Chapter 6 of 8

All 8 chapters
  1. 1Speed, readunderstood
  2. 2Distance and time graphs, readunderstood
  3. 3Balanced and unbalanced forces, readunderstood
  4. 4Mass and weight, readunderstood
  5. 5Stretching and springs, readunderstood
  6. 6Levers and turning forces, readunderstood
  7. 7Pressure, readunderstood
  8. 8Pressure in water and air, readunderstood

S3.7.6 Chapter 6

Levers and turning forces

How can a small child balance a bigger child on a seesaw?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Explain how a lever lets a small force lift a big load
  • Balance a ruler seesaw with coins at different distances

A seesaw is a plank that turns about a middle point. A heavy child and a light child can still balance it. The trick is where each one sits.

The point a plank turns about is the pivot. A force can make a thing turn about a pivot. How strongly it turns is the turning effect.

The turning effect depends on two things. One is the size of the force. The other is how far the force is from the pivot.

In the pictures, each round cap is a bottle top. All the caps are the same, so each one has the same weight. Count each as one unit of force.

Draw it first

Draw a seesaw that balances

  1. A ruler rests on a pivot, with marks numbered 1 to 5 on each side of the pivot. In the first picture it is level with nothing on it. In the second picture 2 caps sit at mark 3 on the left and 1 cap at mark 3 on the right, and the left side goes down. In the third picture 3 caps sit at mark 2 on the right, the ruler is level, and the numbers 6 and 6 are written under it. Labels: 1, 2, 3, 4, 5, pivot, 6 and 6.1234512345pivot

    1 Draw a ruler resting on a pivot at its middle. It is level. Number the marks 1 to 5 on each side.

  2. A ruler rests on a pivot, with marks numbered 1 to 5 on each side of the pivot. In the first picture it is level with nothing on it. In the second picture 2 caps sit at mark 3 on the left and 1 cap at mark 3 on the right, and the left side goes down. In the third picture 3 caps sit at mark 2 on the right, the ruler is level, and the numbers 6 and 6 are written under it. Labels: 1, 2, 3, 4, 5, pivot, 6 and 6.1234512345pivot

    2 Put 2 caps at mark 3 on the left and 1 cap at mark 3 on the right. The left has the bigger turning effect, so it goes down.

  3. A ruler rests on a pivot, with marks numbered 1 to 5 on each side of the pivot. In the first picture it is level with nothing on it. In the second picture 2 caps sit at mark 3 on the left and 1 cap at mark 3 on the right, and the left side goes down. In the third picture 3 caps sit at mark 2 on the right, the ruler is level, and the numbers 6 and 6 are written under it. Labels: 1, 2, 3, 4, 5, pivot, 6 and 6.1234512345pivot6 and 6

    3 Move to 3 caps at mark 2 on the right. Left: 2 × 3 = 6. Right: 3 × 2 = 6. The ruler is level.

turning effect = force × distance from the pivot. A bigger force turns more. A force farther out turns more.

A cap on mark 3 has a turning effect of 1 × 3 = 3. Two caps on mark 3 have 2 × 3 = 6. Add up every cap on a side.

A seesaw balances when the turning effects on the two sides are equal. If one side has the bigger turning effect, that side goes down.

See it three ways

As a picture

A ruler resting level on a pivot, with marks numbered 1 to 5 on each side of the pivot. On the left, 1 cap sits at mark 4. On the right, 2 caps sit at mark 2. Labels: 1, 2, 3, 4, 5, pivot.1234512345pivot

In words

One cap far from the pivot balances two caps closer in. The two sides turn just as strongly, one with more force and one with more distance.

In symbols

Left: 1 × 4 = 4. Right: 2 × 2 = 4. Equal, so balanced.

A lever is a stiff bar that turns about a pivot. A spade, a crowbar, a pair of scissors and a seesaw are all levers. The load is the thing you want to lift. The effort is the force you use.

A ruler resting level on a pivot, with marks numbered 1 to 5 on each side of the pivot. On the left, 5 caps sit at mark 1. On the right, 1 cap sits at mark 5. Labels: 1, 2, 3, 4, 5, pivot.1234512345pivot
A big load of 5 caps close to the pivot is balanced by 1 cap far from it. 5 × 1 = 5 and 1 × 5 = 5.

This is why a long crowbar lifts a heavy stone. Your small push is far from the pivot. The heavy stone is close to it. A little more effort and the stone lifts.

A ruler on a pivot, with marks numbered 1 to 5 on each side of the pivot. On the left, 4 caps sit at mark 3. On the right, 3 caps sit at mark 1, and the left side is down. Labels: 1, 2, 3, 4, 5, pivot.1234512345pivot
The start of the next example. The 3 caps on the right are too near the pivot. They must move out to a mark that makes the ruler level.

Worked example

A ruler has 4 caps at mark 3 on the left. 3 caps go on the right. At which mark must they go to balance?

  1. Turning effect = number of caps × mark.
  2. Left: 4 caps at mark 3, so 4 × 3 = 12.
  3. To balance, the right side must also have a turning effect of 12.
  4. Right: 3 caps at some mark, so 3 × mark = 12.
  5. Mark = 12 ÷ 3 = 4.
  6. Check: 3 × 4 = 12, the same as the left side.

Answer: Mark 4

Try it

Balance a ruler seesaw

You need: a ruler or a flat stick about 30 cm long, a round pencil to be the pivot, about 10 bottle tops of one size, or coins of one size, to use as weights, a pencil for marking.

Be safe: Bottle tops and coins are small. Keep them away from very young children. Work on a table so nothing falls on your feet.

  1. Rest the ruler across the round pencil at its middle, so it is level. This is the pivot.
  2. Make a dot every 3 cm out from the middle on each side. Number the dots 1 to 5.
  3. Put 3 tops on the left at mark 2. Put 2 tops on the right at mark 1. The left goes down.
  4. Slide the 2 tops along the right side until the ruler is level. Note the mark.
  5. Try 3 tops on the right. Find the mark where it balances. For each, write tops × mark on both sides.

What you will see: Two tops balance at mark 3, because 3 × 2 = 6 and 2 × 3 = 6. Three tops balance at mark 2. Each time, tops × mark is the same on both sides. A small nudge may be needed, because a real ruler is not perfect.

If you cannot try it, this is what happens.
A ruler resting level on a pivot, with marks numbered 1 to 5 on each side of the pivot. On the left, 3 caps sit at mark 2. On the right, 2 caps sit at mark 3. Labels: 1, 2, 3, 4, 5, pivot.1234512345pivot

A wrong idea many people have

The heavier side always goes down.

Why it feels right: On a seesaw with children at the ends, the heavier child usually wins.

The test that breaks it: Put 2 tops at mark 1 on the left. Put 1 top at mark 5 on the right. The right side goes down. It has less weight, but it is far from the pivot.

What is true: It is the turning effect that counts, which is force times distance. A small force far out can beat a big force close in.

Key words

pivot
the point a lever turns about.
turning effect
force × distance from the pivot.
lever
a stiff bar that turns about a pivot.
effort
the force you use to move a load.

Back to your guess

The answer is C: The small child sits farther from the middle.

A force farther from the middle has a bigger turning effect. A small child far out can balance a bigger child close in.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. A weight of 5 N hangs 20 cm from the pivot. What is its turning effect? Use N cm as the unit.

    See the answer

    100 N cm

    Turning effect = force × distance from the pivot = 5 × 20 = 100 N cm.

  2. The ruler rests on a block under each end. If you take the blocks away, does it stay level?

    A ruler on a pivot, resting level on a block under each end, with the words held level, with marks numbered 1 to 5 on each side of the pivot. On the left, 3 caps sit at mark 2. On the right, 2 caps sit at mark 3. Labels: 1, 2, 3, 4, 5, held level.1234512345held level
    Tap your answer.

    1. Yes, that is right. Left: 3 × 2 = 6. Right: 2 × 3 = 6. They are equal.

    2. Not this one. You only counted the caps. The distance from the pivot matters too. Work out both turning effects. Go to S3.7.6. Try another.

    3. Not this one. You only looked at the distance. The left has more caps, and the right has fewer but farther out. Work out both turning effects before you decide. Go to S3.7.6. Try another.

    See the answer

    Yes. Both sides have the same turning effect.

    Left: 3 × 2 = 6. Right: 2 × 3 = 6. They are equal.

    • If you chose B: You only counted the caps. The distance from the pivot matters too. Work out both turning effects. Go to S3.7.6.
    • If you chose C: You only looked at the distance. The left has more caps, and the right has fewer but farther out. Work out both turning effects before you decide. Go to S3.7.6.

  3. The ruler rests on a block under each end. If you take the blocks away, which side goes down?

    A ruler on a pivot, resting level on a block under each end, with the words held level, with marks numbered 1 to 5 on each side of the pivot. On the left, 2 caps sit at mark 4. On the right, 3 caps sit at mark 3. Labels: 1, 2, 3, 4, 5, held level.1234512345held level
    Tap your answer.

    1. Not this one. The left caps are farther out, but there are fewer of them. Work out both turning effects and compare. Go to S3.7.6. Try another.

    2. Yes, that is right. Left: 2 × 4 = 8. Right: 3 × 3 = 9. The right has the bigger turning effect.

    3. Not this one. Work out left and right. They are not equal, so one side goes down. Go to S3.7.6. Try another.

    See the answer

    The right side goes down.

    Left: 2 × 4 = 8. Right: 3 × 3 = 9. The right has the bigger turning effect.

    • If you chose A: The left caps are farther out, but there are fewer of them. Work out both turning effects and compare. Go to S3.7.6.
    • If you chose C: Work out left and right. They are not equal, so one side goes down. Go to S3.7.6.

  4. A 6 N weight is 10 cm to the left of the pivot. A 3 N weight is on the right. How far from the pivot must the 3 N weight be to balance?

    Tap your answer.

    1. Not this one. You put it at the same distance, as on a seesaw with equal children. This weight is smaller, so it has to make up for that. Go to S3.7.6. Try another.

    2. Not this one. You moved it nearer, but a smaller force must go farther out. It needs more distance to turn as strongly. Go to S3.7.6. Try another.

    3. Not this one. That number is the turning effect on the left, in N cm. It is not the distance. Divide it by the 3 N on the right. Go to S3.7.6. Try another.

    4. Yes, that is right. Left turning effect = 6 × 10 = 60 N cm. Right: 3 × distance = 60, so distance = 60 ÷ 3 = 20 cm.

    See the answer

    20 cm

    Left turning effect = 6 × 10 = 60 N cm. Right: 3 × distance = 60, so distance = 60 ÷ 3 = 20 cm.

    • If you chose A: You put it at the same distance, as on a seesaw with equal children. This weight is smaller, so it has to make up for that. Go to S3.7.6.
    • If you chose B: You moved it nearer, but a smaller force must go farther out. It needs more distance to turn as strongly. Go to S3.7.6.
    • If you chose C: That number is the turning effect on the left, in N cm. It is not the distance. Divide it by the 3 N on the right. Go to S3.7.6.

  5. Kofi uses a plank as a lever. A stone weighing 80 N sits 15 cm from the pivot. He pushes down on the other side, 60 cm from the pivot. How big a push balances the stone?

    Tap your answer.

    1. Not this one. You gave the weight of the stone. A push far from the pivot turns more. So it can be smaller than the weight. Go to S3.7.6. Try another.

    2. Not this one. That is the turning effect of the stone, in N cm. It is not a force. Divide it by the distance of the push from the pivot. Go to S3.7.6. Try another.

    3. Yes, that is right. The stone's turning effect is 80 × 15 = 1200 N cm. The push needs the same: push × 60 = 1200, so push = 20 N.

    4. Not this one. You swapped the distances, as if a push far from the pivot needs more force. It needs less. Multiply the weight by its own distance, then divide by the distance of the push. Go to S3.7.6. Try another.

    See the answer

    20 N

    The stone's turning effect is 80 × 15 = 1200 N cm. The push needs the same: push × 60 = 1200, so push = 20 N.

    • If you chose A: You gave the weight of the stone. A push far from the pivot turns more. So it can be smaller than the weight. Go to S3.7.6.
    • If you chose B: That is the turning effect of the stone, in N cm. It is not a force. Divide it by the distance of the push from the pivot. Go to S3.7.6.
    • If you chose D: You swapped the distances, as if a push far from the pivot needs more force. It needs less. Multiply the weight by its own distance, then divide by the distance of the push. Go to S3.7.6.

  6. Why does a long spoon handle help open a tin lid more than a short one?

    Tap your answer.

    1. Yes, that is right. The same push farther from the pivot has a bigger turning effect. A small effort can then lift the lid.

    2. Not this one. Strength is not the reason. The handle length changes how far your push is from the pivot. Go to S3.7.6. Try another.

    3. Not this one. The lid weighs the same. What changes is the turning effect of your push. Go to S3.7.6. Try another.

    See the answer

    Your push is farther from the pivot, so it has a bigger turning effect.

    The same push farther from the pivot has a bigger turning effect. A small effort can then lift the lid.

    • If you chose B: Strength is not the reason. The handle length changes how far your push is from the pivot. Go to S3.7.6.
    • If you chose C: The lid weighs the same. What changes is the turning effect of your push. Go to S3.7.6.

  7. From an earlier chapter

    A stone with a mass of 4 kg is the load on a lever. About what is its weight?

    Tap your answer.

    1. Not this one. That is the mass in kilograms. Each kilogram weighs about 10 N on Earth. Go to S3.7.4. Try another.

    2. Yes, that is right. On Earth each kilogram weighs about 10 N. 4 × 10 = 40 N.

    3. Not this one. You added 10 to the mass. Multiply the mass by 10 instead. Go to S3.7.4. Try another.

    See the answer

    40 N

    On Earth each kilogram weighs about 10 N. 4 × 10 = 40 N.

    • If you chose A: That is the mass in kilograms. Each kilogram weighs about 10 N on Earth. Go to S3.7.4.
    • If you chose C: You added 10 to the mass. Multiply the mass by 10 instead. Go to S3.7.4.

Keep it

Copy this into your exercise book.

Turning effect = force × distance from the pivot. A seesaw balances when both sides are equal. A lever lets a small force far from the pivot balance a big load close in.

Draw: A ruler on a pivot. 2 caps at mark 3 on the left, 3 caps at mark 2 on the right. Write 6 and 6.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (881 KB). It opens on any phone.