F × d
Cover E on the triangle: F sits beside d, so you multiply.
Insert
E = 80 N × 2.50 m
The converted distance goes in. The 250 never does.
Fine-tune
80 × 2.50 = 200
Newtons times metres gives joules.
Answer
E = 200 J
Insert 250 instead of 2.50 and the answer comes out 20 000 J — a hundred times too big.
Think again
“A machine that multiplies force gives you energy for free.”
Force and energy are different quantities, and only one of them is conserved. Nothing forbids multiplying a force — a lever does it, a ramp does it, your own forearm does it in reverse every time you lift something. What is forbidden is getting more energy out than you put in, and no arrangement of levers has ever managed it.
Your own runs are the argument. Every row of the table has nearly the same number in the last two columns, whatever you did with the fulcrum. Six times the force, one sixth of the distance, near enough the same product. A machine changes the shape of a job so your muscles can do it; it never changes the size of the job.
And in reality the input column is always slightly the larger of the two, because friction at the fulcrum takes its cut into a thermal store. Real machines need a little more energy in than the job strictly requires — never less.
“A longer lever gets the job done with less energy.”
It gets it done with less FORCE, and you pay for that in distance. Double the length of your side and you halve the force needed, but your end has to travel twice as far — and force × distance, which is the energy, comes out the same. Every simple machine trades one for the other along a line of fixed energy, and friction means the trade is always slightly in the machine’s favour, never in yours.
Key fact
A machine can multiply force or multiply distance, but never both, and never energy. The energy you put in at your end is always at least the energy that comes out at the load end — the rest goes to friction.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
You push down with 150 N and your end of the lever moves 40 cm. How much energy did you transfer?
Rung 2 · The one that catches people
A ramp lets you push a 900 N barrel up to a platform using only 300 N. What must be true?
Rung 3 · Explain
Using your own results from the lever bench, explain why a lever cannot give you energy for free — and explain why your measured input was always slightly larger than the output.
Rung 4 · Take it somewhere new
A gear system is advertised as “doubling the power of your drill for free”. Explain what it can and cannot do, and say what you would measure to check the claim.
Key note
A simple machine trades force against distance and the product of the two — the energy — is what stays fixed. Multiply the force and you divide the distance by the same amount. Friction means you always put in a little more than comes out, and never less.
Going further
People have been trying to build a machine that gives out more than it takes in for at least eight hundred years, and the applications never stopped arriving — so in 1911 the US Patent Office simply refused to consider such applications without a working model, which nobody has ever produced. What makes the whole class impossible is not a flaw in any particular design; it is the sum you have been checking all lesson. If force × distance in must equal force × distance out, there is nothing left over to run the machine with, no matter how the linkages are arranged. Conservation of energy does not need to inspect your invention to know it will not work.
Before this lesson
Connects to
At GCSE this becomes
- Moments and the principle of moments, work done as a calculated quantity, and efficiency expressed as a percentage of the energy supplied.
Where to next
- Next: Energy in food
Energy at home
- Previous: Insulation
Ask Mr Badmus AI
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