--- title: "Real machines lose energy" subtitle: "Mechanisms · Real machines · Lesson 5" --- # Real machines lose energy **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** The ideal block and tackle said more pulleys always means less pull. Real riggers stop at about six. Why? :::teacher-note **In one sentence:** 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. **Students should be able to say:** 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. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **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 My prediction, and why: {{lines-3}} ::: :::teacher-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. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: multiply the losses :::keep-together ### Four pulleys, step by step 1. $0.9 \times 0.9 \times 0.9 \times 0.9 = 0.66$ — Each of the 4 wheels passes on 90% of what it gets: multiply. 2. $\text{pull} = \frac{400}{4 \times 0.66} = 153 \text{ N}$ — The ideal pull (400 ÷ 4) divided by the efficiency. 3. $\text{work in} = 153 \times 4 = 610 \text{ J}$ — You still pull 4 m of rope to lift the sack 1 m. 4. $\text{work out} = 400 \times 1 = 400 \text{ J}$ — The useful work: the sack's weight times the height. 5. $610 - 400 = 210 \text{ J of heat and sound}$ — Efficiency = 400 ÷ 610 = 66%. **Three gear meshes, each 95% efficient. What is the overall efficiency, to the nearest percent?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 86 0.95³ = 0.857, about 86%. ::: :::keep-together ### 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: {{field-15}} ::: :::teacher-note **Answer:** 500 400 ÷ 0.8 = 500 J; 100 J becomes heat and sound. ::: :::keep-together ### 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 ::: :::teacher-note **Answer:** 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. ::: :::typical ## Vary: a brief with friction Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Efficiency :::keep-together ### Two stages **Two stages, 90% and 80% efficient. What is the overall efficiency, in percent?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 72 0.9 × 0.8 = 0.72 = 72%. ::: :::keep-together ### Work in **A winch is 75% efficient. It lifts a 600 N load 2 m. How much work goes in, in joules?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1600 Work out = 600 × 2 = 1200 J; work in = 1200 ÷ 0.75 = 1600 J. ::: :::keep-together ### 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 ::: :::teacher-note **Answer:** 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. ::: ## Make: the winch again, with friction **With friction.** **Evaluate.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **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?** {{lines-3}} ::: :::teacher-note **Answer:** 0.95 × 0.9 = 0.855, about 86%; the other 14% becomes heat and sound in the meshes. :::