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KS3 Science · Year 7Chapter 12 · Moments and pressure
Year 7 · Chapter 12

Moments and pressure

By the end of this chapter you will be able to

  • Say that a force can turn an object about a pivot
  • Calculate a moment: force x perpendicular distance from the pivot, in newton metres
  • Use balanced moments to find a missing force or distance
  • Explain why a longer lever needs a smaller force
  • Calculate pressure = force / area, in pascals (Pa), and explain examples such as knives and snow shoes

You should already know

  • Forces, pushes and pulls, and the newton as the unit of force (Chapter 11 of this book)
  • Area of a rectangle, length x width (primary school maths)

Where this leads

  • Forces and their effects in the later KS3 and GCSE physics courses

National Curriculum for England, Key Stage 3 science, Year 7. Content: P3 a force can turn an object about a pivot; moment = force x perpendicular distance from the pivot (N m); levers and balance, P4 pressure = force / area; simple examples such as knives and snow shoes (basic only).

Exercise P  Do you remember?

1
FWhat is the name of the point that a lever turns about? Write the word.
2
FWhich unit is force measured in? Write the unit.
3
FWhat is 40 divided by 5? Write the number.
4
FA rectangle is 4 m long and 5 m wide. What is its area, in square metres? Write the number.
5
FWhat is the name of the force that pulls an object towards the Earth? Write the word.
12.1

A force can turn an object about a pivot

Year 7
P3: a force can turn an object about a pivot; the turning effect depends on the force and where it is applied
Video lesson: A force can turn an object about a pivotComing soon
Story. Ali pushes a door near its handle, and it swings open easily. “Why is it harder to push near the hinges?” asks his friend. His teacher says, “The hinge is a pivot. A force turns an object about a pivot, and the further from the pivot you push, the easier it is to turn.”

A force can make an object turn, not just move. The point the object turns about is the pivot. A door turns about its hinges; a seesaw turns about its middle; a spanner turns about the bolt.

The turning effect of a force depends on two things: how big the force is, and how far it acts from the pivot.

Key ideas

  • A force can turn an object about a pivot.
  • The pivot is the point the object turns about.
  • A bigger force has a bigger turning effect.
  • A force applied further from the pivot has a bigger turning effect.
Worked example 12.1.1
What is the pivot of a door? Write the word.

Method. Find the point the door turns about.

  1. Look at the door. A door turns about its hinges.
    hinges
  2. Name it. The hinges are the pivot of the door.
    hinges
  3. Write the answer.
    the hinges

Check. The door opens by turning about the hinges. ✓

Worked example 12.1.2
Is it easier to open a door by pushing near the handle or near the hinges? Write the word: handle or hinges.

Method. Compare the distances from the pivot.

  1. Compare. The handle is further from the hinges than a point near the hinges.
    further
  2. Decide. A force further from the pivot turns the door more easily, so the handle.
    handle
  3. Write the answer.
    handle

Check. The further the force from the pivot, the bigger the turning effect. ✓

Worked example 12.1.3
A spanner turns a bolt. What is the pivot? Write the word.

Method. Find the point the spanner turns about.

  1. Look. The spanner turns the bolt, so it turns about the centre of the bolt.
    centre of the bolt
  2. Name it. The pivot is the centre of the bolt.
    centre of the bolt
  3. Write the answer.
    the centre of the bolt

Check. The turning happens around the bolt. ✓

Watch out

Watch out: a force does not always move an object; it can turn it instead. The turning effect depends on the distance from the pivot.

Exam tip

Exam tip. In a turning question, name the pivot first, then say how far the force is from it.

Try it (with your teacher, or a grown-up at home). With a grown-up, push a door near its handle, then near its hinges, using the same push each time. Say which was easier, and why. Name the pivot in each case.

Exercise 12A  A force can turn an object about a pivot

1
FWhat is the name of the point an object turns about? Write the word.
2
FWhat is the pivot of a seesaw? Write the word.
3
FDoes a force have to move an object to turn it? Write yes or no.
4
FIs it easier to turn a bolt with a long spanner or a short spanner? Write the word: long or short.
5
FWhich affects the turning effect of a force: its size, or its colour? Write the word: size.
6
FWhich affects the turning effect: how far the force is from the pivot? Write yes or no.
7
FWhere should you push a door to open it most easily: near the hinges, or near the handle? Write the word: hinges or handle.
8
PSBen says a force near the pivot turns an object more than the same force further away. Is Ben right? Write yes or no.
9
PSA 20 N force is pushed on a spanner at 0.2 m, and the same 20 N force is pushed at 0.4 m. Which gives the bigger moment? Write the number of metres.
10
PSWorking scientifically: a pupil says the pivot of a balanced metre rule is always at the end. Is this right? Write yes or no.
11
RExplain why a door is easier to open when pushed near the handle. Write one sentence.
12
RChallenge: explain why a seesaw can stay balanced even when the two people have different weights. Write one sentence.
12.2

Moments: force x distance from the pivot

Year 7
P3: moment = force x perpendicular distance from the pivot, measured in newton metres (N m)
Video lesson: Moments: force x distance from the pivotComing soon
Story. Sam is trying to lift a heavy bag using a long plank as a lever. “How do I know how much turning effect I am making?” he asks. His teacher says, “Multiply the force by the distance from the pivot. That gives the moment.”

The moment of a force is its turning effect about a pivot. It is found using:

moment = force x perpendicular distance from the pivot

The perpendicular distance is measured at a right angle to the line of the force, from the pivot. The unit of moment is the newton metre (N m).

The table gives three moments: a force, the distance from the pivot, and the moment.

Force (N)Distance from pivot (m)Moment (N m)
403120
602120
200.36.0

Key ideas

  • moment = force x perpendicular distance from the pivot
  • The distance is measured at a right angle to the force, from the pivot.
  • The unit of moment is the newton metre, N m.
  • A bigger force or a bigger distance gives a bigger moment.
Worked example 12.2.1
A force of 40 N acts at a perpendicular distance of 3 m from the pivot. What is the moment? Write the number of N m.

Method. Use moment = force x distance.

  1. Write the values. The force is 40 N and the distance is 3 m.
    40 and 3
  2. Multiply. Moment = 40 x 3.
    40 x 3 = 120
  3. Write the answer.
    120 N m

Check. 120 divided by 3 is 40. ✓

Worked example 12.2.2
A spanner has a force of 20 N acting 0.3 m from the bolt. What is the moment? Write the number of N m.

Method. Use moment = force x distance.

  1. Write the values. The force is 20 N and the distance is 0.3 m.
    20 and 0.3
  2. Multiply. Moment = 20 x 0.3 = 6.
    20 x 0.3 = 6
  3. Write the answer.
    6 N m

Check. 6 divided by 0.3 is 20. ✓

Worked example 12.2.3
A force of 60 N acts 2 m from the pivot. What is the moment? Write the number of N m.

Method. Use moment = force x distance.

  1. Write the values. The force is 60 N and the distance is 2 m.
    60 and 2
  2. Multiply. Moment = 60 x 2.
    60 x 2 = 120
  3. Write the answer.
    120 N m

Check. 120 divided by 60 is 2 m. ✓

Watch out

Watch out: use the perpendicular distance, which is at a right angle to the force. If the force is at an angle, the distance must still be measured at right angles.

Exam tip

Exam tip. Write the moment formula, put in the force and distance with their units, multiply, and give the unit N m.

Try it (with your teacher, or a grown-up at home). With a grown-up, hang a small mass from a metre rule balanced on a pivot at one end. Measure the distance from the pivot to the mass. Multiply by the weight in newtons, using the mass in kg x 10, to find the moment in N m.

Exercise 12B  Moments: force x distance from the pivot

1
FWhat is the formula for the moment of a force? Write the words.
2
FWhat is the unit of moment? Write the unit.
3
FA force of 10 N acts 2 m from the pivot. What is the moment? Write the number of N m.
4
FA force of 5 N acts 4 m from the pivot. What is the moment? Write the number of N m.
5
FA force of 40 N acts 3 m from the pivot. What is the moment? Write the number of N m.
6
FA force of 20 N acts 0.3 m from the pivot. What is the moment? Write the number of N m.
7
PSA force of 8 N acts 5 m from the pivot. What is the moment? Write the number of N m.
8
PSA spanner has a force of 20 N at 0.2 m from the bolt. What is the moment? Write the number of N m.
9
PSA spanner has a force of 20 N at 0.4 m from the bolt. What is the moment? Write the number of N m.
10
PSA force of 15 N acts 4 m from the pivot. What is the moment? Write the number of N m.
11
PSBen says the moment of a 20 N force at 3 m is 23 N m, because he added the numbers. Is Ben right? Write yes or no.
12
PSWorking scientifically: a pupil measures the distance from the pivot along the ruler, but the force is at an angle. Name the mistake. Write one sentence.
13
RExplain why the moment is given in newton metres and not in newtons. Write one sentence.
14
RChallenge: a force of 12 N gives a moment of 36 N m. What is the distance from the pivot? Write the number of metres.
12.3

Balanced moments

Year 7
P3: an object is balanced when the clockwise moments equal the anticlockwise moments about the pivot
Video lesson: Balanced momentsComing soon
Story. Ruby and Priya sit on a seesaw. It is perfectly level. “We are balanced,” says Ruby. “Why does a heavier person need to sit closer to the pivot?” asks Priya. Her teacher says, “Because the turning effects must be equal. Each side turns about the pivot, and the two moments must match.”

An object is in balance about a pivot when the moments on each side are equal. A moment that turns the object clockwise is balanced by an equal moment that turns it anticlockwise.

total clockwise moment = total anticlockwise moment

200 N2 m160 N2.5 mpivotbalanced: 200 x 2 = 160 x 2.5 = 400 N m
A balanced seesaw: 200 N at 2 m on one side, and 160 N at 2.5 m on the other.

Key ideas

  • A balanced object has equal clockwise and anticlockwise moments.
  • A heavier force must be closer to the pivot to balance a lighter one.
  • The moments on each side can be compared by multiplying force and distance.
  • If the moments are not equal, the object turns towards the bigger moment.
Worked example 12.3.1
On the seesaw, what is the moment on the left? Write the number of N m.

Method. Use moment = force x distance.

  1. Write the values. The left force is 200 N at 2 m from the pivot.
    200 and 2
  2. Multiply. Moment = 200 x 2 = 400.
    200 x 2 = 400
  3. Write the answer.
    400 N m

Check. The right side also gives 400 N m. ✓

Worked example 12.3.2
On the seesaw, what is the moment on the right? Write the number of N m.

Method. Use moment = force x distance.

  1. Write the values. The right force is 160 N at 2.5 m from the pivot.
    160 and 2.5
  2. Multiply. Moment = 160 x 2.5 = 400.
    160 x 2.5 = 400
  3. Write the answer.
    400 N m

Check. The two moments are equal, so the seesaw balances. ✓

Worked example 12.3.3
A 60 N force acts 2 m from the pivot. For a balance, how far from the pivot must a 30 N force act, on the other side? Write the number of metres.

Method. Make the moments equal.

  1. Find the moment. The moment on the first side is 60 x 2 = 120 N m.
    120 N m
  2. Find the distance. Distance = 120 / 30 = 4 m, so the 30 N force must act 4 m from the pivot.
    120 / 30 = 4
  3. Write the answer.
    4 m

Check. 30 x 4 = 120 N m, which balances. ✓

Watch out

Watch out: a balance needs the moments to be equal, not the forces. The forces can be different, if the distances are different.

Exam tip

Exam tip. For a balance question, work out one moment, then find the missing force or distance on the other side.

Try it (with your teacher, or a grown-up at home). With a grown-up, balance a metre rule on a pivot with two small masses. Move one mass until the rule balances. Measure the two distances from the pivot, and check that the moments are equal.

Exercise 12C  Balanced moments

1
FWhen is an object balanced about a pivot? Write the words.
2
FOn the seesaw, what is the moment on the left? Write the number of N m.
3
FOn the seesaw, what is the moment on the right? Write the number of N m.
4
FDoes the seesaw balance? Write yes or no.
5
FA 60 N force acts 2 m from the pivot. What is the moment? Write the number of N m.
6
PSA 30 N force acts on the other side of the pivot. What distance gives a balancing moment? Write the number of metres.
7
PSA 10 N force acts 6 m from the pivot. What force at 3 m balances it? Write the number of newtons.
8
PSTwo children balance a seesaw: one is 300 N at 1 m from the pivot. How far from the pivot must a 150 N child sit? Write the number of metres.
9
PSA rule balances with 40 N at 0.5 m on one side, and 20 N on the other side. How far from the pivot is the 20 N force? Write the number of metres.
10
PSBen says a heavier child must always sit further from the pivot to balance a seesaw. Is Ben right? Write yes or no.
11
PSWorking scientifically: a pupil says a seesaw is balanced because the two forces are equal. Is this a correct reason? Write yes or no.
12
RExplain why an object is balanced when the moments are equal, even if the forces are different. Write one sentence.
13
RChallenge: a rule is balanced with 30 N at 1 m on one side, and a force at 3 m on the other side. What is the force at 3 m? Write the number of newtons.
12.4

Levers and the size of the force

Year 7
P3: a lever is a bar that turns about a pivot; a longer distance from the pivot needs a smaller force to produce the same moment
Video lesson: Levers and the size of the forceComing soon
Story. Mo struggles to undo a stiff bolt with a short spanner. His teacher gives him a longer spanner. “Why is this easier?” he asks. His teacher says, “The longer handle puts your force further from the bolt, so you need a smaller force for the same turning effect.”

A lever is a bar that turns about a pivot. Levers are used to lift or turn things with less effort: a spanner, a wheelbarrow, a bottle opener, a crowbar.

For the same moment, a longer distance from the pivot needs a smaller force. A short spanner needs a bigger force, but a long spanner needs less force.

Key ideas

  • A lever is a bar that turns about a pivot.
  • The moment = force x distance from the pivot.
  • For the same moment, a longer distance means a smaller force.
  • A longer handle makes a job easier.
Worked example 12.4.1
A spanner with a short handle has a moment of 4 N m from a force of 20 N. What is the distance from the pivot? Write the number of metres.

Method. Use distance = moment / force.

  1. Write the values. The moment is 4 N m and the force is 20 N.
    4 and 20
  2. Divide. Distance = 4 / 20 = 0.2 m.
    4 / 20 = 0.2
  3. Write the answer.
    0.2 m

Check. 20 x 0.2 = 4. ✓

Worked example 12.4.2
The same moment of 8 N m is needed with a force of 20 N. What distance from the pivot is needed? Write the number of metres.

Method. Use distance = moment / force.

  1. Write the values. The moment is 8 N m and the force is 20 N.
    8 and 20
  2. Divide. Distance = 8 / 20 = 0.4 m.
    8 / 20 = 0.4
  3. Write the answer.
    0.4 m

Check. 20 x 0.4 = 8. ✓

Worked example 12.4.3
Which spanner needs the smaller force for the same moment: the 0.2 m handle or the 0.4 m handle? Write the number of metres.

Method. Compare the distances.

  1. Compare. For the same moment, the longer distance needs a smaller force.
    smaller force
  2. Decide. So the 0.4 m handle needs the smaller force.
    0.4 m
  3. Write the answer.
    0.4 m

Check. A longer handle is easier. ✓

Watch out

Watch out: a longer lever does not give more moment for the same force. It gives the same moment with a smaller force, or a bigger moment for the same force.

Exam tip

Exam tip. Say that a longer lever needs a smaller force to produce the same moment, and explain why.

Try it (with your teacher, or a grown-up at home). With a grown-up, use a spanner with a short handle and a long handle to turn the same bolt, or use a bottle opener and a lever such as a ruler. Describe which handle needed less force, and explain why, using the word moment.

Exercise 12D  Levers and the size of the force

1
FWhat is a lever? Write the words.
2
FName one everyday lever. Write the word.
3
FFor the same moment, does a longer distance need a bigger or a smaller force? Write the word: bigger or smaller.
4
FWhich spanner handle is longer: 0.2 m or 0.4 m? Write the number of metres.
5
FA spanner has a 20 N force at 0.2 m. What is its moment? Write the number of N m.
6
PSA spanner with a 0.4 m handle has the same moment as the short one, 4 N m. What force is needed? Write the number of newtons.
7
PSA lever has a force of 5 N at 6 m. What is the moment? Write the number of N m.
8
PSA wheelbarrow has a moment of 60 N m. The handles are 3 m from the wheel. What force is needed? Write the number of newtons.
9
PSA spanner with a 0.2 m handle needs a force of 20 N. A spanner with a 0.4 m handle needs what force, for the same moment? Write the number of newtons.
10
PSAli says a longer spanner needs a bigger force to turn the same bolt. Is Ali right? Write yes or no.
11
PSWorking scientifically: a pupil says a longer lever always makes the moment bigger for the same force. Is this right? Write yes or no.
12
RChallenge: explain why a long bar makes it easier to lift a heavy stone with a lever. Write one sentence.
12.5

Pressure: force divided by area

Year 7
P4: pressure = force / area; a large force on a small area gives a high pressure; examples such as knives and snow shoes
Video lesson: Pressure: force divided by areaComing soon
Story. Priya walks on fresh snow in ordinary shoes and sinks in deeply. Her friend wears wide snow shoes and barely sinks at all. “We weigh about the same,” says Priya. Her teacher says, “It is the pressure that matters. The same force spread over a bigger area gives a smaller pressure.”

Pressure is the force acting on each square metre of a surface. It is found using:

pressure = force / area

Force is in newtons (N) and area is in square metres (m²). Pressure is measured in newtons per square metre (N/m²), which is also called the pascal (Pa).

A small area gives a high pressure, so a sharp knife cuts easily. A large area gives a low pressure, so snow shoes stop you sinking.

small area: high pressurelarge area: low pressure
A small foot on snow has high pressure; a wide snow shoe has low pressure.

The table gives the force and area of three objects, and the pressure on the surface.

ObjectForce (N)Area (m squared)Pressure (Pa)
a block on the table6000.51200
a child's shoe, standing still5000.0225000
a snow shoe, standing on snow5000.51000

Key ideas

  • pressure = force / area, in pascals (Pa) when force is in N and area in m².
  • A small area gives a high pressure.
  • A large area gives a low pressure, for the same force.
  • Sharp knives cut with high pressure because the blade has a small area.
Worked example 12.5.1
A block of weight 600 N rests on a table with an area of 0.5 m². What is the pressure? Write the number of pascals.

Method. Use pressure = force / area.

  1. Write the values. The force is 600 N and the area is 0.5 m².
    600 and 0.5
  2. Divide. Pressure = 600 / 0.5 = 1200.
    600 / 0.5 = 1200
  3. Write the answer.
    1200 Pa

Check. 1200 x 0.5 = 600. ✓

Worked example 12.5.2
A child stands on one shoe, with a force of 500 N over an area of 0.02 m². What is the pressure? Write the number of pascals.

Method. Use pressure = force / area.

  1. Write the values. The force is 500 N and the area is 0.02 m².
    500 and 0.02
  2. Divide. Pressure = 500 / 0.02 = 25000.
    500 / 0.02 = 25000
  3. Write the answer.
    25000 Pa

Check. 25000 x 0.02 = 500. ✓

Worked example 12.5.3
The same 500 N is spread over a snow shoe of area 0.5 m². What is the pressure? Write the number of pascals.

Method. Use pressure = force / area.

  1. Write the values. The force is 500 N and the area is 0.5 m².
    500 and 0.5
  2. Divide. Pressure = 500 / 0.5 = 1000.
    500 / 0.5 = 1000
  3. Write the answer.
    1000 Pa

Check. The snow shoe gives a much lower pressure than the shoe. ✓

Watch out

Watch out: a larger area reduces the pressure, but does not reduce the force. Snow shoes spread the same weight over a bigger area.

Exam tip

Exam tip. In a pressure question, use the area in m², then give the unit Pa or N/m².

Try it (with your teacher, or a grown-up at home). With a teacher, look at a sharp knife and a blunt one, and say which has the smaller area at the edge. Compare the pressure they would make with the same force. Do not cut anything; use a piece of paper folded into a point and a flat edge to show the idea.

Exercise 12E  Pressure: force divided by area

1
FWhat is the formula for pressure? Write the words.
2
FWhat is the unit of pressure, when force is in N and area is in m²? Write the name.
3
FDoes a small area give a high or a low pressure, for the same force? Write the word: high or low.
4
FWhy does a snow shoe stop you sinking? Write the words: wider or narrower.
5
FA block of weight 600 N has an area of 0.5 m². What is the pressure? Write the number of pascals.
6
FA force of 500 N acts on a snow shoe of area 0.5 m². What is the pressure? Write the number of pascals.
7
PSA force of 10 N acts on an area of 2 m². What is the pressure? Write the number of pascals.
8
PSA force of 24 N acts on an area of 4 m². What is the pressure? Write the number of pascals.
9
PSA force of 300 N is spread over 6 m². What is the pressure? Write the number of pascals.
10
PSA pressure of 40 Pa is caused by a force of 80 N. What is the area? Write the number of m².
11
PSBen says a sharp knife has a high pressure at its edge because the edge has a small area. Is Ben right? Write yes or no.
12
PSWorking scientifically: a pupil says a bigger force always gives a higher pressure. Is this always true? Write yes or no.
13
RExplain why a snow shoe reduces the pressure on snow, even though the weight is the same. Write one sentence.
14
RChallenge: explain why a pin pushed into a board needs only a small force to make a high pressure at its tip. Write one sentence.

Chapter summary

SkillMethod
Pivot and turningA force turns an object about a pivot. Its turning effect depends on size and distance.
Momentmoment = force x perpendicular distance from the pivot, in N m.
BalanceBalanced when the clockwise moments equal the anticlockwise moments.
LeversFor the same moment, a longer distance needs a smaller force.
Pressurepressure = force / area, in Pa. A small area gives a high pressure; a large area a low pressure.

Can you…?

  • I can say that a force can turn an object about a pivot
  • I can calculate a moment, in N m, from a force and its perpendicular distance
  • I can use balanced moments to find a missing force or distance
  • I can explain why a longer lever needs a smaller force
  • I can calculate pressure = force / area, in pascals, and explain snow shoes and knives

Key terms

pivot
the point an object turns about
moment
the turning effect of a force about a pivot: force x perpendicular distance, in N m
perpendicular distance
the distance from the pivot measured at a right angle to the force
balance
an object is balanced when its clockwise and anticlockwise moments are equal
lever
a bar that turns about a pivot
pressure
force per unit area; pressure = force / area
pascal (Pa)
the unit of pressure, equal to one newton per square metre

Exercise 12Z  Check-up

1
What is the name of the point a force turns an object about? Write the word.
2
A force of 40 N acts 3 m from the pivot. What is the moment? Write the number of N m.
3
What is the unit of moment? Write the unit.
4
On the seesaw, the moment on the left is 400 N m. What is the moment on the right? Write the number of N m.
5
A 60 N force acts 2 m from the pivot. What distance is needed for a 30 N force to balance it? Write the number of metres.
6
For the same moment, does a longer distance need a bigger or smaller force? Write the word: bigger or smaller.
7
What is the formula for pressure? Write the words.
8
What is the unit of pressure? Write the name.
9
A block has a weight of 600 N and an area of 0.5 m². What is its pressure? Write the number of pascals.
10
Why does a sharp knife cut more easily than a blunt one, for the same force? Write one sentence.

Total 22 marks. Allow about 22 minutes.

Exercise 12X  Practice test questions

1
PSA force of 12 N acts 3 m from the pivot. Write the moment in N m.[2 marks]
2
FName the point about which an object turns. Write the word.[1 mark]
3
PSA seesaw is balanced, with 200 N at 2 m on one side. What is the moment on the other side? Write the number of N m.[2 marks]
4
PSA lever has a moment of 60 N m and a force of 20 N. What is the distance from the pivot? Write the number of metres.[2 marks]
5
RExplain why a longer spanner is easier to turn than a short one. Write one sentence.[2 marks]
6
FWrite the formula for pressure. Write the words.[1 mark]
7
PSA force of 500 N acts on an area of 0.5 m². What is the pressure? Write the number of pascals.[2 marks]
8
FWhich gives a higher pressure for the same force: a small area or a large area? Write the words.[1 mark]
9
RA snow shoe is wider than a foot. Explain why it reduces sinking. Write one sentence.[2 marks]
10
PSA force of 300 N is spread over 6 m². What is the pressure? Write the number of pascals.[2 marks]
11
PSA seesaw has 30 N at 1 m on one side. What force at 3 m balances it? Write the number of newtons.[2 marks]
12
RExplain why a pin has a high pressure at its tip. Write one sentence.[2 marks]
13
FWrite the unit of moment. Write the unit.[1 mark]
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