--- title: "Gear up the winch" subtitle: "Mechanisms · Gears · Lesson 1" --- # Gear up the winch **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A small motor can lift 200 g. The bucket is 450 g. You can't change the motor, but you have a box of gears. How do you lift it, and what do you give up? :::teacher-note **In one sentence:** Students fit gears to a motor-driven winch, find by testing that a small gear driving a big one is slower and stronger by the same factor, work out ratio, speed, strength and lift time, choose pairs for a brief, meet a brief where constraints conflict, then write a brief of their own. **Students should be able to say:** I can work out a gear ratio as driven teeth ÷ driver teeth. I can explain that a ratio makes the output slower and stronger by the same factor. I can check a design against every criterion in a brief. I can explain what to do when no design meets every constraint. **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 **The 8-tooth gear on the motor drives the 24-tooth gear on the winch. Compared with the motor, the winch turns…** ☐ 3 times slower, but no stronger ☐ The same speed, but 3 times stronger ☐ 3 times slower and 3 times stronger ☐ 3 times faster and 3 times stronger My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 3 times slower and 3 times stronger. The speed and the strength change by the same factor, in opposite directions. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: does 8 → 24 meet the brief? :::keep-together ### Check 8 → 24, then 16 → 40 1. $\text{ratio} = 24 \div 8 = 3$ — Ratio = driven teeth ÷ driver teeth. The winch needs 3 motor turns for each of its own. 2. $120 \div 3 = 40 \text{ turns a minute}$ — Slower by the ratio: divide the motor's speed. 3. $200 \times 3 = 600 \text{ g}$ — Stronger by the same ratio: multiply what the motor lifts. 4. $1 \div 0.1 = 10 \text{ winch turns}$ — The drum winds 0.1 m each turn, so 1 m takes 10 turns. 5. $10 \div 40 = 0.25 \text{ min} = 15 \text{ s}$ — Time = turns ÷ turns a minute; times 60 for seconds. 6. $600 \ge 450 \;\checkmark \quad 15 \le 15 \;\checkmark$ — Check both criteria: strong enough and fast enough. 8 → 24 passes. Now do the same for 16 → 40. The ratio is $40 \div 16 = 2.5$. Start with the winch's speed. **Now 16 → 40 (ratio 2.5). How many turns a minute does the winch make?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 48 120 ÷ 2.5 = 48 turns a minute. ::: :::keep-together ### Strength **16 → 40: what is the heaviest bucket it can lift, in grams?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 500 200 × 2.5 = 500 g. ::: :::keep-together ### Time and criteria **16 → 40: how many seconds to lift the bucket 1 m?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12.5 1 m needs 10 winch turns. 10 ÷ 48 = 0.208 minutes = 12.5 s. It lifts 450 g (500 ≥ 450) within 15 s, so 16 → 40 passes too. ::: :::keep-together ### Find the mistake **Sam's winch stalls with the 450 g bucket. Click the line where Sam's working first goes wrong.** ``` 1 Sam puts the 24-tooth gear on the motor and the 8-tooth gear on the winch. 2 ratio = 24 ÷ 8 = 3 3 So the winch is 3 times stronger: it lifts 3 × 200 = 600 g. 4 600 g is more than 450 g, so it will lift the bucket. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: the ratio is driven ÷ driver. The 8-tooth gear is now the driven one, so the ratio is 8 ÷ 24 = 1/3. The winch turns 3 times faster and is 3 times weaker: it lifts only about 67 g. ::: :::typical ## Vary: change one thing **A lighter bucket.** **A faster motor.** **Too heavy.** **When nothing passes.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Ratios :::keep-together ### Ratio **The 16-tooth gear on the motor drives the 24-tooth gear on the winch. What is the ratio?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1.5 24 ÷ 16 = 1.5. ::: :::keep-together ### Speed **Motor 120 turns a minute, ratio 5. How many turns a minute does the winch make?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 24 120 ÷ 5 = 24. ::: :::keep-together ### Strength **The 24-tooth gear on the motor drives the 16-tooth gear on the winch. The motor lifts 200 g with no gears. What is the heaviest lift now, to the nearest gram?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 133 Ratio 16 ÷ 24 = 2/3, so 200 × 2/3 ≈ 133 g. Faster, but weaker. ::: :::keep-together ### A bike **On a bike's lowest gear (small gear at the pedals, big gear at the back wheel) hills feel easy. What do you give up?** ☐ Speed: you pedal many times for each turn of the wheel ☐ Strength: it is harder to push ☐ Grip on the road ☐ Nothing: lower gears are just better ::: :::teacher-note **Answer:** Speed: you pedal many times for each turn of the wheel Small driving big: slower and stronger. Easy on hills, slow on the flat. ::: ## Make: write a brief **Exactly one pair.** **Evaluate.** Stretch: write a brief where no pair passes, then argue which constraint the client should relax, and why. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **An 8-tooth gear drives a 40-tooth gear. The motor turns 100 times a minute and lifts 50 g on its own. How fast does the output turn, and what can it lift?** {{lines-3}} ::: :::teacher-note **Answer:** Ratio 40 ÷ 8 = 5, so 100 ÷ 5 = 20 turns a minute, and 50 × 5 = 250 g. :::