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# Real machines lose energy

Mechanisms · Real machines

<!-- Speaker note: 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. About 45 minutes (Predict and Try 12 min · Worked example 10 min · Vary 6 min · Practise and Make 17 min). Sources: TeachEngineering: K-12 engineering design challenges (benchmark; the briefs and wording are our own), https://www.teachengineering.org/ (checked 12 October 2026). -->

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## Today

**We are learning to** every real gear mesh and pulley wheel turns a little of the work into heat and sound. Students find a gear train lifts less than the ideal, that adding pulleys stops helping, work out overall efficiency by multiplying, and redesign a brief with friction in it.

- 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.

<!-- Speaker note: 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. Teacher: Try: have students say the frictionless answer before each test. Teacher: Worked example: build the 0.9 × 0.9 × … chain on the board and stop to ask what each 0.9 is 90% of. -->

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## Why it matters

> The ideal block and tackle said more pulleys always means less pull. Real riggers stop at about six. Why?

<!-- Speaker note: The earlier Mechanisms boards had no friction, so **work in = work out**: a smaller force over a longer distance did exactly the same work. Real machines rub. Each gear mesh and each pulley wheel turns a little of the work into **heat** and **sound**, and the energy is still all there (it is conserved), but less of it is **useful**. **Efficiency** = useful work out ÷ work in. Here each **gear mesh** passes on **95%** of the turning force, and each **pulley wheel** passes on **90%** of the pull. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**Each pulley wheel loses 10% of the pull. You keep adding pulleys. The pull you need…**

- Stays the same: friction cancels out
- Gets smaller at first, then stops getting smaller
- Gets bigger straight away
- Keeps getting smaller for ever, as before

<!-- Speaker note: What happens: 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. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: most expect 'keep getting smaller'. Ask why riggers stop at about six. -->

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## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fengineering%2Fmechanisms%2Flosses%2Fstep-2&code=widget%3A+train%0Atrain%3A+8+%3E+24+%3D+8+%3E+40%0Aefficiency%3A+95%0Aload%3A+2500%0Aaddload%3A+on%0Anumbers%3A+off%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/engineering/mechanisms/losses/?full=step-2#step-2)

<!-- Speaker note:  -->

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## What happened?

* 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.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Four pulleys, step by step

$$0.9 \times 0.9 \times 0.9 \times 0.9 = 0.66$$

1) $\text{pull} = \frac{400}{4 \times 0.66} = 153 \text{ N}$ — The ideal pull (400 ÷ 4) divided by the efficiency.
2) $\text{work in} = 153 \times 4 = 610 \text{ J}$ — You still pull 4 m of rope to lift the sack 1 m.
3) $\text{work out} = 400 \times 1 = 400 \text{ J}$ — The useful work: the sack's weight times the height.
4) $610 - 400 = 210 \text{ J of heat and sound}$ — Efficiency = 400 ÷ 610 = 66%.

<!-- Speaker note: Model this live on the board before revealing anything: write each line and say why, pausing to ask the class what comes next. Then click to reveal the lines and compare. Script. Start: write 0.9 × 0.9 × 0.9 × 0.9 = 0.66 and say "Each of the 4 wheels passes on 90% of what it gets: multiply." Line 1: write pull = 400 ÷ 4 × 0.66 = 153 N and say "The ideal pull (400 ÷ 4) divided by the efficiency." Line 2: write work in = 153 × 4 = 610 J and say "You still pull 4 m of rope to lift the sack 1 m." Line 3: write work out = 400 × 1 = 400 J and say "The useful work: the sack's weight times the height." Line 4: write 610 - 400 = 210 J of heat and sound and say "Efficiency = 400 ÷ 610 = 66%." -->

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## Four pulleys, step by step

**Three gear meshes, each 95% efficient. What is the overall efficiency, to the nearest percent?**

* Answer: 86

<!-- Speaker note: 0.95³ = 0.857, about 86%. -->

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## The work in

**A machine is 80% efficient and must do 400 J of useful work. How much work must go in, in joules?**

* Answer: 500

<!-- Speaker note: 400 ÷ 0.8 = 500 J; 100 J becomes heat and sound. -->

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## Where it goes

**Where does the 'lost' work go?**

- It stays in the rope
- It goes back into the motor
- It is destroyed by friction
- It becomes heat and sound in the rubbing parts: the energy is still there, just not useful

* Answer: It becomes heat and sound in the rubbing parts: the energy is still there, just not useful

<!-- Speaker note: Energy is conserved. Friction transfers some of it to heat (and a little sound), which is no use for lifting. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Vary: a brief with friction



[Open this step](https://studio.learningwaypoints.com/tutorials/engineering/mechanisms/losses/?full=step-4#step-4)

<!-- Speaker note: What this step is for: Students redo a pulley brief with losses: the frictionless answer (3 ropes) now fails, and the rule of thumb becomes 'test it'. Hints, in order: Without friction, 900 ÷ 300 = 3 ropes would do. Try it. / Each extra rope helps less. Keep adding and test each time. For students who need more support: Give a table: ropes, ideal pull, efficiency (0.9ⁿ), real pull. Fill rows 1 to 4 together. For early finishers: For 90% wheels, which number of ropes gives the smallest pull? Work out n × 0.9ⁿ for n = 8, 9, 10, 11. 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: A student subtracts the losses. Ask: The second mesh gets 95% of what? Fix: Of what the first passed on: multiply. / A student says friction destroys energy. Ask: What do the gears feel like after a long run? Fix: Warm: the energy became heat. / A student keeps adding pulleys. Ask: Did the last one make the pull smaller? Fix: Each extra wheel wastes more; past about 9 it costs more than it saves. -->

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## Two stages

**Two stages, 90% and 80% efficient. What is the overall efficiency, in percent?**

* Answer: 72

<!-- Speaker note: 0.9 × 0.8 = 0.72 = 72%. -->

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## Work in

**A winch is 75% efficient. It lifts a 600 N load 2 m. How much work goes in, in joules?**

* Answer: 1600

<!-- Speaker note: Work out = 600 × 2 = 1200 J; work in = 1200 ÷ 0.75 = 1600 J. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Better

**Which change makes a gear train more efficient?**

- More meshes
- Heavier gears
- A faster motor
- Fewer meshes (for example one bigger stage instead of two small ones), or better lubrication

* Answer: Fewer meshes (for example one bigger stage instead of two small ones), or better lubrication

<!-- Speaker note: Every mesh loses some energy, so fewer meshes and less rubbing (oil, bearings) mean less waste. That trades against gear size. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Make: the winch again, with friction



- **With friction:** 
- **Evaluate:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/engineering/mechanisms/losses/?full=step-6#step-6)

<!-- Speaker note: What this step is for: 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. Hints, in order: With friction the train lifts 200 × ratio × 0.9 grams (two meshes). / 1500 ÷ (200 × 0.9025) ≈ 8.3: you need a ratio of at least 8.3. / The time is 5 × ratio seconds, so 45 s allows a ratio up to 9. Which two stages multiply to between 8.3 and 9? -->

<!-- Speaker note: Teacher: compare the frictionless and friction answers to the same brief. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## 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.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: Next: Linkages and cams; Structures. Science: Year 9 Efficiency and Where does the energy go? (the Builds on links on this page). -->