One pulley changes the direction of a pull, not its size. Ropes that hold up a moving block share the load, so the pull shrinks, but you pull more rope by the same factor. Students test pulleys, work out pulls and rope lengths, see that work in equals work out, and choose a pulley system for a brief.
A 400 N sack has to go up onto a stage. You can pull 150 N. How many pulleys do you need, and how much rope will you pull?
A pulley is a wheel with a rope over it. A block holds one or more pulleys. In this lesson a top block hangs from a beam, a bottom block carries the load, and ropes run between them. The rope you pull goes over the top block.
The job: lift a 400 N sack (about 40 kg) 1 m. You can pull 150 N at most.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
One pulley
TryTry it on the board and compare the result with your prediction.
Try: add ropes
Was your prediction right? One pulley changes only the direction. Ropes that hold the moving block share the load.
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With one rope holding the sack, press Pull.
Use the board. This ticks when you get there.
Add ropes (more pulleys) until your 150 N lifts the sack. Use as few as you can.
Use the board. This ticks when you get there.
With 3 ropes, how much rope did you pull to lift the sack 1 m (in metres)?
InvestigateWork out why it happens, one step at a time.
Worked example: count the ropes
Worked exampleBefore each step, say what you think comes next.
4 ropes hold the bottom blockCount only the ropes between the blocks. The rope you pull goes over the top, so it does not hold the load up.
400÷4=100 NThe ropes share the load: each holds 100 N, and so does your hand.
4×1=4 mTo lift the block 1 m, each of the 4 ropes must get 1 m shorter: you pull 4 m.
100×4=400400×1=400Work = force × distance. Work in (100 N × 4 m) equals work out (400 N × 1 m): no free lunch.
Now 6 ropes hold up a 600 N load. Start with the pull.
Mia builds a block and tackle with 4 ropes between the blocks.
6 ropes hold up the bottom block, and the load is 600 N. What pull lifts it, in newtons?
With those 6 ropes, how much rope do you pull to lift the load 2 m, in metres?
Mia thinks she needs only 80 N. Click the line where Mia's working first goes wrong.
ModifyChange the problem on purpose and see what happens.
Vary: choose a system
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A 900 N engine, and you can pull 200 N. Lift it with as few ropes as you can (fewer ropes means less rope to pull).
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Pulleys
3 ropes hold up a 750 N load. What pull lifts it, in newtons?
A crane's hook hangs on 8 ropes. To raise the hook 5 m, how much rope does the winch wind in, in metres?
Each mechanism trades one thing for another. Match each to what it gives up to make your force bigger.
Gears, small driving big
Lever, pivot near the load
Block and tackle
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
A brief that needs four ropes
Need a hint?
With 4 ropes the pull is load ÷ 4. With 3 ropes it is load ÷ 3.
Another hint
You need the 3-rope pull to be too big for you, and the 4-rope pull to be small enough.
Another hint
For example, a 600 N load: 3 ropes need 200 N, 4 ropes need 150 N. Which pull would you choose?
Stretch: real pulleys have friction, and the bottom block has weight. Would you need more or fewer ropes in real life? Why?
Try it yourselfYour edits are saved in this browser.
Set a load and your pull so that 4 ropes is the fewest that works. Then choose 4 ropes and lift.
Use the board. This ticks when you get there.
For teachers
Students find that one fixed pulley changes only the direction of a pull, add ropes until 150 N lifts a 400 N sack, work out the pull (load ÷ supporting ropes) and the rope pulled (height × ropes), see that work in equals work out, choose a system for a brief and write a brief that needs four ropes. About 45 minutes.
I can explain that one fixed pulley changes the direction of a pull, not its size.
I can work out the pull and the rope pulled by counting the ropes that hold the load up.
I can explain that a pulley system's work in equals its work out.
I can choose the fewest pulleys that meet a brief.
Before class
Do Levers first: the Practise match ties gears, levers and pulleys together as one trade.
A pair of broom handles and a rope makes a striking demonstration: wrap the rope between them 3 or 4 times and one student can pull two others together.
Simplifications: no friction, and the pulleys, blocks and rope weigh nothing. Real systems lose a lot to friction, so they need more ropes than the model says.
Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Science, forces and simple machines (Year 7), energy and work (Year 8–9); Maths, multiplication and division.
Running the lesson
Predict: most students choose 200 N. After the Try, ask why one pulley did not help.
Try: ask students to count the rope they pulled before the note appears.
Worked example: trace each rope with a finger and ask: does this one hold the block up?
Find the mistake: Mia's fifth rope goes over the top block. Point at where it is tied.
Vary: link the fixed pulley back to the idler gear: direction, not size.
Make: compare briefs; whose load ÷ pull ratio is closest to 4?
The hard part (on purpose)
Students count the rope they pull as a supporting rope, and expect any pulley to help. Ask 'does this rope hold the bottom block up?' for every rope.
When students get stuck
A student counts the rope they pull. Ask: Does this rope hold the bottom block up, or does it go over the top? Fix: Count only the ropes between the blocks.
A student thinks one pulley halves the pull. Ask: How many ropes hold the sack up? Fix: One rope: the whole load. A fixed pulley only turns the pull round.
A student thinks more ropes means less work. Ask: How much rope did you pull, and with what force? Fix: Pull × rope pulled = load × height, whatever the number of ropes.
Stretch and support
Stretch: Each pulley wheel loses about 5% of the force to friction. With 4 ropes (and so 4 wheels), roughly what pull lifts the 400 N sack now?
Support: Give a table with columns ropes, pull, rope pulled for 1 m, work in, and fill the 1-rope and 2-rope rows together.
Where it leads
Next: the Capstone projects (Physical computing) include a lift and a winch where these trade-offs meet a motor.
Real examples: cranes, sailing boats (a mainsheet), flagpoles, window blinds, gym machines, rescue hauling systems.
one pulley: Many students expect any pulley to make lifting easier. Committing first makes the result stick: a single fixed pulley only changes direction, like an idler gear. Each wrong option is a real slip: halving, or the turning wheel helping.
Try: add ropes: One rope fails at 150 N; adding ropes that hold the bottom block until it lifts settles the size question, and the rope pulled is reported, so students meet the cost before the rule.
Worked example: count the ropes: The worked example gives two rules from one count: pull = load ÷ supporting ropes, rope pulled = height × supporting ropes, and shows work in = work out. The faded example uses 6 ropes. Mia counts the rope she pulls, planted after the method.
Vary: choose a system: Students reason from the brief to the fewest ropes, then connect the fixed pulley back to the idler gear: a mechanism can change direction without changing force.
pulleys: Count the supporting ropes, divide for the pull, multiply for the rope, and the same trade as levers and gears.
a brief that needs four ropes: Writing a brief with a given answer reverses the reasoning: the load ÷ the pull must be more than 3 and no more than 4.
Now you can
Explain that one fixed pulley changes the direction of a pull, not its size.
Work out the pull and the rope pulled by counting the ropes that hold the load up.
Explain that a pulley system's work in equals its work out.