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# Levers

Mechanisms · Levers and pulleys

<!-- Speaker note: Students slide a pivot along a bar until a 200 N push lifts a 600 N rock, learn that turning effects (force × distance from the pivot) balance and that the hand moves farther by the same factor, meet class 2 and class 3 levers in a wheelbarrow and their own arm, and design a lever that meets two competing criteria. About 45 minutes (Predict and Try 8 min · Worked example 12 min · Vary 12 min · Practise and Make 13 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** a lever trades force for distance: a small push far from the pivot lifts a big load near it, and your hand moves farther than the load. Students find where to put a pivot by testing, work out the push from turning effects, meet the three classes of lever (including the one in their arm), and design a lever to a brief.

- I can work out the push a lever needs from force × distance on each side of the pivot.
- I can explain that a lever makes my push bigger by the same factor it makes my hand move farther.
- I can say whether a lever is class 1, 2 or 3 from where the pivot, the load and the push are.
- I can design a lever that meets more than one criterion.

<!-- Speaker note: Before class: Do Gear up the winch first if you can: this lesson makes the same trade (force for distance, not speed) and the Practise match ties the two together. A metre ruler on a pencil with coins makes a good start: balance two coins against one and measure from the pencil. Simplifications: the bar weighs nothing and does not bend, there is no friction at the pivot, and the push and the load act straight down (or up). The board exaggerates the bar's tilt so the movement is easy to see. Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Science, forces and simple machines (Year 7 forces); Maths, multiplying and dividing decimals. Teacher: Try: when the rock lifts, ask how far the hand would have to move. Teacher: Worked example: write force × distance on both sides of a drawn pivot. Point at where each distance starts. Teacher: Find the mistake: ask Leo's question back: 2 m from where? Teacher: Vary, arm: have students hold a bag at the hand and then at the elbow. Which is easier, and why? -->

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## Why it matters

> A 600 N rock, a 2 m bar, and a block to rest it on. You can push 200 N at most. Where does the block go?

<!-- Speaker note: Gears trade speed for turning force. A **lever** makes the same kind of trade with a bar and a **pivot** (the point it turns on, also called a fulcrum). The job: a **600 N** rock (about 60 kg) sits on one end of a **2 m** bar. You can push down on the other end with **200 N** at most. Where should the pivot go? Forces are in **newtons** (N); 10 N is about the weight of 1 kg. -->

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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

**The pivot starts in the middle of the bar. You move it closer to the rock. The push you need…**

- Stays the same: the rock weighs the same
- Gets bigger
- Is smallest with the pivot in the middle
- Gets smaller

<!-- Speaker note: What happens: Smaller. With the pivot near the rock, your push is far from the pivot and the rock is close to it, so each newton of push turns the bar more. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: take a vote, then ask someone who chose 'middle is best' to explain. Keep their reason for after the Try. -->

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## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fengineering%2Fmechanisms%2Flevers%2Fstep-2&code=widget%3A+lever%0Alength%3A+2%0Aloadat%3A+0%0Aeffortat%3A+2%0Apivot%3A+1%0Aload%3A+600%0Apush%3A+200%0Amove%3A+pivot%0Anumbers%3A+off%0A&fresh=1}}

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

<!-- Speaker note:  -->

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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>

## What happened?

* Smaller. With the pivot near the rock, your push is far from the pivot and the rock is close to it, so each newton of push turns the bar 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>

## Balance 600 N with the pivot at 0.5 m, then 0.4 m

Now the pivot is 0.4 m from the rock. Start with the push.

$$600 \times 0.5 = 300$$

1) $2 - 0.5 = 1.5 \text{ m}$ — Your push is at the other end: 1.5 m from the pivot.
2) $300 \div 1.5 = 200 \text{ N}$ — Your push must turn as much: push × 1.5 = 300.
3) $\text{advantage} = 600 \div 200 = 3$ — The lever makes your push 3 times as strong (its mechanical advantage).
4) $1.5 \div 0.5 = 3$ — Your hand is 3 times as far from the pivot as the rock…
5) $0.1 \times 3 = 0.3 \text{ m}$ — …so to lift the rock 0.1 m, your hand moves 0.3 m. Less force, more distance.

<!-- 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 600 × 0.5 = 300 and say "The rock's turning effect: its force times its distance from the pivot." Line 1: write 2 - 0.5 = 1.5 m and say "Your push is at the other end: 1.5 m from the pivot." Line 2: write 300 ÷ 1.5 = 200 N and say "Your push must turn as much: push × 1.5 = 300." Line 3: write advantage = 600 ÷ 200 = 3 and say "The lever makes your push 3 times as strong (its mechanical advantage)." Line 4: write 1.5 ÷ 0.5 = 3 and say "Your hand is 3 times as far from the pivot as the rock…." Line 5: write 0.1 × 3 = 0.3 m and say "…so to lift the rock 0.1 m, your hand moves 0.3 m. Less force, more distance." -->

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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>

## Balance 600 N with the pivot at 0.5 m, then 0.4 m

**Now the pivot is 0.4 m from the 600 N rock, and you push at the other end. What push balances it, in newtons?**

* Answer: 150

<!-- Speaker note: 600 × 0.4 = 240, and 240 ÷ 1.6 = 150 N. -->

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## Distance

**With the pivot at 0.4 m, how far does your hand move to lift the rock 0.1 m, in metres?**

* Answer: 0.4

<!-- Speaker note: 1.6 ÷ 0.4 = 4, so your hand moves 4 × 0.1 = 0.4 m. A quarter of the force, four times the distance. -->

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## Find the mistake

**Leo thinks the push is 120 N. Click the line where Leo's working first goes wrong.**

```
 1  The pivot is 0.4 m from the 600 N rock. I push at the other end of the 2 m bar.
 2  Turning effect of the rock = 600 × 0.4 = 240
 3  My push is 2 m from the end of the bar, so push = 240 ÷ 2 = 120 N.
 4  120 N is less than 200 N, so I can lift it easily.
```

* Answer: line 3

<!-- Speaker note: Line 3: distances are measured from the pivot, not the end of the bar. The push is 1.6 m from the pivot, so it is 240 ÷ 1.6 = 150 N. -->

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## Vary: three kinds of lever



- **A wheelbarrow:** 
- **Your arm:** 
- **Muscle force:** 
- **Why?:** 

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

<!-- Speaker note: What this step is for: The pivot need not be in the middle. In a wheelbarrow the load sits between the pivot (the wheel) and the push; in an arm the push (the muscle) sits between the pivot (the elbow) and the load. The arm needs more force than the load, and the question asks why a body would do that: it gains distance and speed. For students who need more support: Give a drawn bar with the pivot marked and a table: force, distance from pivot, force × distance, for each side. For early finishers: A 2 m bar that weighs 50 N has its weight at its middle. With the pivot 0.5 m from the 600 N rock, the bar's own weight is 0.5 m on your side. What push do you need now? The hard part, on purpose: Students measure distances from the end of the bar, not the pivot, and expect a stronger push to come free. Keep asking 'from where?' and 'how far did your hand move?' When students get stuck: A student measures from the end of the bar. Ask: Where does the bar turn? Measure from there. Fix: Every distance starts at the pivot. / A student thinks the lever gives extra force for nothing. Ask: How far did your hand move to lift the rock 10 cm? Fix: Less force, more distance, by the same factor. / A student cannot tell the classes apart. Ask: Find the pivot first. What is in the middle? Fix: Pivot in the middle: 1. Load in the middle: 2. Push in the middle: 3. / A student says class 3 levers are useless. Ask: What happens to the end of a fishing rod when you move the handle a little? Fix: Class 3 gives up force to gain distance and speed. -->

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## Seesaw

**A seesaw: a 300 N child sits 1.2 m from the pivot. Where must a 400 N child sit to balance, in metres from the pivot?**

* Answer: 0.9

<!-- Speaker note: 300 × 1.2 = 360, and 360 ÷ 400 = 0.9 m. -->

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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>

## Crowbar

**A crowbar: the load is 0.1 m from the pivot and you push 0.8 m from it. How many times as strong is your push (the mechanical advantage)?**

* Answer: 8

<!-- Speaker note: 0.8 ÷ 0.1 = 8: your push is 8 times as strong, and your hand moves 8 times as far. -->

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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>

## Three kinds

**Where is the pivot? Sort each tool by its kind of lever.**

Groups: Class 1: pivot in the middle · Class 2: load in the middle · Class 3: push in the middle

Scissors · Crowbar lifting a rock · Wheelbarrow · Nutcracker · Bottle opener · Tweezers · Fishing rod

* Answer: Scissors → Class 1: pivot in the middle; Crowbar lifting a rock → Class 1: pivot in the middle; Wheelbarrow → Class 2: load in the middle; Nutcracker → Class 2: load in the middle; Bottle opener → Class 2: load in the middle; Tweezers → Class 3: push in the middle; Fishing rod → Class 3: push in the middle

<!-- Speaker note: Find the pivot first. Then ask which is in the middle: the pivot, the load or the push. Classes 1 and 2 can make your push stronger; class 3 always makes it weaker, but faster. -->

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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>

## Distance

**A lever lets a 100 N push lift a 500 N load. The load rises 4 cm. How far does the push move?**

- 0.8 cm
- 4 cm
- 20 cm
- 500 cm

* Answer: 20 cm

<!-- Speaker note: 5 times the force, so 5 times the distance: 5 × 4 = 20 cm. -->

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## Make: a lever to a brief



- **Two criteria:** 
- **Evaluate:** Stretch: a real bar has weight. Which side of the pivot would its weight help, and which would it hinder?

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

<!-- Speaker note: What this step is for: Two criteria pull against each other: more advantage means more hand travel. Students reason from both to a narrow band of pivot positions (or move the push in), the same move as the gear briefs. Hints, in order: The load is 900 N and you push 200 N: you need an advantage of at least 900 ÷ 200 = 4.5. / Your hand may move 0.5 m to lift the load 0.1 m: an advantage of at most 5. / Your distance from the pivot ÷ the load's distance must be between 4.5 and 5. With the push at the end, try a pivot between 0.3 m and 0.4 m. -->

<!-- Speaker note: Teacher: compare designs. Who moved the push instead of the pivot? -->

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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 400 N load is 0.25 m from a pivot. You push 1 m from the pivot on the other side. What push balances it, and how far does your hand move to lift the load 0.1 m?**

* 400 × 0.25 = 100, so 100 ÷ 1 = 100 N; the hand is 4 times as far from the pivot, so it moves 0.4 m.

<!-- 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: Pulleys, the same trade with ropes. Real examples: crowbars, scissors, wheelbarrows, nutcrackers, oars, tweezers, the arm, a hockey or cricket swing. -->