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.
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?
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.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Move the pivot
TryTry it on the board and compare the result with your prediction.
Try: find the spot
Was your prediction right? The closer the pivot is to the load, the smaller the push.
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With the pivot in the middle, press Push.
Use the board. This ticks when you get there.
Slide the pivot towards the rock, pushing each time, until the rock lifts.
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What is the farthest from the rock the pivot can be, and still lift it (in metres)?
InvestigateWork out why it happens, one step at a time.
Worked example: turning effects balance
Worked exampleBefore each step, say what you think comes next.
600×0.5=300The rock's turning effect: its force times its distance from the pivot.
2−0.5=1.5 mYour push is at the other end: 1.5 m from the pivot.
300÷1.5=200 NYour push must turn as much: push × 1.5 = 300.
advantage=600÷200=3The lever makes your push 3 times as strong (its mechanical advantage).
1.5÷0.5=3Your hand is 3 times as far from the pivot as the rock…
0.1×3=0.3 m…so to lift the rock 0.1 m, your hand moves 0.3 m. Less force, more distance.
Now the pivot is 0.4 m from the rock. Start with the push.
Leo puts the pivot 0.4 m from the rock.
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?
With the pivot at 0.4 m, how far does your hand move to lift the rock 0.1 m, in metres?
Leo thinks the push is 120 N. Click the line where Leo's working first goes wrong.
ModifyChange the problem on purpose and see what happens.
Vary: three kinds of lever
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A wheelbarrow: the wheel is the pivot and you lift the handles. Slide the 600 N load towards the wheel until your 200 N lifts it.
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Your forearm: the elbow is the pivot, the muscle pulls 5 cm from it, and a 50 N ball is in your hand 35 cm away. Lift the ball.
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How hard must the muscle pull to hold the 50 N ball (in newtons)?
PractiseA few on your own, to check you have it.
Levers
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?
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)?
Where is the pivot? Sort each tool by its kind of lever.
Scissors
Crowbar lifting a rock
Wheelbarrow
Nutcracker
Bottle opener
Tweezers
Fishing rod
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
A lever to a brief
Need a hint?
The load is 900 N and you push 200 N: you need an advantage of at least 900 ÷ 200 = 4.5.
Another hint
Your hand may move 0.5 m to lift the load 0.1 m: an advantage of at most 5.
Another hint
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.
Stretch: a real bar has weight. Which side of the pivot would its weight help, and which would it hinder?
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Lift 900 N with a 200 N push, with your hand moving no more than 0.5 m. Move the pivot (or your push) and lift.
Use the board. This ticks when you get there.
For teachers
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.
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.
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.
Running the lesson
Predict: take a vote, then ask someone who chose 'middle is best' to explain. Keep their reason for after the Try.
Try: when the rock lifts, ask how far the hand would have to move.
Worked example: write force × distance on both sides of a drawn pivot. Point at where each distance starts.
Find the mistake: ask Leo's question back: 2 m from where?
Vary, arm: have students hold a bag at the hand and then at the elbow. Which is easier, and why?
Make: compare designs. Who moved the push instead of the pivot?
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.
Stretch and support
Stretch: 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?
Support: Give a drawn bar with the pivot marked and a table: force, distance from pivot, force × distance, for each side.
Where it leads
Next: Pulleys, the same trade with ropes.
Real examples: crowbars, scissors, wheelbarrows, nutcrackers, oars, tweezers, the arm, a hockey or cricket swing.
move the pivot: Committing to which way the push changes as the pivot moves tests the new move before the board shows it. Each wrong option is a real slip: the middle is best, nothing changes, or the push depends on speed.
Try: find the spot: Testing settles the prediction: with the pivot in the middle the rock does not move; slide it towards the rock until a 200 N push lifts it. The numbers are hidden so students find the spot.
Worked example: turning effects balance: The worked example gives the rule: force × distance from the pivot (a turning effect, or moment) is the same on both sides when it balances. Then the trade: the hand moves farther by the same factor. The faded example has a pivot at 0.4 m. Leo measures from the end of the bar, planted after the method.
Vary: three kinds of lever: 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.
levers: Turning effects from the pivot, the distance trade, and the three classes by where the pivot, the load and the push sit.
a lever to a brief: 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.
Now you can
Work out the push a lever needs from force × distance on each side of the pivot.
Explain that a lever makes my push bigger by the same factor it makes my hand move farther.
Say whether a lever is class 1, 2 or 3 from where the pivot, the load and the push are.
Design a lever that meets more than one criterion.