Students meet friction in the gear train and pulley boards, find the winch lifts 2700 g instead of 3000 g and that pulleys beyond about nine stop helping, multiply stage efficiencies, account for the lost work as heat and sound, and redo two earlier briefs with friction in them.
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Students will be able to
I can work out a machine's overall efficiency by multiplying the efficiency of each stage.
I can explain where the 'lost' work goes, and why energy is still conserved.
I can explain why adding more pulleys or gears eventually stops helping.
I can redesign a machine so it still meets its brief with friction.
Timing
Predict and Try 12 min · Worked example 10 min · Vary 6 min · Practise and Make 17 min
Before class
Do Gear trains and Pulleys first; Science › Year 9 Efficiency and Conservation are the Science homes of the ideas (the page links them).
The model: each gear mesh passes on a fixed fraction of the turning force (95%) and each pulley wheel a fixed fraction of the pull (90%), whatever the load; speed and rope length are unchanged. Real losses depend on lubrication, load and speed; 90–98% per stage is typical.
A hands-on check: a spring balance on a real block and tackle reads more than load ÷ ropes, and the gap grows with more pulleys.
Curriculum hooks: Design and Technologies, engineering principles and systems; Science, energy conservation and efficiency (Year 9); Maths, percentages and repeated multiplication.
Running the lesson
Predict: most expect 'keep getting smaller'. Ask why riggers stop at about six.
Try: have students say the frictionless answer before each test.
Worked example: build the 0.9 × 0.9 × … chain on the board and stop to ask what each 0.9 is 90% of.
Make: compare the frictionless and friction answers to the same brief.
The hard part (on purpose)
Students subtract the losses (95% − 5% − 5%) or think energy is destroyed. Keep asking 'of what?': each stage passes on 95% of what it received.
When students get stuck
What you will see
A question to ask
The fix
A student subtracts the losses.
The second mesh gets 95% of what?
Of what the first passed on: multiply.
A student says friction destroys energy.
What do the gears feel like after a long run?
Warm: the energy became heat.
A student keeps adding pulleys.
Did the last one make the pull smaller?
Each extra wheel wastes more; past about 9 it costs more than it saves.
Answers to the checks
more and more pulleys: Each pulley wheel loses 10% of the pull. You keep adding pulleys. The pull you need… Smaller at first, then it levels off (here at about 9 ropes) and starts to grow. Each new rope shares the load, but each new wheel wastes 10% more.
The winch: The winch's compound train (ratio 15) should lift 3000 g with no friction. Add 50 g at a time and lift, until it stalls.
It lifts 2700 g and stalls at 2750 g: two meshes at 95% pass on 90% of the force.
Its heaviest lift: What is the heaviest bucket it lifted, in grams? 2700 2700 g. 3000 × 0.95 × 0.95 = 2707.5, so 2700 g lifts and 2750 g stalls.
Fewest ropes: Pulleys with friction: find the fewest ropes that let your 150 N lift the 400 N sack.
5 ropes (135 N). With no friction 3 would do; with friction 3 ropes need 183 N and 4 need 153 N.
9 or 10?: Now try 9 ropes, then 10. Compare the pulls.
Both need about 115 N. The tenth rope shares the load, but its wheel wastes as much as it saves.
Four pulleys, step by step: Three gear meshes, each 95% efficient. What is the overall efficiency, to the nearest percent? 86 0.95³ = 0.857, about 86%.
The work in: A machine is 80% efficient and must do 400 J of useful work. How much work must go in, in joules? 500 400 ÷ 0.8 = 500 J; 100 J becomes heat and sound.
Where it goes: Where does the 'lost' work go? It becomes heat and sound in the rubbing parts: the energy is still there, just not useful Energy is conserved. Friction transfers some of it to heat (and a little sound), which is no use for lifting.
Vary: a brief with friction: Lift a 900 N engine with a pull of at most 300 N, using the fewest ropes. Each wheel is 90% efficient.
6 ropes (282 N). 5 ropes need 305 N: just too much. Without friction 3 would do.
Two stages: Two stages, 90% and 80% efficient. What is the overall efficiency, in percent? 72 0.9 × 0.8 = 0.72 = 72%.
Work in: A winch is 75% efficient. It lifts a 600 N load 2 m. How much work goes in, in joules? 1600 Work out = 600 × 2 = 1200 J; work in = 1200 ÷ 0.75 = 1600 J.
Better: Which change makes a gear train more efficient? Fewer meshes (for example one bigger stage instead of two small ones), or better lubrication Every mesh loses some energy, so fewer meshes and less rubbing (oil, bearings) mean less waste. That trades against gear size.
With friction: Lift 1500 g within 45 s with a compound train, now that each mesh is 95% efficient.
A ratio of 9 (8 → 24 = 8 → 24, 45 s) or 8.33 (8 → 40 = 24 → 40, 41.7 s). Ratio 7.5, the frictionless answer, now lifts only 1354 g.
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: a brief with friction
Open task: any program that does what the step asks.
the winch again, with friction › With friction
Open task: any program that does what the step asks.
the winch again, with friction › Evaluate
Open task: any program that does what the step asks.
Stretch and support
Stretch: For 90% wheels, which number of ropes gives the smallest pull? Work out n × 0.9ⁿ for n = 8, 9, 10, 11.
Support: Give a table: ropes, ideal pull, efficiency (0.9ⁿ), real pull. Fill rows 1 to 4 together.
Exit ticket
A two-stage gear train has stages of 95% and 90%. What is its overall efficiency, and where does the rest of the energy go?
0.95 × 0.9 = 0.855, about 86%; the other 14% becomes heat and sound in the meshes.
What each step is for
more and more pulleys: The frictionless rule (more ropes, less pull) invites 'add pulleys for ever'. Committing first makes the levelling-off a surprise worth explaining.
Try: friction in the winch and the pulleys: The gear train lifts less than its ideal 3000 g; the pulley's fewest ropes rise from 3 to 5, and ropes 9 and 10 give the same pull.
Worked example: multiply the losses: Each stage passes on a fraction of what it gets, so efficiencies multiply. Work in = work out ÷ efficiency, and the difference is the energy lost as heat and sound.
Vary: a brief with friction: Students redo a pulley brief with losses: the frictionless answer (3 ropes) now fails, and the rule of thumb becomes 'test it'.
efficiency: Multiply stage efficiencies, divide for work in, and the losses link to Science's efficiency.
the winch again, with friction: The Gear trains brief, redone with 95% per mesh: the frictionless answer (ratio 7.5) now stalls, so students need a slightly bigger ratio and a looser time limit.
Where it leads
Next: Linkages and cams; Structures.
Science: Year 9 Efficiency and Where does the energy go? (the Builds on links on this page).