--- title: "Pulleys" subtitle: "Mechanisms · Levers and pulleys · Lesson 4" --- # Pulleys **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** 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? :::teacher-note **In one sentence:** 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. **Students should be able to say:** 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. **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 **One pulley at the top, and the rope goes from the sack, over the pulley and down to your hand. To lift the 400 N sack you pull…** ☐ 800 N: the rope goes up and down ☐ 400 N, but downwards ☐ Less than 400 N, because the wheel turns ☐ 200 N: the pulley halves it My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 400 N. One fixed pulley changes the direction of the pull (you can pull down, using your weight), not its size. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: count the ropes :::keep-together ### Four ropes, then six 1. $4 \text{ ropes hold the bottom block}$ — Count only the ropes between the blocks. The rope you pull goes over the top, so it does not hold the load up. 2. $400 \div 4 = 100 \text{ N}$ — The ropes share the load: each holds 100 N, and so does your hand. 3. $4 \times 1 = 4 \text{ m}$ — To lift the block 1 m, each of the 4 ropes must get 1 m shorter: you pull 4 m. 4. $100 \times 4 = 400 \quad 400 \times 1 = 400$ — Work = 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. **6 ropes hold up the bottom block, and the load is 600 N. What pull lifts it, in newtons?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 100 600 ÷ 6 = 100 N. ::: :::keep-together ### Rope **With those 6 ropes, how much rope do you pull to lift the load 2 m, in metres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12 6 × 2 = 12 m. Work in: 100 N × 12 m = 1200 J. Work out: 600 N × 2 m = 1200 J. ::: :::keep-together ### Find the mistake **Mia thinks she needs only 80 N. Click the line where Mia's working first goes wrong.** ``` 1 Mia's block and tackle: 4 ropes hold up the bottom block, and she pulls a fifth rope that goes over the top. 2 That is 5 ropes, so it shares the 400 N five ways. 3 Pull = 400 ÷ 5 = 80 N. 4 To lift the sack 1 m she pulls 5 × 1 = 5 m of rope. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: the rope she pulls goes over the top block, so it does not hold the bottom block up. Four ropes share the load: 400 ÷ 4 = 100 N, and she pulls 4 m. ::: :::typical ## Vary: choose a system **Fewest ropes.** **Why one pulley?.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Pulleys :::keep-together ### Pull **3 ropes hold up a 750 N load. What pull lifts it, in newtons?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 250 750 ÷ 3 = 250 N. ::: :::keep-together ### Rope **A crane's hook hangs on 8 ropes. To raise the hook 5 m, how much rope does the winch wind in, in metres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 40 8 × 5 = 40 m. ::: :::keep-together ### Trade-off **Which uses less rope to lift a 600 N load 2 m: 3 ropes or 6 ropes?** ☐ They use the same rope ☐ 3 ropes: 6 m of rope instead of 12 m, but a 200 N pull instead of 100 N ☐ 6 ropes: more pulleys always means less work ☐ You cannot tell without the pulley sizes ::: :::teacher-note **Answer:** 3 ropes: 6 m of rope instead of 12 m, but a 200 N pull instead of 100 N Rope = ropes × height. Fewer ropes: more pull, less rope. ::: :::keep-together ### Same idea everywhere **Each mechanism trades one thing for another. Match each to what it gives up to make your force bigger.** A. Length of rope you pull B. Distance your hand moves C. Speed of the output {{columns 60% 40%}} {{rows 1}} | Part | Letter | |---|---| | `Gears, small driving big` | | | `Lever, pivot near the load` | | | `Block and tackle` | | ::: :::teacher-note **Answer:** Gears, small driving big → C. Speed of the output; Lever, pivot near the load → B. Distance your hand moves; Block and tackle → A. Length of rope you pull All three make your force bigger, and all three make you move farther or faster by the same factor: work in equals work out. ::: ## Make: a brief that needs four ropes **Four ropes.** **Evaluate.** Stretch: real pulleys have friction, and the bottom block has weight. Would you need more or fewer ropes in real life? Why? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **5 ropes hold up a 1000 N load. What pull lifts it, and how much rope do you pull to lift it 2 m?** {{lines-3}} ::: :::teacher-note **Answer:** 1000 ÷ 5 = 200 N, and 5 × 2 = 10 m. :::