--- title: "Gear trains" subtitle: "Mechanisms · Gears · Lesson 2" --- # Gear trains **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** The bucket is now 1500 g: more than any pair in the box can lift. You can use as many gears as you like. How? :::teacher-note **In one sentence:** Students add a third gear between two others and find it changes only the direction (an idler), then put two gears on one axle to make a compound train, work out that stage ratios multiply, choose a train for a load no single pair can lift, and see why big ratios come in stages. **Students should be able to say:** I can explain that an idler gear changes the direction of a turn but not the ratio. I can work out the overall ratio of a compound train by multiplying its stage ratios. I can choose a gear train that meets every criterion in a brief. I can explain why big ratios are built in stages. **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 **Put a 40-tooth gear between the 8 and the 24: 8 → 40 → 24. Compared with 8 → 24 on its own, the winch now…** ☐ Turns at the same speed with the same strength, but the other way round ☐ Turns faster, because the big gear spins it ☐ Turns 5 times slower and is 5 times stronger (40 ÷ 8) ☐ Turns 15 times slower and is 15 times stronger (5 × 3) My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Same speed, same strength, other direction. 40 ÷ 8 × 24 ÷ 40 = 24 ÷ 8: the idler's teeth cancel out, and each mesh reverses the turn. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: two gears on one axle :::keep-together ### Check 8 → 24 = 8 → 40, then 16 → 40 = 8 → 24 1. $\text{stage 1: } 24 \div 8 = 3$ — The motor's 8 drives a 24: a ratio of 3, as before. 2. $\text{stage 2: } 40 \div 8 = 5$ — An 8 on the 24's axle turns with it, and drives a 40: the next stage starts small again. 3. $3 \times 5 = 15$ — Stages multiply: the second stage slows down a gear that is already 3 times slower. 4. $120 \div 15 = 8 \text{ turns a minute}$ — Slower by the overall ratio. 5. $200 \times 15 = 3000 \text{ g}$ — Stronger by the same ratio. 6. $10 \div 8 = 1.25 \text{ min} = 75 \text{ s}$ — 1 m takes 10 winch turns. 7. $3000 \ge 1500 \;\checkmark \quad 75 \le 40 \;\times$ — Strong enough, but too slow. Too much ratio costs time. Now 16 → 40 = 8 → 24. Stage 1 is $40 \div 16 = 2.5$. Start with the overall ratio. **Now 16 → 40, then 8 → 24 on the same axle as the 40. What is the overall ratio?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 7.5 40 ÷ 16 = 2.5, 24 ÷ 8 = 3, and 2.5 × 3 = 7.5. ::: :::keep-together ### Strength **16 → 40 = 8 → 24: what is the heaviest bucket it can lift, in grams?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1500 200 × 7.5 = 1500 g: just enough. ::: :::keep-together ### Time and criteria **16 → 40 = 8 → 24: how many seconds to lift the bucket 1 m?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 37.5 The winch turns 120 ÷ 7.5 = 16 times a minute. 10 turns ÷ 16 = 0.625 min = 37.5 s. It lifts 1500 g within 40 s: it passes. ::: :::keep-together ### Find the mistake **Kai thinks the train lifts the 1500 g bucket. Click the line where Kai's working first goes wrong.** ``` 1 Kai's train: 8 → 24, then an 8-tooth gear on the same axle as the 24 drives a 40. 2 Stage 1: 24 ÷ 8 = 3 3 Stage 2: 40 ÷ 8 = 5 4 Overall ratio = 3 + 5 = 8 5 Heaviest lift = 200 × 8 = 1600 g, so it lifts the 1500 g bucket. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 4 Line 4: stage ratios multiply, they don't add. Each stage makes the next one 3 times (then 5 times) slower and stronger again: 3 × 5 = 15, so it lifts 3000 g (but takes 75 s). ::: :::typical ## Vary: choose your train **Meet the brief.** **Heavier still.** **Why stages?.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Trains :::keep-together ### Compound ratio **10 → 30, then 10 → 20 on the same axle. What is the overall ratio?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 30 ÷ 10 = 3, 20 ÷ 10 = 2, and 3 × 2 = 6. ::: :::keep-together ### Idler **A simple train 8 → 16 → 24: the 16 is an idler. What is the ratio?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3 Last ÷ first: 24 ÷ 8 = 3. The idler cancels out. ::: :::keep-together ### Direction **Three gears in a row, each meshing with the next. The motor gear turns clockwise. Which way does the last gear turn?** ☐ Anticlockwise ☐ Clockwise ☐ It depends on the sizes of the gears ::: :::teacher-note **Answer:** Clockwise Two meshes: clockwise, then anticlockwise, then clockwise again. ::: :::keep-together ### Speed **Motor 120 turns a minute, train 8 → 40 = 8 → 24 (ratio 15). How many turns a minute does the winch make?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 8 120 ÷ 15 = 8. ::: :::keep-together ### A clock **A clock's hour hand turns 12 times slower than its minute hand. Its gears do this in two stages, 3 × 4. Which pairs could do it?** ☐ 8 → 96 in one pair, then an idler ☐ 8 → 24, then 8 → 40 on the same axle ☐ 12 → 24, then 12 → 36 on the same axle ☐ 8 → 24, then 10 → 40 on the same axle ::: :::teacher-note **Answer:** 8 → 24, then 10 → 40 on the same axle 24 ÷ 8 = 3 and 40 ÷ 10 = 4: 3 × 4 = 12. ::: ## Make: a brief only a train can meet **A brief for a train.** **Evaluate.** Stretch: real meshes each lose about 5% of the turning force. Work out what your train can really lift, and whether it still meets your brief. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A motor turning 240 times a minute drives 10 → 30, then 10 → 40 on the same axle. How fast does the output turn, and how many times stronger is it?** {{lines-3}} ::: :::teacher-note **Answer:** Ratio 3 × 4 = 12, so 240 ÷ 12 = 20 turns a minute, 12 times stronger. :::