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.
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Students will be able to
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.
Timing
Predict and Try 8 min · Worked example 12 min · Vary 12 min · Practise and Make 13 min
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
What you will see
A question to ask
The fix
A student measures from the end of the bar.
Where does the bar turn? Measure from there.
Every distance starts at the pivot.
A student thinks the lever gives extra force for nothing.
How far did your hand move to lift the rock 10 cm?
Less force, more distance, by the same factor.
A student cannot tell the classes apart.
Find the pivot first. What is in the middle?
Pivot in the middle: 1. Load in the middle: 2. Push in the middle: 3.
A student says class 3 levers are useless.
What happens to the end of a fishing rod when you move the handle a little?
Class 3 gives up force to gain distance and speed.
Answers to the checks
move the pivot: The pivot starts in the middle of the bar. You move it closer to the rock. The push you need… 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.
Middle: With the pivot in the middle, press Push.
It does not move: in the middle, you would need to push as hard as the rock weighs, 600 N.
Find the spot: Slide the pivot towards the rock, pushing each time, until the rock lifts.
Close enough to the rock, your 200 N lifts it.
How far?: What is the farthest from the rock the pivot can be, and still lift it (in metres)? 0.5 0.5 m. Any closer also works, but 0.5 m is the last spot where 200 N is enough.
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? 150 600 × 0.4 = 240, and 240 ÷ 1.6 = 150 N.
Distance: With the pivot at 0.4 m, how far does your hand move to lift the rock 0.1 m, in metres? 0.4 1.6 ÷ 0.4 = 4, so your hand moves 4 × 0.1 = 0.4 m. A quarter of the force, four times the distance.
Find the mistake: Leo thinks the push is 120 N. Click the line where Leo's working first goes wrong. line 3 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.
A wheelbarrow: 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.
At 0.5 m from the wheel: 600 × 0.5 = 300 = 200 × 1.5. The load between the pivot and the push is a class 2 lever.
Your arm: 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.
It lifts, but the muscle pulls 350 N: 7 times the ball's weight. A push between the pivot and the load is a class 3 lever.
Muscle force: How hard must the muscle pull to hold the 50 N ball (in newtons)? 350 50 × 0.35 = 17.5, and 17.5 ÷ 0.05 = 350 N.
Why?: Your arm needs 350 N to hold 50 N. Why is it built that way? The hand moves 7 times as far and as fast as the muscle, so a small muscle movement swings the hand a long way Every lever trades force for distance. A class 3 lever gives up force to gain distance and speed: arms, tweezers, fishing rods, a hockey stick.
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? 0.9 300 × 1.2 = 360, and 360 ÷ 400 = 0.9 m.
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)? 8 0.8 ÷ 0.1 = 8: your push is 8 times as strong, and your hand moves 8 times as far.
Three kinds: Where is the pivot? Sort each tool by its kind of lever. 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 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.
Distance: A lever lets a 100 N push lift a 500 N load. The load rises 4 cm. How far does the push move? 20 cm 5 times the force, so 5 times the distance: 5 × 4 = 20 cm.
Two criteria: 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.
An advantage between 4.5 and 5 meets both: for example the pivot at 0.35 m (advantage 4.7, hand moves 0.47 m).
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: three kinds of lever › A wheelbarrow
Open task: any program that does what the step asks.
Vary: three kinds of lever › Your arm
Open task: any program that does what the step asks.
Vary: three kinds of lever › Muscle force
Open task: any program that does what the step asks.
Vary: three kinds of lever › Why?
Open task: any program that does what the step asks.
a lever to a brief › Two criteria
Open task: any program that does what the step asks.
a lever to a brief › Evaluate
Open task: any program that does what the step asks.
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.
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.
What each step is for
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.
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.