Level 3 · Science S3.7

Speed, forces and pressure

Forces change how things move, and pressure tells you how spread out a force is.

Work out speed and draw it as a graph, add up forces on an object, tell mass from weight, stretch a rubber band and plot the pattern, balance a ruler seesaw, and find out why a knife cuts and a camel does not sink.

You are ready for this book if

You can measure a distance in metres with a stick or a string.

Written and drawn by attnom. Free to read, print and share.

S3.7.1 Chapter 1

Speed

How fast do I walk? Can I measure it at home?

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

Amina and her brother go to the well. Amina walks and her brother runs. He gets there first, so he was faster. But how much faster? To say, we need a number.

The speed of a thing tells how far it goes in one second. We measure speed in metres per second. We write m/s.

A speed of 2 m/s means 2 metres every second. A person walking goes about 1 to 1.5 metres each second.

A track marked in metres with the numbers 0, 2, 4, 6 and 8 and the label metres. A walker is shown as a dot at 0 s, 1 s, 2 s, 3 s and 4 s, each dot 2 metres farther on than the one before, with arrows between them. The label above says every second: 2 m. Labels: every second: 2 m, 0 s, 1 s, 2 s, 3 s, 4 s, 0, 2, 4, 6, 8, metres.0 s1 s2 s3 s4 s02468metresevery second: 2 m
A walker at 2 m/s is 2 metres farther on every second. After 4 seconds she has gone 8 metres.

Draw it first

Draw a walk and its speed

  1. A straight track with marks at 0, 6, 12 and 18, with the label metres. In the first picture a person stands at 0, labelled start. In the second the person is at 18, labelled end, and an arrow runs along the track, labelled 18 m in 12 s. In the third the speed is written: speed = 18 m ÷ 12 s = 1.5 m/s.061218metresstart

    1 Draw a track. Mark 0, 6, 12 and 18 metres. Draw the walker at the start.

  2. A straight track with marks at 0, 6, 12 and 18, with the label metres. In the first picture a person stands at 0, labelled start. In the second the person is at 18, labelled end, and an arrow runs along the track, labelled 18 m in 12 s. In the third the speed is written: speed = 18 m ÷ 12 s = 1.5 m/s.061218metresend18 m in 12 s

    2 Move the walker to the end. Write the distance and the time: 18 m in 12 s.

  3. A straight track with marks at 0, 6, 12 and 18, with the label metres. In the first picture a person stands at 0, labelled start. In the second the person is at 18, labelled end, and an arrow runs along the track, labelled 18 m in 12 s. In the third the speed is written: speed = 18 m ÷ 12 s = 1.5 m/s.061218metresend18 m in 12 sspeed = 18 m ÷ 12 s = 1.5 m/s

    3 Divide the distance by the time. 18 ÷ 12 = 1.5. The speed is 1.5 m/s.

To find a speed you need two measurements. One is the distance, how far the thing went, in metres. The other is the time it took, in seconds.

Then share the distance out among the seconds. That gives the metres for each second.

See it three ways

As a picture

A table with two columns, time in seconds and distance in metres. At 0 seconds the distance is 0. Then 2 and 3, 4 and 6, 6 and 9, 8 and 12.secondsmetres00234669812

In words

A walker goes 1.5 metres every second. In 2 seconds she goes 3 metres. The distance grows by the same amount each second.

In symbols

speed = distance ÷ time. 18 m ÷ 12 s = 1.5 m/s.

A track marked 0, 10, 20, 30 and 40 with the label metres. The label start is at 0 and the label end is above a runner at 40. An arrow runs along the track, labelled 40 m in 10 s. Labels: start, end, 0, 10, 20, 30, 40, metres, 40 m in 10 s.010203040metresstartend40 m in 10 s
The runner in the next worked example. Read the distance and the time from the picture.

Worked example

Kofi runs 40 m in 10 s. What is his speed?

  1. Speed = distance ÷ time.
  2. The distance is 40 m. The time is 10 s.
  3. Speed = 40 ÷ 10 = 4 m/s.

Answer: 4 m/s

You can turn the rule around. If you know the speed and the time, then distance = speed × time. If you know the distance and the speed, then time = distance ÷ speed.

A real walk is never perfectly even. You slow down on a hill and speed up on flat ground. So the number you find is the average speed: the total distance divided by the total time.

A track marked 0, 30 and 60 with the label metres. The first part, labelled walk, is 30 m, 30 s. The second part, labelled run, is 30 m, 10 s. Below is written 60 m ÷ 40 s = 1.5 m/s. Labels: walk, run, 0, 30, 60, metres, 30 m, 30 s, 30 m, 10 s, 60 m ÷ 40 s = 1.5 m/s.03060metreswalkrun30 m, 30 s30 m, 10 s60 m ÷ 40 s = 1.5 m/s
A slow part and a fast part. The average speed uses the whole distance and the whole time.

Try it

Measure your walking speed

You need: a string or stick to measure 12 metres, two stones to mark the start and the end, a clock, or a friend who counts seconds ("one thousand and one, one thousand and two"), paper and a pencil.

Be safe: Walk on flat ground, well away from roads and holes. Do not run.

  1. Mark a start and an end 12 metres apart on flat ground. Put a stone at each.
  2. Stand at the start. Your friend says "go" and starts counting seconds.
  3. Walk at your normal pace to the end stone. Do not run.
  4. Write the time in seconds. Do the walk three times.
  5. For each walk, divide 12 by the time. Write the speed in metres per second.

What you will see: Your three speeds will be close, but not the same. Ours are 1.2, 1.2, 1 m/s. A walk usually comes out between 1 and 1.5 m/s. Your numbers will differ from ours, and that is fine.

If you cannot try it, this is what happens.
A table of one learner's walks of 12 metres. The head row says walk, seconds and m/s. Walk 1: 10 seconds, 1.2 m/s. Walk 2: 10 seconds, 1.2 m/s. Walk 3: 12 seconds, 1 m/s.walksecondsm/s1101.22101.23121
A bar chart called speed (m/s). The bar for Ravi reaches 1. The bar for Mei reaches 3. The scale goes from 0 to 4 in steps of 1. Labels: speed (m/s), Ravi, Mei, 0, 1, 2, 3, 4.01234RaviMeispeed (m/s)
Ravi walks 60 m in 60 s. Mei runs 30 m in 10 s. Ravi goes farther, but Mei is faster.

A wrong idea many people have

The one that goes the farthest is the fastest.

Why it feels right: Going a long way looks like hard work, so it seems to need more speed.

The test that breaks it: Ravi walks 60 m in 60 s. Mei runs 30 m in 10 s. Ravi went farther. Divide each: Ravi 1 m/s, Mei 3 m/s. Mei is faster.

What is true: Speed needs the distance and the time together. A short trip in a short time can be faster than a long, slow trip.

Key words

speed
how far a thing goes in one second.
metres per second
the unit of speed. We write m/s.
distance
how far a thing goes, measured in metres.
average speed
the total distance divided by the total time.

Back to your guess

The answer is A: Measure a distance, time your walk, then divide the distance by the time.

Measure a distance, time your walk, then divide the distance by the time. A string and a clock are enough. Speed needs both numbers, not only the time.

Check yourself

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

  1. Mei walks 36 m in 30 s. What is her speed?

    See the answer

    1.2 m/s

    Speed = distance ÷ time = 36 ÷ 30 = 1.2 m/s.

  2. A cyclist rides at 4 m/s for 10 s. How far does she go?

    Tap your answer.

    1. Not this one. You divided the time by the speed. To find a distance, multiply the speed by the time. Go to S3.7.1. Try another.

    2. Yes, that is right. Distance = speed × time = 4 × 10 = 40 m.

    3. Not this one. You added the speed and the time. A speed of 4 m/s means 4 metres every second, so multiply by the seconds. Go to S3.7.1. Try another.

    See the answer

    40 m

    Distance = speed × time = 4 × 10 = 40 m.

    • If you chose A: You divided the time by the speed. To find a distance, multiply the speed by the time. Go to S3.7.1.
    • If you chose C: You added the speed and the time. A speed of 4 m/s means 4 metres every second, so multiply by the seconds. Go to S3.7.1.

  3. Joseph walks at 2 m/s. How long does he take to walk 50 m?

    Tap your answer.

    1. Not this one. You divided the speed by the distance, upside down. Time = distance ÷ speed. Go to S3.7.1. Try another.

    2. Not this one. You multiplied the distance by the speed. That gives a distance, not a time. Divide the distance by the speed. Go to S3.7.1. Try another.

    3. Yes, that is right. Time = distance ÷ speed = 50 ÷ 2 = 25 s.

    4. Not this one. You added the distance and the speed. They are different kinds of number, so they cannot be added. Divide instead. Go to S3.7.1. Try another.

    See the answer

    25 s

    Time = distance ÷ speed = 50 ÷ 2 = 25 s.

    • If you chose A: You divided the speed by the distance, upside down. Time = distance ÷ speed. Go to S3.7.1.
    • If you chose B: You multiplied the distance by the speed. That gives a distance, not a time. Divide the distance by the speed. Go to S3.7.1.
    • If you chose D: You added the distance and the speed. They are different kinds of number, so they cannot be added. Divide instead. Go to S3.7.1.

  4. Ana walks 20 m in 10 s. Tariq walks 30 m in 20 s. Who is faster?

    Tap your answer.

    1. Yes, that is right. Ana: 20 ÷ 10 = 2 m/s. Tariq: 30 ÷ 20 = 1.5 m/s. Ana has the bigger number.

    2. Not this one. Tariq went farther, but he also took longer. Divide each distance by its time and compare. Go to S3.7.1. Try another.

    3. Not this one. Work out each speed. Distance ÷ time is not the same for both. Go to S3.7.1. Try another.

    See the answer

    Ana

    Ana: 20 ÷ 10 = 2 m/s. Tariq: 30 ÷ 20 = 1.5 m/s. Ana has the bigger number.

    • If you chose B: Tariq went farther, but he also took longer. Divide each distance by its time and compare. Go to S3.7.1.
    • If you chose C: Work out each speed. Distance ÷ time is not the same for both. Go to S3.7.1.

  5. Kofi walks 40 m in 40 s. Then he runs 40 m in 10 s. What is his average speed for the whole trip?

    Tap your answer.

    1. Not this one. You added the two speeds and halved them. Use the total distance and the total time instead. Go to S3.7.1. Try another.

    2. Yes, that is right. Total distance = 40 + 40 = 80 m. Total time = 40 + 10 = 50 s. 80 ÷ 50 = 1.6 m/s.

    3. Not this one. That is only the running part. Average speed uses the whole trip. Go to S3.7.1. Try another.

    See the answer

    1.6 m/s

    Total distance = 40 + 40 = 80 m. Total time = 40 + 10 = 50 s. 80 ÷ 50 = 1.6 m/s.

    • If you chose A: You added the two speeds and halved them. Use the total distance and the total time instead. Go to S3.7.1.
    • If you chose C: That is only the running part. Average speed uses the whole trip. Go to S3.7.1.

  6. To find your walking speed at home, which two measurements do you need?

    Tap your answer.

    1. Not this one. The time alone cannot tell the speed. A short walk takes little time even when it is slow. Go to S3.7.1. Try another.

    2. Not this one. The distance alone cannot tell the speed. A long walk is slow if it takes a long time. Go to S3.7.1. Try another.

    3. Yes, that is right. Speed is distance divided by time, so you need both. Mark a distance with stones, time the walk, then divide. Do it three times, because a walk is never perfectly even.

    See the answer

    The distance you walk and the time it takes.

    Speed is distance divided by time, so you need both. Mark a distance with stones, time the walk, then divide. Do it three times, because a walk is never perfectly even.

    • If you chose A: The time alone cannot tell the speed. A short walk takes little time even when it is slow. Go to S3.7.1.
    • If you chose B: The distance alone cannot tell the speed. A long walk is slow if it takes a long time. Go to S3.7.1.

Keep it

Copy this into your exercise book.

Speed is how far a thing goes in one second. Speed = distance ÷ time. We write it in metres per second, m/s. Distance = speed × time.

Draw: A track marked 0 and 12 metres. Under it write 12 m ÷ 10 s = 1.2 m/s.

S3.7.2 Chapter 2

Distance and time graphs

Can a picture show how a whole journey went?

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

Mei walks to the market. She goes quickly, stops to talk, then walks on slowly. A list of numbers would be hard to read. A picture shows the whole journey at once.

A distance and time graph shows how far something is from home as time goes by. Time goes across. Distance goes up. Both start at 0.

Start with a table. It says where Mei was after each 10 seconds. Each row is one point on the line we draw.

A table with the columns seconds and metres from home. At 0 seconds, 0 metres. At 10 seconds, 20 metres. At 20 seconds, 40 metres. At 30 seconds, 40 metres. At 40 seconds, 40 metres. At 50 seconds, 45 metres. At 60 seconds, 50 metres.secondsmetres from home00102020403040404050456050
Mei is at 0 metres from home when she starts. Read down to see her move, stop and move on.

Draw it first

Draw the graph of a journey

  1. A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. First, a line climbs steeply from 0 to 40 metres in 20 seconds. Next it runs flat to 40 seconds. Last it climbs gently to 50 metres at 60 seconds. The three parts are labelled fast, still and slow. Labels: time in seconds, distance from home (m), fast, still, slow.01020304050600102030405060time in secondsdistance from home (m)

    1 Draw the axes. Mei walks 40 m in 20 s. Mark that point and join it to the start.

  2. A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. First, a line climbs steeply from 0 to 40 metres in 20 seconds. Next it runs flat to 40 seconds. Last it climbs gently to 50 metres at 60 seconds. The three parts are labelled fast, still and slow. Labels: time in seconds, distance from home (m), fast, still, slow.01020304050600102030405060time in secondsdistance from home (m)

    2 She stands still for 20 s. Her distance stays at 40 m, so draw a flat line.

  3. A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. First, a line climbs steeply from 0 to 40 metres in 20 seconds. Next it runs flat to 40 seconds. Last it climbs gently to 50 metres at 60 seconds. The three parts are labelled fast, still and slow. Labels: time in seconds, distance from home (m), fast, still, slow.01020304050600102030405060faststillslowtime in secondsdistance from home (m)

    3 Then she walks 10 m in 20 s. Draw a gentle line. Write fast, still and slow.

Read the graph from left to right, like a story. A flat line means the distance is not changing. The thing is still.

A line that climbs means the thing is moving away from home. The steeper the line, the faster the thing is going. A gentle climb is slow.

Two graphs with the same scale. Time in seconds runs across to 60. Distance from home goes up to 60 metres. Kofi: 60 m in 30 s, a steep line, labelled faster. Lucía: 60 m in 60 s, a gentle line, labelled slower. Labels: Kofi, Lucía, faster, slower, time in seconds, distance from home (m).Kofi: 60 m in 30 s01020304050600204060fastertime in secondsdistance from home (m)Lucía: 60 m in 60 s01020304050600204060slowertime in secondsdistance from home (m)
Both walkers go the same distance. Kofi takes less time, so his line is steeper.

You can find the speed of any part of a journey. Take the distance that part covers and divide it by the time it takes. This is the same rule as before.

See it three ways

As a picture

A table of Mei's journey with the columns part, seconds, metres and m/s. Part 1st: 20 seconds, 40 metres, 2 m/s. Part 2nd: 20 seconds, 0 metres, 0 m/s. Part 3rd: 20 seconds, 10 metres, 0.5 m/s.partsecondsmetresm/s1st204022nd20003rd20100.5

In words

The steep part has the biggest speed. The flat part has a speed of zero. The gentle part is in between.

In symbols

Fast part: 40 ÷ 20 = 2 m/s. Still part: 0 ÷ 20 = 0 m/s. Slow part: 10 ÷ 20 = 0.5 m/s.

A graph of the first part of Mei's journey. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. A line climbs from 0 to 40 metres at 20 seconds, labelled first part. Labels: time in seconds, distance from home (m), first part.01020304050600102030405060first parttime in secondsdistance from home (m)
Read two numbers from this part: how far, and how long. Then divide.

Worked example

Use Mei's graph. What is her speed in the first part, from 0 s to 20 s?

  1. At 20 s the graph is at 40 m.
  2. The part starts at 0 s and ends at 20 s. It lasts 20 s.
  3. Speed = distance ÷ time = 40 ÷ 20 = 2 m/s.
  4. The line is steep, so this is the fast part.

Answer: 2 m/s

All the graphs here show distance from home. So a line that goes down means the walker is coming back towards home.

Try it

Draw the graph of your own walk

You need: five stones, a string and a stick to space them 3 metres apart, a clock, or a friend who counts seconds, paper with a ruler for the lines, and a pencil.

Be safe: Walk on flat ground, well away from roads. Do not run.

  1. Put the stones in a straight line, 3 metres apart. Stand at the first stone.
  2. Your friend says "go". Walk at your normal pace past all the stones.
  3. Your friend writes the second you reach each stone.
  4. On paper, draw time across and distance up. Both start at 0.
  5. Mark a point for each stone. Join the points with straight lines.

What you will see: The line is close to straight, with a few small bends. A walk is never perfectly even. A straight line means a steady speed. The dashed line shows the pattern.

If you cannot try it, this is what happens.
A graph of one learner's walk. Time in seconds runs across to 10, with 0, 2, 4, 6, 8, 10. Distance walked goes up to 12 metres, with 0, 3, 6, 9, 12. The points are 0 s and 0 m, 2 s and 3 m, 5 s and 6 m, 8 s and 9 m, 10 s and 12 m. A dashed straight line runs close to all the points. Labels: time in seconds, distance walked (m).0246810036912time in secondsdistance walked (m)

A wrong idea many people have

A line that goes up on the graph means the walker is going uphill.

Why it feels right: The line looks like a hill, so it is tempting to read it as a path.

The test that breaks it: Walk 10 steps on flat ground, then stand still for 10 seconds. Draw the graph. It climbs, then goes flat. The ground was flat the whole way.

What is true: The graph is not a picture of the path. Up means farther from home as time goes by. Flat means not moving.

Key words

distance and time graph
a graph with time across and distance from home up.
still
not moving. The graph line is flat.
steeper
climbing more quickly. A steeper line means a faster speed.

Back to your guess

The answer is A: A flat line on the graph means the walker is standing still.

A flat line means the distance is not changing, so the walker is standing still. The graph shows distance from home against time. It does not show the shape of the ground.

Check yourself

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

  1. Look at Ravi's graph. In which part is he standing still?

    A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. A line climbs to 10 metres at 10 seconds, climbs more steeply to 50 metres at 30 seconds, then runs flat until 50 seconds. Labels: time in seconds, distance from home (m).01020304050600102030405060time in secondsdistance from home (m)
    Tap your answer.

    1. Not this one. The line climbs here, so the distance is growing. He is moving. Look for the flat part. Go to S3.7.2. Try another.

    2. Yes, that is right. A flat line means the distance does not change. He is still from 30 s to 50 s.

    3. Not this one. The line climbs steeply here. A fast walk is not standing still. Look for the flat part. Go to S3.7.2. Try another.

    See the answer

    From 30 s to 50 s

    A flat line means the distance does not change. He is still from 30 s to 50 s.

    • If you chose A: The line climbs here, so the distance is growing. He is moving. Look for the flat part. Go to S3.7.2.
    • If you chose C: The line climbs steeply here. A fast walk is not standing still. Look for the flat part. Go to S3.7.2.

  2. Use the same graph. In which part does Ravi move fastest?

    A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. A line climbs to 10 metres at 10 seconds, climbs more steeply to 50 metres at 30 seconds, then runs flat until 50 seconds. Labels: time in seconds, distance from home (m).01020304050600102030405060time in secondsdistance from home (m)
    Tap your answer.

    1. Not this one. This part is flat, so he is not moving. The fastest part is the steepest. Go to S3.7.2. Try another.

    2. Not this one. The line climbs here, but not as steeply as later. Find the steepest part. Go to S3.7.2. Try another.

    3. Yes, that is right. The middle part is the steepest. He goes 40 m in 20 s, which is 2 m/s.

    See the answer

    From 10 s to 30 s

    The middle part is the steepest. He goes 40 m in 20 s, which is 2 m/s.

    • If you chose A: This part is flat, so he is not moving. The fastest part is the steepest. Go to S3.7.2.
    • If you chose B: The line climbs here, but not as steeply as later. Find the steepest part. Go to S3.7.2.

  3. Ana's graph shows her distance from home. What does she do between 30 s and 40 s?

    A graph of Ana's distance from home. Time in seconds runs across to 60, with 0, 10, 20, 30, 40, 50, 60. Distance from home goes up to 60 metres, with 0, 10, 20, 30, 40, 50, 60. The line climbs to 20 metres at 10 seconds, runs flat until 30 seconds, then goes down to 10 metres at 40 seconds. Labels: time in seconds, distance from home (m).01020304050600102030405060time in secondsdistance from home (m)
    Tap your answer.

    1. Yes, that is right. The line goes down, so her distance from home gets smaller.

    2. Not this one. Her distance from home gets smaller here, so she is coming closer. Check which way the line goes. Go to S3.7.2. Try another.

    3. Not this one. A still walker has a flat line. This line goes down. Go to S3.7.2. Try another.

    See the answer

    She walks back towards home.

    The line goes down, so her distance from home gets smaller.

    • If you chose B: Her distance from home gets smaller here, so she is coming closer. Check which way the line goes. Go to S3.7.2.
    • If you chose C: A still walker has a flat line. This line goes down. Go to S3.7.2.

  4. Mei is 40 m from home after 20 s. You draw her graph. Where do you mark this point?

    Tap your answer.

    1. Not this one. You swapped the two scales. On this graph time goes across and distance goes up, so start with the time. Go to S3.7.2. Try another.

    2. Yes, that is right. Time goes across and distance goes up. The point is 20 s across and 40 m up.

    3. Not this one. That puts the point at 0 seconds, on the up line. Go across to the time first, then up. Go to S3.7.2. Try another.

    See the answer

    Across to 20 on the time scale, then up to 40 on the distance scale

    Time goes across and distance goes up. The point is 20 s across and 40 m up.

    • If you chose A: You swapped the two scales. On this graph time goes across and distance goes up, so start with the time. Go to S3.7.2.
    • If you chose C: That puts the point at 0 seconds, on the up line. Go across to the time first, then up. Go to S3.7.2.

  5. Tariq walks 30 m away from home in 10 s. He stands still for 10 s. Then he walks 5 m farther from home in 20 s. What does his distance and time graph look like?

    Tap your answer.

    1. Not this one. Standing still makes his speed 0, not his distance. He stays 30 m from home, so the line stays flat at 30 m. Go to S3.7.2. Try another.

    2. Not this one. You swapped fast and slow. The first part covers more distance in less time, so it is the steeper line. Go to S3.7.2. Try another.

    3. Not this one. The last part covers a short distance in a long time. That is slow, so the last line is gentle, not steep. Go to S3.7.2. Try another.

    4. Yes, that is right. First he goes at 3 m/s, which is the steepest part. Then his speed is 0 m/s, so the line is flat. Last he goes at 0.25 m/s, a gentle climb.

    See the answer

    It climbs steeply, then goes flat, then climbs gently.

    First he goes at 3 m/s, which is the steepest part. Then his speed is 0 m/s, so the line is flat. Last he goes at 0.25 m/s, a gentle climb.

    • If you chose A: Standing still makes his speed 0, not his distance. He stays 30 m from home, so the line stays flat at 30 m. Go to S3.7.2.
    • If you chose B: You swapped fast and slow. The first part covers more distance in less time, so it is the steeper line. Go to S3.7.2.
    • If you chose C: The last part covers a short distance in a long time. That is slow, so the last line is gentle, not steep. Go to S3.7.2.

  6. At 4 s a walker is 6 m from home. At 10 s the walker is 21 m from home. What is the speed between these times?

    See the answer

    2.5 m/s

    Distance covered = 21 − 6 = 15 m. Time = 10 − 4 = 6 s. Speed = 15 ÷ 6 = 2.5 m/s.

  7. From an earlier chapter

    Review: Tariq runs 60 m in 12 s. What is his speed?

    Tap your answer.

    1. Not this one. You added the two numbers. Speed is distance divided by time. Go to S3.7.1. Try another.

    2. Not this one. You divided time by distance. Put the distance first: distance ÷ time. Go to S3.7.1. Try another.

    3. Yes, that is right. Speed = distance ÷ time = 60 ÷ 12 = 5 m/s.

    See the answer

    5 m/s

    Speed = distance ÷ time = 60 ÷ 12 = 5 m/s.

    • If you chose A: You added the two numbers. Speed is distance divided by time. Go to S3.7.1.
    • If you chose B: You divided time by distance. Put the distance first: distance ÷ time. Go to S3.7.1.

Keep it

Copy this into your exercise book.

A distance and time graph has time across and distance from home up. A flat line is still. A steeper line is faster. A line going down is coming back home.

Draw: Axes marked 0 to 60. A line that climbs steeply, goes flat, then climbs gently. Write fast, still, slow.

S3.7.3 Chapter 3

Balanced and unbalanced forces

Why does a bag of rice on a table not move, when gravity is pulling it down?

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

Almost nothing has only one force on it. A bag of rice on a table has two. Gravity pulls it down. The table pushes it up.

We draw a force as an arrow. The arrow points the way the force acts. A longer arrow is a bigger force. We write the size in newtons, N.

Often there are two forces in opposite directions. To see what happens, we add them up into one: the overall force.

Draw it first

Draw the forces on a pushed box

  1. A box on the floor. In the first picture an arrow points right, labelled 25 N, with the word push above it. In the second picture a short arrow points left, labelled 10 N, with the word friction above it. In the third picture one arrow points right, labelled 15 N, with the words overall force above it. Labels: push, 25 N, friction, 10 N, overall force, 15 N.25 Npush

    1 Draw the box. Draw the push as an arrow to the right. It is 25 N.

  2. A box on the floor. In the first picture an arrow points right, labelled 25 N, with the word push above it. In the second picture a short arrow points left, labelled 10 N, with the word friction above it. In the third picture one arrow points right, labelled 15 N, with the words overall force above it. Labels: push, 25 N, friction, 10 N, overall force, 15 N.25 N10 Npushfriction

    2 Friction pulls the other way. Draw a shorter arrow to the left. It is 10 N.

  3. A box on the floor. In the first picture an arrow points right, labelled 25 N, with the word push above it. In the second picture a short arrow points left, labelled 10 N, with the word friction above it. In the third picture one arrow points right, labelled 15 N, with the words overall force above it. Labels: push, 25 N, friction, 10 N, overall force, 15 N.15 Noverall force

    3 Take the small force from the big one. 25 − 10 = 15. The overall force is 15 N to the right.

When two forces act on a thing in opposite directions, the overall force is the difference between them. It points the way of the bigger force.

If the two forces are the same size, the overall force is zero. We say the forces are balanced. If they are not the same size, they are unbalanced.

A bag, drawn as a box. An arrow points up from the bag, labelled table 20 N. An arrow of the same length points down, labelled weight 20 N.table 20 Nweight 20 N
The table pushes up with 20 N. Gravity pulls down with 20 N. The forces are balanced, so the bag does not move.

Balanced forces change nothing. A thing that is still stays still. A thing that is moving keeps moving at the same speed in the same direction.

A box moving right at 2 metres per second, with the label steady 2 m/s. An arrow points right, labelled 10 N, with the word push above it. An arrow of the same length points left, labelled 10 N, with the word friction above it. Labels: steady 2 m/s, push, 10 N, friction.10 N10 Npushfrictionsteady 2 m/s
The push and the friction are balanced. The box keeps its steady speed. It does not speed up and it does not slow down.

See it three ways

As a picture

A table with the columns push, friction and overall. Push 25 N, friction 10 N, overall 15 N right. Push 20 N, friction 20 N, overall 0 N. Push 10 N, friction 25 N, overall 15 N left.pushfrictionoverall25 N10 N15 N right20 N20 N0 N10 N25 N15 N left

In words

If the push is bigger, the overall force is forward and the box speeds up. If the two are equal, nothing changes. If friction is bigger, a box that is already sliding slows down.

In symbols

overall force = bigger force − smaller force. 25 − 10 = 15 N.

Worked example

A box is pushed to the right with 25 N. Friction pulls it to the left with 10 N. What is the overall force?

  1. The forces point in opposite directions, so we take one from the other.
  2. The bigger force is the push: 25 N to the right.
  3. The smaller force is friction: 10 N to the left.
  4. Overall force = 25 − 10 = 15 N.
  5. The overall force points right, so the box speeds up to the right.

Answer: 15 N to the right

Try it

Pull a shoe at a steady speed

You need: an old shoe or a small box, a rubber band and a piece of string, a ruler, a smooth floor indoors.

Be safe: Pull on a clear floor. Keep your face away from the band in case it slips.

  1. Tie the band to the shoe with the string. Hold the other end of the band.
  2. Pull the shoe along the floor slowly. Try to keep it going at a steady speed.
  3. Hold the ruler beside the band while you pull. Look at how long the band is.
  4. Now pull harder so that the shoe speeds up. Watch the band.
  5. Let go. Watch how the shoe slows down and stops.

What you will see: At a steady speed the band stays the same length. Your pull and the friction are balanced. When you pull harder the band gets longer and the shoe speeds up. When you let go, friction slows it down until it stops.

If you cannot try it, this is what happens.
A shoe, shown as a box, moves right at a steady speed. An arrow points right, labelled 4 N, with the word pull above it. An arrow of the same length points left, labelled 4 N, with the word friction above it. Labels: pull, 4 N, friction.4 N4 Npullfriction

A wrong idea many people have

A moving thing needs a force to keep it moving.

Why it feels right: In daily life things stop when we stop pushing them.

The test that breaks it: Slide a book across a table and let go. It stops quickly. Now put the book on three round pencils and push it the same way. It rolls much farther. The less friction, the farther it goes.

What is true: A moving thing keeps its speed and direction unless the forces on it are unbalanced. Friction and air resistance are the forces that slow things down.

Key words

overall force
all the forces on a thing added up into one.
balanced
two forces that are equal and opposite. The overall force is zero.
unbalanced
forces that are not equal. There is an overall force.

Back to your guess

The answer is A: The forces on it are balanced.

Two forces act on the bag. Gravity pulls it down and the table pushes it up. They are the same size, so they are balanced and the bag stays still.

Check yourself

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

  1. A box is pushed to the right with 45 N. Friction pulls it to the left with 15 N. What is the overall force?

    See the answer

    30 N to the right

    The forces are opposite, so take one from the other. 45 − 15 = 30 N. The push is bigger, so the overall force points right.

  2. Two children pull a rope from opposite ends. Kofi pulls with 60 N. Ana pulls with 45 N. What is the overall force on the rope?

    Tap your answer.

    1. Not this one. You added the two pulls. They are in opposite directions, so they work against each other. Take one from the other. Go to S3.7.3. Try another.

    2. Not this one. The size is right, but the direction is not. The overall force points the way of the bigger pull, and Kofi pulls harder. Go to S3.7.3. Try another.

    3. Not this one. Zero is only for equal pulls. These two are different, so the rope moves towards the stronger one. Go to S3.7.3. Try another.

    4. Yes, that is right. The pulls are opposite, so take one from the other. 60 − 45 = 15 N. Kofi pulls harder, so the rope moves towards Kofi.

    See the answer

    15 N towards Kofi

    The pulls are opposite, so take one from the other. 60 − 45 = 15 N. Kofi pulls harder, so the rope moves towards Kofi.

    • If you chose A: You added the two pulls. They are in opposite directions, so they work against each other. Take one from the other. Go to S3.7.3.
    • If you chose B: The size is right, but the direction is not. The overall force points the way of the bigger pull, and Kofi pulls harder. Go to S3.7.3.
    • If you chose C: Zero is only for equal pulls. These two are different, so the rope moves towards the stronger one. Go to S3.7.3.

  3. A bag of rice lies on a table. Its weight is 20 N down and the table pushes up with 20 N. What is the overall force on the bag?

    A bag, drawn as a box. An arrow points up, labelled table 20 N. An arrow of the same length points down, labelled weight 20 N.table 20 Nweight 20 N
    Tap your answer.

    1. Not this one. You added the two forces. They point in opposite directions, so take one from the other. Go to S3.7.3. Try another.

    2. Yes, that is right. The forces are equal and opposite, so 20 − 20 = 0 N. The bag stays still.

    3. Not this one. The forces are equal. Neither one is bigger, so there is no overall force. Go to S3.7.3. Try another.

    See the answer

    0 N. Nothing changes.

    The forces are equal and opposite, so 20 − 20 = 0 N. The bag stays still.

    • If you chose A: You added the two forces. They point in opposite directions, so take one from the other. Go to S3.7.3.
    • If you chose C: The forces are equal. Neither one is bigger, so there is no overall force. Go to S3.7.3.

  4. A skater glides on smooth ice in a straight line at a steady speed. What can you say about the forces on her?

    Tap your answer.

    1. Not this one. A moving thing does not need a force to keep it moving. This is the idea the wrong idea box talks about. Go to S3.7.3. Try another.

    2. Not this one. Gravity pulls her down and the ice pushes her up. They are balanced, not missing. Go to S2.5.1. Try another.

    3. Yes, that is right. Her speed and direction do not change, so the overall force is zero. The forces are balanced.

    See the answer

    The forces on her are balanced.

    Her speed and direction do not change, so the overall force is zero. The forces are balanced.

    • If you chose A: A moving thing does not need a force to keep it moving. This is the idea the wrong idea box talks about. Go to S3.7.3.
    • If you chose B: Gravity pulls her down and the ice pushes her up. They are balanced, not missing. Go to S2.5.1.

  5. A box slides along the floor at a steady speed. The push is 10 N and the friction is 10 N. You keep pushing in the same way. What does the box do?

    A box moving right at a steady speed. An arrow points right, labelled 10 N, with the word push above it. An arrow of the same length points left, labelled 10 N, with the word friction above it. Labels: push, 10 N, friction.10 N10 Npushfriction
    Tap your answer.

    1. Yes, that is right. The push is 10 N and the friction is 10 N, so the overall force is 0 N. Balanced forces do not change speed or direction.

    2. Not this one. A push only speeds a box up when it is bigger than the friction. Here the two are equal. Go to S3.7.3. Try another.

    3. Not this one. Friction does pull back, but the push pulls forward just as hard. The overall force is zero, so the speed does not change. Go to S3.7.3. Try another.

    See the answer

    It keeps the same speed in the same direction.

    The push is 10 N and the friction is 10 N, so the overall force is 0 N. Balanced forces do not change speed or direction.

    • If you chose B: A push only speeds a box up when it is bigger than the friction. Here the two are equal. Go to S3.7.3.
    • If you chose C: Friction does pull back, but the push pulls forward just as hard. The overall force is zero, so the speed does not change. Go to S3.7.3.

  6. A box slides to the right. You push it right with 12 N. Friction pulls it left with 20 N. What happens to the box?

    A box. An arrow points right, labelled 12 N, with the word push above it. A longer arrow points left, labelled 20 N, with the word friction above it. Labels: push, 12 N, friction, 20 N.12 N20 Npushfriction
    Tap your answer.

    1. Not this one. A push only speeds a box up when it is bigger than the friction. Here the friction is bigger. Go to S3.7.3. Try another.

    2. Not this one. Only balanced forces keep the speed the same. These two forces are not equal, so the speed changes. Go to S3.7.3. Try another.

    3. Not this one. Friction slows a moving thing and stops it. It does not make it turn round and go the other way. Go to S3.7.3. Try another.

    4. Yes, that is right. The forces are opposite, so take one from the other. 20 − 12 = 8 N. Friction is bigger, so the overall force points left, against the movement, and the box slows down.

    See the answer

    It slows down. The overall force is 8 N to the left.

    The forces are opposite, so take one from the other. 20 − 12 = 8 N. Friction is bigger, so the overall force points left, against the movement, and the box slows down.

    • If you chose A: A push only speeds a box up when it is bigger than the friction. Here the friction is bigger. Go to S3.7.3.
    • If you chose B: Only balanced forces keep the speed the same. These two forces are not equal, so the speed changes. Go to S3.7.3.
    • If you chose C: Friction slows a moving thing and stops it. It does not make it turn round and go the other way. Go to S3.7.3.

  7. From an earlier chapter

    A walker's graph is flat from 40 s to 50 s. She is 40 m from home the whole time. What is her speed in these 10 seconds?

    Tap your answer.

    1. Not this one. You divided the distance from home by the time. Speed uses the distance she moved during those seconds. Go to S3.7.2. Try another.

    2. Yes, that is right. On a distance and time graph a flat line means she is still. She moves 0 m in 10 s, so the speed is 0 ÷ 10 = 0 m/s.

    3. Not this one. That is the time. Find how far she moved in that time and divide. Go to S3.7.2. Try another.

    See the answer

    0 m/s

    On a distance and time graph a flat line means she is still. She moves 0 m in 10 s, so the speed is 0 ÷ 10 = 0 m/s.

    • If you chose A: You divided the distance from home by the time. Speed uses the distance she moved during those seconds. Go to S3.7.2.
    • If you chose C: That is the time. Find how far she moved in that time and divide. Go to S3.7.2.

Keep it

Copy this into your exercise book.

Forces in opposite directions: take one from the other. That is the overall force. Balanced forces give zero, so speed and direction do not change.

Draw: A box with a long arrow right, 25 N, and a short arrow left, 10 N. Write overall force 15 N.

S3.7.4 Chapter 4

Mass and weight

Would I weigh less on the Moon? Would I get smaller?

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

Mei says her bag is 3 kilograms. A scientist says it weighs about 30 newtons. Both are right. They are telling you about two different things.

The mass of a thing is how much stuff is in it. We measure mass in kilograms, kg. Your bag has the same mass in a room, on a mountain or on the Moon.

Two bags drawn as boxes with an equals sign between them. The left bag is labelled Earth and the right bag is labelled Moon. Under each box is the label mass 3 kg. Labels: Earth, Moon, =, mass 3 kg.EarthMoon=mass 3 kgmass 3 kg
The same bag has the same mass on the Earth and on the Moon. It is the same amount of stuff.

The weight of a thing is the pull of gravity on it. Weight is a force, so we measure it in newtons, N.

On Earth, each kilogram weighs about 10 N. So a mass of 3 kg weighs about 30 N. To find a weight on Earth, multiply the mass in kilograms by 10.

Draw it first

Draw the mass and weight of a bag

  1. A bag drawn as a box, with the words mass 3 kg beside it. In the second picture an arrow points down from the box, labelled weight 30 N. In the third picture the sum 3 × 10 = 30 N is written underneath. Labels: mass 3 kg, weight 30 N, 3 × 10 = 30 N.mass 3 kg

    1 Draw the bag. Write its mass: 3 kg. This is the amount of stuff.

  2. A bag drawn as a box, with the words mass 3 kg beside it. In the second picture an arrow points down from the box, labelled weight 30 N. In the third picture the sum 3 × 10 = 30 N is written underneath. Labels: mass 3 kg, weight 30 N, 3 × 10 = 30 N.mass 3 kgweight 30 N

    2 Draw an arrow down from the bag. This is its weight, the pull of gravity. Write 30 N.

  3. A bag drawn as a box, with the words mass 3 kg beside it. In the second picture an arrow points down from the box, labelled weight 30 N. In the third picture the sum 3 × 10 = 30 N is written underneath. Labels: mass 3 kg, weight 30 N, 3 × 10 = 30 N.mass 3 kgweight 30 N3 × 10 = 30 N

    3 Show where the number comes from. 3 kg × 10 = 30 N.

A table with the columns mass and weight on Earth. 1 kg weighs 10 N. 2 kg weighs 20 N. 3 kg weighs 30 N. 5 kg weighs 50 N.massweight1 kg10 N2 kg20 N3 kg30 N5 kg50 N
Weight on Earth, about. Each kilogram adds about 10 N.

The Moon has much less mass than the Earth, so its gravity is weaker. On the Moon each kilogram weighs only about 1.6 N. That is about one sixth of the Earth number.

A 10 kg rock has a mass of 10 kg on the Earth and on the Moon. Its weight is not the same. Gravity pulls it less on the Moon.

A table with the columns mass, Earth and Moon. 1 kg weighs 10 N on Earth and 1.6 N on the Moon. 2 kg weighs 20 N on Earth and 3.2 N on the Moon. 5 kg weighs 50 N on Earth and 8 N on the Moon.massEarthMoon1 kg10 N1.6 N2 kg20 N3.2 N5 kg50 N8 N
Each row is one thing. Its mass stays the same. Its weight is smaller on the Moon, about one sixth as big.

See it three ways

As a picture

A bar chart called weight in newtons (N) for a rock of mass 10 kg. The bar for Earth reaches 100. The bar for Moon reaches 16. The scale goes from 0 to 100 in steps of 20. Labels: weight in newtons (N), Earth, Moon, 0, 20, 40, 60, 80, 100.020406080100EarthMoonweight in newtons (N)

In words

The rock is the same amount of stuff in both places. The Moon pulls on it much less, so it weighs much less there.

In symbols

Earth: 10 kg × 10 = 100 N, about. Moon: 10 kg × 1.6 = 16 N, about.

A shop scale with a spring really measures weight. A balance with two pans compares mass. On the Moon the balance gives the same answer. Gravity is weaker on both pans by the same amount, so they still match.

Two ruler balances, one labelled Earth and one labelled Moon. Each has 2 stones at mark 3 on the left and 2 stones at mark 3 on the right. Both rulers are level. Marks are numbered 1 to 5 on each side. Labels: Earth, Moon, 1, 2, 3, 4, 5.Earth1234512345Moon1234512345
Equal masses balance on the Earth. They balance on the Moon too, because gravity weakens on both sides together.

Try it

Make a balance and find mass

You need: a ruler or a flat stick, a round pencil, about 15 bottle tops that are all the same, or small stones of the same size, a few small things: a pebble, a key, a teaspoon, a pencil and paper.

Be safe: Keep stones off your feet. Do not drop things from a table.

  1. Rest the ruler across the round pencil at its middle, so it balances level.
  2. Put the thing you want to measure 5 cm from the middle on one side.
  3. Put bottle tops 5 cm from the middle on the other side, one at a time. Stop when the ruler is level again.
  4. Count the tops. This is the mass of the thing, in bottle tops.
  5. Do the same for each thing. Write your counts in a table.

What you will see: A heavy stone needs more tops than a light one. The tops measure mass by comparing. This would work in the same way on the Moon.

If you cannot try it, this is what happens.
A table with the heads thing and bottle tops. small stone: 5. big stone: 12. key: 4.thingbottle topssmall stone5big stone12key4

A wrong idea many people have

Mass and weight are the same thing, so I would have less mass on the Moon.

Why it feels right: In daily life people say "she weighs 40 kilograms". They use one word for both.

The test that breaks it: Balance a stone on your ruler with 5 tops. On the Moon the stone and the tops are both pulled less, so the ruler still balances. The same 5 tops match the same stone. The amount of stuff did not change.

What is true: Mass is the amount of stuff, in kg. It is the same everywhere. Weight is the pull of gravity, in N. It changes with the place.

Key words

mass
how much stuff is in a thing. It is measured in kilograms.
weight
the pull of gravity on a thing. It is measured in newtons.
kilogram
the unit of mass. We write kg.
newton
the unit of force and of weight. We write N.

Back to your guess

The answer is C: My weight would be less, but my mass would stay the same.

Your weight would be less, because the Moon pulls less than the Earth. Your mass stays the same, because you are still the same amount of stuff.

Check yourself

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

  1. Ravi's bag has a mass of 4 kg. About what is its weight on Earth?

    See the answer

    40 N

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

  2. A stone weighs about 70 N on Earth. What is its mass?

    Tap your answer.

    1. Yes, that is right. Each kilogram weighs about 10 N. 70 ÷ 10 = 7 kg.

    2. Not this one. You wrote the weight as if it were the mass. 70 is in newtons. Each kilogram weighs about 10 N, so divide by 10. Go to S3.7.4. Try another.

    3. Not this one. You multiplied. To go from a weight back to a mass, divide by 10. Each kilogram weighs about 10 N. Go to S3.7.4. Try another.

    See the answer

    7 kg

    Each kilogram weighs about 10 N. 70 ÷ 10 = 7 kg.

    • If you chose B: You wrote the weight as if it were the mass. 70 is in newtons. Each kilogram weighs about 10 N, so divide by 10. Go to S3.7.4.
    • If you chose C: You multiplied. To go from a weight back to a mass, divide by 10. Each kilogram weighs about 10 N. Go to S3.7.4.

  3. On the Moon each kilogram weighs about 1.6 N. A rock has a mass of 20 kg. About what is its weight on the Moon?

    Tap your answer.

    1. Not this one. That is the weight on the Earth. The Moon pulls less, so the weight there is smaller. Go to S3.7.4. Try another.

    2. Not this one. That is the weight of one kilogram on the Moon. The rock has 20 kg, so multiply by the mass. Go to S3.7.4. Try another.

    3. Not this one. You added the mass and the pull for each kilogram. Multiply them instead. Go to S3.7.4. Try another.

    4. Yes, that is right. The weight is the mass times the pull for each kilogram. 20 × 1.6 = 32 N.

    See the answer

    32 N

    The weight is the mass times the pull for each kilogram. 20 × 1.6 = 32 N.

    • If you chose A: That is the weight on the Earth. The Moon pulls less, so the weight there is smaller. Go to S3.7.4.
    • If you chose B: That is the weight of one kilogram on the Moon. The rock has 20 kg, so multiply by the mass. Go to S3.7.4.
    • If you chose C: You added the mass and the pull for each kilogram. Multiply them instead. Go to S3.7.4.

  4. An astronaut goes from the Earth to the Moon. Which one stays the same?

    Tap your answer.

    1. Not this one. Weight is the pull of gravity, and the Moon pulls less. Her weight is smaller there. Go to S2.5.5. Try another.

    2. Yes, that is right. Her mass is the amount of stuff in her, so it stays the same. Her weight changes, because the Moon pulls less.

    3. Not this one. Her mass is the amount of stuff in her. That does not change when she travels. Go to S3.7.4. Try another.

    See the answer

    Her mass

    Her mass is the amount of stuff in her, so it stays the same. Her weight changes, because the Moon pulls less.

    • If you chose A: Weight is the pull of gravity, and the Moon pulls less. Her weight is smaller there. Go to S2.5.5.
    • If you chose C: Her mass is the amount of stuff in her. That does not change when she travels. Go to S3.7.4.

  5. A rock weighs less on the Moon than on the Earth. What is the reason?

    Tap your answer.

    1. Not this one. The rock is the same amount of stuff everywhere, so its mass does not change. Only the pull on it changes. Go to S3.7.4. Try another.

    2. Not this one. Weight is the pull of gravity, not the push of air. The Moon has gravity, but a weaker one. Go to S2.5.5. Try another.

    3. Not this one. The Moon does pull. Each kilogram weighs about 1.6 N there. That is less than on Earth, but not zero. Go to S3.7.4. Try another.

    4. Yes, that is right. Weight is the pull of gravity on a thing. The Moon pulls less than the Earth, so the same rock weighs less there. Its mass stays the same.

    See the answer

    The Moon pulls on the rock less than the Earth does.

    Weight is the pull of gravity on a thing. The Moon pulls less than the Earth, so the same rock weighs less there. Its mass stays the same.

    • If you chose A: The rock is the same amount of stuff everywhere, so its mass does not change. Only the pull on it changes. Go to S3.7.4.
    • If you chose B: Weight is the pull of gravity, not the push of air. The Moon has gravity, but a weaker one. Go to S2.5.5.
    • If you chose C: The Moon does pull. Each kilogram weighs about 1.6 N there. That is less than on Earth, but not zero. Go to S3.7.4.

  6. Which of these is a weight?

    Tap your answer.

    1. Not this one. Kilograms measure mass, the amount of stuff. A weight is a force, in newtons. Go to S3.7.4. Try another.

    2. Not this one. Metres per second is a speed. A weight is a force, in newtons. Go to S3.7.4. Try another.

    3. Yes, that is right. Weight is a force. Forces are measured in newtons, N.

    See the answer

    50 N

    Weight is a force. Forces are measured in newtons, N.

    • If you chose A: Kilograms measure mass, the amount of stuff. A weight is a force, in newtons. Go to S3.7.4.
    • If you chose B: Metres per second is a speed. A weight is a force, in newtons. Go to S3.7.4.

  7. From an earlier chapter

    A bag with a mass of 3 kg rests on a table. It does not move. About how hard does the table push up on it?

    Tap your answer.

    1. Yes, that is right. The weight is 3 × 10 = 30 N. The bag does not move, so the forces are balanced. The table pushes up with the same force.

    2. Not this one. That is the mass in kilograms, not a force. First find the weight in newtons. Go to S3.7.4. Try another.

    3. Not this one. Zero is the overall force, not the push. The table pushes up, and the push matches the weight. Go to S3.7.3. Try another.

    See the answer

    30 N

    The weight is 3 × 10 = 30 N. The bag does not move, so the forces are balanced. The table pushes up with the same force.

    • If you chose B: That is the mass in kilograms, not a force. First find the weight in newtons. Go to S3.7.4.
    • If you chose C: Zero is the overall force, not the push. The table pushes up, and the push matches the weight. Go to S3.7.3.

Keep it

Copy this into your exercise book.

Mass is the amount of stuff, in kg, the same everywhere. Weight is the pull of gravity, in N. On Earth weight is about mass × 10. The Moon pulls about one sixth as much.

Draw: A box marked 3 kg with an arrow down marked about 30 N. Next to it, the same box with a short arrow marked about 5 N, for the Moon.

S3.7.5 Chapter 5

Stretching and springs

If I hang twice as many stones on a rubber band, does it stretch twice as far?

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

Kofi hangs a stone on a rubber band and it gets longer. He hangs a second stone and it gets longer again. He wants to know the pattern.

The original length is how long the band is with only the empty bag on it. The stretch is how much longer it gets.

To find the stretch, take the original length from the new length. The stones you hang are the load. A bigger load is a bigger pull.

Draw it first

Draw a band with more and more stones

  1. Rubber bands hang from a bar, beside a ruler marked in centimetres. In the first picture one band with 0 stones is 8 cm long. In the second picture a second band with 1 stone is 10 cm long. In the third picture bands with 0, 1, 3 and 5 stones are 8, 10, 13.4 and 16 cm long. Labels: cm, 0, 5, 10, 15, 0 stones, 1 stone, 3 stones, 5 stones.051015cm0 stones

    1 Hang a band with an empty bag. Read its length on a ruler. This is the original length: 8 cm.

  2. Rubber bands hang from a bar, beside a ruler marked in centimetres. In the first picture one band with 0 stones is 8 cm long. In the second picture a second band with 1 stone is 10 cm long. In the third picture bands with 0, 1, 3 and 5 stones are 8, 10, 13.4 and 16 cm long. Labels: cm, 0, 5, 10, 15, 0 stones, 1 stone, 3 stones, 5 stones.051015cm0 stones1 stone

    2 Put in one stone. The band gets longer, to 10 cm.

  3. Rubber bands hang from a bar, beside a ruler marked in centimetres. In the first picture one band with 0 stones is 8 cm long. In the second picture a second band with 1 stone is 10 cm long. In the third picture bands with 0, 1, 3 and 5 stones are 8, 10, 13.4 and 16 cm long. Labels: cm, 0, 5, 10, 15, 0 stones, 1 stone, 3 stones, 5 stones.051015cm0 stones1 stone3 stones5 stones

    3 Do it with more stones. Each time the band gets longer. With 5 stones it is 16 cm.

Write the results in a table, one row for each number of stones. Then work out the stretch each time.

See it three ways

As a picture

A table of one learner's rubber band with the columns stones, cm long and stretch. 0 stones: 8 cm long, stretch 0 cm. 1 stones: 10 cm long, stretch 2 cm. 2 stones: 11.8 cm long, stretch 3.8 cm. 3 stones: 13.4 cm long, stretch 5.4 cm. 4 stones: 14.8 cm long, stretch 6.8 cm. 5 stones: 16 cm long, stretch 8 cm.stonescm longstretch0801102211.83.8313.45.4414.86.85168

In words

These are one learner's results. More stones give more stretch. The band does not grow by the same amount each time. Your band will give different numbers.

In symbols

stretch = new length − original length. With 3 stones: 13.4 − 8 = 5.4 cm.

A graph shows the pattern better than a table. Put the number of stones across and the stretch up. Plot a point for each row.

Two graphs with the same scales. Stones run across from 0 to 5. Stretch in centimetres goes up, with 0, 2, 4, 6, 8, 10. The first graph, spring, is a straight line through 0, rising 2 cm for each stone to 10 cm. The second graph, rubber band, climbs to 8 cm at 5 stones and bends away from a dashed straight line. Labels: spring, rubber band, stones, stretch in cm.spring0123450246810stonesstretch in cmrubber band0123450246810stonesstretch in cm
A spring gives a straight line. The rubber band bends away from the dashed straight line.
Coil springs hang from a bar beside a ruler marked in centimetres. With 0 stones the spring is 10 cm long. With 2 stones it is 14 cm long. With 4 stones it is 18 cm long. Each stone adds the same 2 cm. Labels: cm, 0, 5, 10, 15, 20, 0 stones, 2 stones, 4 stones.05101520cm0 stones2 stones4 stones
A spring: 0 stones, 10 cm. 2 stones, 14 cm. 4 stones, 18 cm. Each stone adds the same 2 cm.

A steel spring stretches by equal amounts for equal loads. Here each stone adds 2 cm. This holds until the spring is stretched too far. A spring pulled too far stays long.

A rubber band is different. In these results the first stone adds 2 cm. The fifth adds only 1.2 cm. Your band may bend another way. The graph is not a straight line, so we say it bends.

Try it

Stretch a rubber band with stones

You need: a rubber band, a nail or a pencil to hang it from, held firm between two piles of books, a small bag with string, and 5 stones of the same size, a ruler, or a strip of card marked in centimetres, paper and a pencil.

Be safe: Keep your face away from the band. Stones can hurt feet, so work over a table or a soft cloth. Stop if the band looks thin.

  1. Hang the band from the pencil. Hang the empty bag from the band.
  2. Hold the ruler beside it with 0 at the top of the band. Read the length. This is the original length.
  3. Put in one stone. Read the length again and write it down.
  4. Add one stone at a time up to five. Read the length each time.
  5. Work out the stretch for each row. Plot stones across and stretch up.

What you will see: The band gets longer with every stone, so the points climb. Join them with a smooth line. Look at it. Is it a straight line or does it bend? The dashed line is a straight line for comparison.

If you cannot try it, this is what happens.
A graph of one learner's rubber band. Stones run across from 0 to 5. Stretch in centimetres goes up, with 0, 2, 4, 6, 8, 10. The points rise to 8 cm at 5 stones. A dashed straight line goes from 0 to the last point, and the points bend above it. Labels: stones, stretch in cm.0123450246810stonesstretch in cm

A wrong idea many people have

Twice the load always makes twice the stretch.

Why it feels right: A spring does behave like this, so it is tempting to think every stretchy thing does.

The test that breaks it: Look at the band results. 2 stones stretch it 3.8 cm. Twice the stretch would be 7.6 cm. But 4 stones stretch it only 6.8 cm.

What is true: A spring stretches by equal amounts for equal loads. A rubber band does not quite. Its graph bends, so measure before you trust a pattern.

Key words

original length
how long a band or spring is with no stones, only the empty bag.
stretch
how much longer it gets: new length minus original length.
load
the weight hanging on a band or spring.

Back to your guess

The answer is B: It stretches more, but not always in an even way.

More stones give more stretch, but a rubber band does not stretch quite evenly. The best way to see the pattern is to measure and plot it.

Check yourself

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

  1. A band is 8 cm long with no stones. With 3 stones it is 13.4 cm long. What is the stretch?

    Tap your answer.

    1. Not this one. That is the new length. The stretch is how much longer it got: take away the original length. Go to S3.7.5. Try another.

    2. Not this one. You added the two lengths. Take the original length away from the new length. Go to S3.7.5. Try another.

    3. Yes, that is right. Stretch = new length − original length = 13.4 − 8 = 5.4 cm.

    See the answer

    5.4 cm

    Stretch = new length − original length = 13.4 − 8 = 5.4 cm.

    • If you chose A: That is the new length. The stretch is how much longer it got: take away the original length. Go to S3.7.5.
    • If you chose B: You added the two lengths. Take the original length away from the new length. Go to S3.7.5.

  2. Look at the graph of the spring. How far does it stretch with 4 stones?

    A graph of a spring. Stones run across from 0 to 5. Stretch in centimetres goes up, with 0, 2, 4, 6, 8, 10. The points lie on a straight line from 0, rising 2 cm for each stone. Labels: stones, stretch in cm.0123450246810stonesstretch in cm
    Tap your answer.

    1. Yes, that is right. Go up from 4 stones to the line, then across. The stretch is 8 cm. Each stone adds 2 cm.

    2. Not this one. You read the number of stones across. Go up from 4 on the stones scale to the line, then read the stretch. Go to S3.7.5. Try another.

    3. Not this one. That is the stretch for 3 stones. Find 4 on the bottom scale. Go to S3.7.5. Try another.

    See the answer

    8 cm

    Go up from 4 stones to the line, then across. The stretch is 8 cm. Each stone adds 2 cm.

    • If you chose B: You read the number of stones across. Go up from 4 on the stones scale to the line, then read the stretch. Go to S3.7.5.
    • If you chose C: That is the stretch for 3 stones. Find 4 on the bottom scale. Go to S3.7.5.

  3. A spring stretches 2 cm for each stone. How far will it stretch with 6 stones? Assume it is not overstretched.

    Tap your answer.

    1. Not this one. You added the stones and the stretch for each stone. A spring adds the same stretch for every stone, so multiply. Go to S3.7.5. Try another.

    2. Yes, that is right. A spring stretches by equal amounts for equal loads. 6 × 2 = 12 cm.

    3. Not this one. You divided. Each stone adds 2 cm, so 6 stones add 6 lots of 2 cm. That is a multiplication. Go to S3.7.5. Try another.

    See the answer

    12 cm

    A spring stretches by equal amounts for equal loads. 6 × 2 = 12 cm.

    • If you chose A: You added the stones and the stretch for each stone. A spring adds the same stretch for every stone, so multiply. Go to S3.7.5.
    • If you chose C: You divided. Each stone adds 2 cm, so 6 stones add 6 lots of 2 cm. That is a multiplication. Go to S3.7.5.

  4. Look at the rubber band results in the table. Which sentence describes them best?

    A table of one learner's rubber band with the columns stones, cm long and stretch. 0 stones: 8 cm long, stretch 0 cm. 1 stones: 10 cm long, stretch 2 cm. 2 stones: 11.8 cm long, stretch 3.8 cm. 3 stones: 13.4 cm long, stretch 5.4 cm. 4 stones: 14.8 cm long, stretch 6.8 cm. 5 stones: 16 cm long, stretch 8 cm.stonescm longstretch0801102211.83.8313.45.4414.86.85168
    Tap your answer.

    1. Not this one. That is true for a spring. In this table the extra stretch for each stone gets smaller. Look at the stretch column. Go to S3.7.5. Try another.

    2. Not this one. Read down the stretch column. It gets bigger, not smaller. Go to S2.5.2. Try another.

    3. Yes, that is right. The stretch grows from 0 to 8 cm, so more stones give more stretch. The steps are 2, 1.8, 1.6, 1.4, 1.2 cm. They get smaller, so each stone adds a little less.

    See the answer

    More stones give more stretch, but each stone adds a little less.

    The stretch grows from 0 to 8 cm, so more stones give more stretch. The steps are 2, 1.8, 1.6, 1.4, 1.2 cm. They get smaller, so each stone adds a little less.

    • If you chose A: That is true for a spring. In this table the extra stretch for each stone gets smaller. Look at the stretch column. Go to S3.7.5.
    • If you chose B: Read down the stretch column. It gets bigger, not smaller. Go to S2.5.2.

  5. From an earlier chapter

    Each stone has a mass of 0.1 kg. About what does one stone weigh on Earth?

    Tap your answer.

    1. Yes, that is right. On Earth each kilogram weighs about 10 N. 0.1 × 10 = 1 N.

    2. Not this one. That is the mass in kilograms, not the weight. Each kilogram weighs about 10 N. Go to S3.7.4. Try another.

    3. Not this one. That would be a mass of 1 kg. Multiply 0.1 by 10. Go to S3.7.4. Try another.

    See the answer

    1 N

    On Earth each kilogram weighs about 10 N. 0.1 × 10 = 1 N.

    • If you chose B: That is the mass in kilograms, not the weight. Each kilogram weighs about 10 N. Go to S3.7.4.
    • If you chose C: That would be a mass of 1 kg. Multiply 0.1 by 10. Go to S3.7.4.

  6. You stretch a spring much too far and then take the load off. What happens?

    Tap your answer.

    1. Not this one. That is true for a spring that is not overstretched. Too much load changes its shape for good. Go to S3.7.5. Try another.

    2. Yes, that is right. A spring only stretches evenly and springs back if it is not overstretched. Too much load changes it for good.

    3. Not this one. A spring does not shrink below its first length. An overstretched one stays longer. Go to S3.7.5. Try another.

    See the answer

    It stays longer than before.

    A spring only stretches evenly and springs back if it is not overstretched. Too much load changes it for good.

    • If you chose A: That is true for a spring that is not overstretched. Too much load changes its shape for good. Go to S3.7.5.
    • If you chose C: A spring does not shrink below its first length. An overstretched one stays longer. Go to S3.7.5.

Keep it

Copy this into your exercise book.

Stretch is new length minus original length. A spring stretches by equal amounts for equal loads, so its graph is straight. A rubber band bends. Measure and plot to see the pattern.

Draw: Axes: stones across, stretch up. A straight line for a spring and a bending line for a band.

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

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.

S3.7.7 Chapter 7

Pressure

Why does a sharp knife cut, when a blunt one only squashes?

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

Press the flat end of a pencil gently into your palm. Then press the sharp tip with the same push. The tip hurts more. The push is the same, but the feeling is not.

The area is how much surface the force touches. We measure it in square centimetres, cm². A tip touches a tiny area. A flat end touches a bigger one.

Pressure tells you how much force pushes on each square centimetre. Look at 10 N pushing down on a flat patch.

Two patches of squares, each square 1 cm². Over the left patch of 5 squares an arrow pushes down, labelled 10 N. Under it are the labels 5 cm² and 2 N/cm². Over the right patch of 1 square another arrow is labelled 10 N, with the labels 1 cm² and 10 N/cm². Labels: 10 N, 5 cm², 2 N/cm², 1 cm², 10 N/cm².10 N10 N5 cm²1 cm²2 N/cm²10 N/cm²
The same 10 N. On 5 squares each square takes 2 N. On 1 square it takes all 10 N.

Share the force out over the squares. 10 N over 5 squares is 2 N on each. So pressure = force ÷ area. We read N/cm² as "newtons for each square centimetre".

Draw it first

Draw one block on a big face and a small face

  1. A block lies flat on the ground, with an arrow pushing down on it labelled 24 N. Under it are the labels 12 cm² and 2 N/cm². In the second picture the same block stands on its end beside it, with an arrow labelled 24 N and the label 3 cm². In the third picture the label 8 N/cm² is added under the block that stands on its end. Labels: 24 N, 12 cm², 2 N/cm², 3 cm², 8 N/cm².24 N12 cm²2 N/cm²

    1 Draw a light block lying flat. Press down on it with 24 N. The push is on 12 cm². Pressure = 24 ÷ 12 = 2 N/cm².

  2. A block lies flat on the ground, with an arrow pushing down on it labelled 24 N. Under it are the labels 12 cm² and 2 N/cm². In the second picture the same block stands on its end beside it, with an arrow labelled 24 N and the label 3 cm². In the third picture the label 8 N/cm² is added under the block that stands on its end. Labels: 24 N, 12 cm², 2 N/cm², 3 cm², 8 N/cm².24 N12 cm²2 N/cm²24 N3 cm²

    2 Stand the same block on its end and press down with the same 24 N. Now the push is on only 3 cm².

  3. A block lies flat on the ground, with an arrow pushing down on it labelled 24 N. Under it are the labels 12 cm² and 2 N/cm². In the second picture the same block stands on its end beside it, with an arrow labelled 24 N and the label 3 cm². In the third picture the label 8 N/cm² is added under the block that stands on its end. Labels: 24 N, 12 cm², 2 N/cm², 3 cm², 8 N/cm².24 N12 cm²2 N/cm²24 N3 cm²8 N/cm²

    3 Pressure = 24 ÷ 3 = 8 N/cm². The same force on a smaller area gives more pressure.

Scientists often give pressure in N/m², which is called the pascal, Pa. We stay with N/cm² here, because the sums are smaller.

See it three ways

As a picture

A table with the columns area, force and pressure. The block lying flat: 12 cm², 24 N, 2 N/cm². The block standing on its end: 3 cm², 24 N, 8 N/cm².areaforcepressure12 cm²24 N2 N/cm²3 cm²24 N8 N/cm²

In words

The force stays the same. The area gets smaller, so the pressure gets bigger. A small area means a big pressure.

In symbols

pressure = force ÷ area. 24 ÷ 12 = 2 N/cm². 24 ÷ 3 = 8 N/cm².

A person labelled Joseph with the label mass 40 kg beside him. Two footprints are drawn, with the label 100 cm² each. Labels: Joseph, mass 40 kg, 100 cm² each.Josephmass 40 kg100 cm² each
The start of the next example. Joseph stands on two feet, then on one.

Worked example

Joseph has a mass of 40 kg. Each of his soles touches the ground over 100 cm². What pressure does he put on the ground on two feet, and on one foot?

  1. Pressure = force ÷ area. His weight is the force.
  2. Weight = 40 × 10 = 400 N.
  3. Both soles: 2 × 100 = 200 cm².
  4. Pressure on two feet = 400 ÷ 200 = 2 N/cm².
  5. On one foot the area is only 100 cm².
  6. Pressure on one foot = 400 ÷ 100 = 4 N/cm².
  7. The pressure doubles when the area halves.

Answer: 2 N/cm² on two feet, 4 N/cm² on one foot

Now the camel. A camel weighs about 6000 N. Its four wide feet touch the sand over about 2000 cm². The pressure is 6000 ÷ 2000 = 3 N/cm². That is small, so the camel does not sink far.

A bar chart called pressure (N/cm²). The bar for wide feet reaches 3. The bar for hooves reaches 15. The scale goes from 0 to 16 in steps of 4. Labels: pressure (N/cm²), wide feet, hooves, 0, 4, 8, 12, 16.0481216wide feethoovespressure (N/cm²)
The same camel on wide feet puts 3 N/cm² on the sand. On small hooves of 400 cm² in all it would put 15 N/cm², and it would sink.

A knife works the other way. Push a knife with 20 N. A blunt edge touches 4 cm², so the pressure is 5 N/cm². A sharp edge may touch only 0.2 cm², so the pressure is 100 N/cm². That is much bigger, and it cuts.

A table for a knife pushed with 20 N, with the columns edge, area and pressure. Blunt edge: 4 cm², 5 N/cm². Sharp edge: 0.2 cm², 100 N/cm².edgeareapressureblunt4 cm²5 N/cm²sharp0.2 cm²100 N/cm²
The same 20 N push on a sharp edge gives 20 times the pressure.

Try it

Make a box press into sand

You need: a tray or a wide bowl of dry sand or fine soil, a shoe box with the lid taped shut and stones inside to make it heavy, a ruler or a stick, and paper.

Be safe: The box is heavy. Lower it slowly and keep it off your feet. Keep sand away from your eyes and mouth.

  1. Smooth the sand flat with your hand. Lay the box on its widest face. Count five seconds.
  2. Lift the box straight up. Measure how deep the dent is with the ruler.
  3. Smooth the sand flat again.
  4. Stand the box on its narrowest end. Count five seconds, then lift it.
  5. Measure the new dent. Compare the two. The box is the same, so its weight is the same.

What you will see: The dent is deeper when the box stands on its narrow end. The weight is the same. The area is smaller, so the pressure is bigger. Our dents were 2 mm and 8 mm. Yours will differ.

If you cannot try it, this is what happens.
A table with the heads box on its and dent in mm. wide face: 2. narrow end: 8.box on itsdent in mmwide face2narrow end8

A wrong idea many people have

A bigger force always means a bigger pressure.

Why it feels right: In daily talk, people use "pressure" and "push" to mean the same thing.

The test that breaks it: Joseph on one foot puts 4 N/cm² on the ground. The camel puts 3 N/cm². The camel's force is 15 times bigger, but its pressure is smaller.

What is true: Pressure is force divided by area. A big force spread over a big area can give a small pressure.

Key words

area
how much surface a force touches. We measure it in cm².
pressure
the force on each unit of area, such as each square centimetre: force ÷ area.
pascal
the unit of pressure in N/m². We write Pa.

Back to your guess

The answer is C: The sharp edge is so thin that the same push is on a much smaller area.

The push can be the same. A sharp edge touches a tiny area, so the force is squeezed into a very small space. That makes a very big pressure.

Check yourself

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

  1. A force of 60 N pushes on an area of 20 cm². What is the pressure?

    See the answer

    3 N/cm²

    Pressure = force ÷ area = 60 ÷ 20 = 3 N/cm².

  2. A knife is pushed with 20 N. Its edge touches the food over 0.5 cm². What is the pressure?

    Tap your answer.

    1. Yes, that is right. Pressure = force ÷ area = 20 ÷ 0.5 = 40 N/cm². A small area gives a big pressure.

    2. Not this one. You multiplied the force by the area. Pressure is the force shared out over the area, so divide. Go to S3.7.7. Try another.

    3. Not this one. You divided the area by the force, upside down. Put the force first: force ÷ area. Go to S3.7.7. Try another.

    See the answer

    40 N/cm²

    Pressure = force ÷ area = 20 ÷ 0.5 = 40 N/cm². A small area gives a big pressure.

    • If you chose B: You multiplied the force by the area. Pressure is the force shared out over the area, so divide. Go to S3.7.7.
    • If you chose C: You divided the area by the force, upside down. Put the force first: force ÷ area. Go to S3.7.7.

  3. Ravi has a mass of 50 kg. He stands on two feet that touch the ground over 250 cm² in all. What pressure does he put on the ground?

    Tap your answer.

    1. Not this one. You divided the mass in kilograms. Pressure needs a force in newtons, so find the weight first: kilograms × 10. Go to S3.7.4. Try another.

    2. Yes, that is right. His weight is 50 × 10 = 500 N. Pressure = 500 ÷ 250 = 2 N/cm².

    3. Not this one. That is his weight in newtons. You still have to divide it by the area to get the pressure. Go to S3.7.7. Try another.

    See the answer

    2 N/cm²

    His weight is 50 × 10 = 500 N. Pressure = 500 ÷ 250 = 2 N/cm².

    • If you chose A: You divided the mass in kilograms. Pressure needs a force in newtons, so find the weight first: kilograms × 10. Go to S3.7.4.
    • If you chose C: That is his weight in newtons. You still have to divide it by the area to get the pressure. Go to S3.7.7.

  4. Two knives are pushed with the same force. One is sharp and one is blunt. Why does the sharp knife cut better?

    Tap your answer.

    1. Not this one. The force is the same here. What differs is the area the edge touches. Go to S3.7.7. Try another.

    2. Not this one. The weight is not the reason. A thin edge puts the same force on a tiny area. Go to S3.7.4. Try another.

    3. Yes, that is right. Pressure = force ÷ area. The same force on a smaller area gives a bigger pressure.

    See the answer

    The sharp edge touches a much smaller area, so the pressure is much bigger.

    Pressure = force ÷ area. The same force on a smaller area gives a bigger pressure.

    • If you chose A: The force is the same here. What differs is the area the edge touches. Go to S3.7.7.
    • If you chose B: The weight is not the reason. A thin edge puts the same force on a tiny area. Go to S3.7.4.

  5. A camel walks on soft sand and does not sink far. Why?

    Tap your answer.

    1. Yes, that is right. Pressure = force ÷ area. The camel is heavy. Its wide feet give a big area, so the pressure on the sand is small.

    2. Not this one. Small feet would put the weight on a small area and sink deep. A camel has wide feet. Go to S3.7.7. Try another.

    3. Not this one. A camel is heavy. It is the wide feet that matter: the same weight on a bigger area gives a smaller pressure. Go to S3.7.7. Try another.

    See the answer

    Its wide feet spread its weight over a big area, so the pressure is small.

    Pressure = force ÷ area. The camel is heavy. Its wide feet give a big area, so the pressure on the sand is small.

    • If you chose B: Small feet would put the weight on a small area and sink deep. A camel has wide feet. Go to S3.7.7.
    • If you chose C: A camel is heavy. It is the wide feet that matter: the same weight on a bigger area gives a smaller pressure. Go to S3.7.7.

  6. Amina has a mass of 60 kg. Her feet touch the ground over 300 cm² in all. Kofi has a mass of 30 kg. His feet touch the ground over 60 cm² in all. Who puts the bigger pressure on the ground?

    Tap your answer.

    1. Not this one. A bigger force does not always mean a bigger pressure. You must divide the weight by the area of the feet. Go to S3.7.7. Try another.

    2. Yes, that is right. Kofi weighs 30 × 10 = 300 N, so his pressure is 300 ÷ 60 = 5 N/cm². Amina weighs 600 N, so her pressure is 600 ÷ 300 = 2 N/cm².

    3. Not this one. Wider feet spread the weight over more area, which makes the pressure smaller, not bigger. Go to S3.7.7. Try another.

    See the answer

    Kofi. He puts 5 N/cm² on the ground, and Amina puts 2 N/cm².

    Kofi weighs 30 × 10 = 300 N, so his pressure is 300 ÷ 60 = 5 N/cm². Amina weighs 600 N, so her pressure is 600 ÷ 300 = 2 N/cm².

    • If you chose A: A bigger force does not always mean a bigger pressure. You must divide the weight by the area of the feet. Go to S3.7.7.
    • If you chose C: Wider feet spread the weight over more area, which makes the pressure smaller, not bigger. Go to S3.7.7.

  7. From an earlier chapter

    Review: a skater glides 30 m in 6 s. What is her speed?

    Tap your answer.

    1. Not this one. You added the two numbers. Speed is distance divided by time. Go to S3.7.1. Try another.

    2. Not this one. You divided time by distance. Speed is distance divided by time. Go to S3.7.1. Try another.

    3. Yes, that is right. Speed = distance ÷ time = 30 ÷ 6 = 5 m/s.

    See the answer

    5 m/s

    Speed = distance ÷ time = 30 ÷ 6 = 5 m/s.

    • If you chose A: You added the two numbers. Speed is distance divided by time. Go to S3.7.1.
    • If you chose B: You divided time by distance. Speed is distance divided by time. Go to S3.7.1.

Keep it

Copy this into your exercise book.

Pressure = force ÷ area, in N/cm². The same force on a smaller area gives a bigger pressure. Sharp edges cut. Wide feet spread weight out.

Draw: A block with 24 N on 12 cm², and the same block on 3 cm². Write 2 N/cm² and 8 N/cm².

S3.7.8 Chapter 8

Pressure in water and air

Why does water shoot out of a bottle, and why does it go farthest from the lowest hole?

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

Make a hole in the side of a bottle full of water. A jet of water shoots out. Water is pushing on the sides of the bottle, and it pushes out through the hole.

Water pushes in every direction: down, up and sideways. This push is water pressure. The depth is how far you are below the surface.

The deeper you go, the more water is above you. So the pressure grows with depth.

A tank of water drawn with dots, with the label surface at the top. Three arrows push sideways out of the wall, at depths 5, 10, 15 cm, which are labelled 5 cm, 10 cm, 15 cm. The arrow at 5 cm is short and labelled small. The arrow at 10 cm is longer and labelled bigger. The arrow at 15 cm is longest and labelled biggest. Labels: surface, 5 cm, 10 cm, 15 cm, small, bigger, biggest.surface5 cm10 cm15 cmsmallbiggerbiggest
The water pushes out of the wall. The deeper the point, the longer the arrow, because the pressure is bigger.

Draw it first

Draw a bottle with jets

  1. A bottle of water stands on a tall block. A line marks the water surface, with the label water surface. In the first picture one hole near the top, labelled high, sends a short jet. In the second picture a middle hole, labelled mid, sends a longer jet. In the third picture a low hole, labelled low, sends the longest jet. Labels: water surface, high, mid, low.water surfacehigh

    1 Draw a bottle with water 20 cm deep, on a tall block. Make a hole 4 cm below the surface. A short jet leaves it.

  2. A bottle of water stands on a tall block. A line marks the water surface, with the label water surface. In the first picture one hole near the top, labelled high, sends a short jet. In the second picture a middle hole, labelled mid, sends a longer jet. In the third picture a low hole, labelled low, sends the longest jet. Labels: water surface, high, mid, low.water surfacehighmid

    2 Add a hole 10 cm below the surface. Its jet leaves faster and lands farther out.

  3. A bottle of water stands on a tall block. A line marks the water surface, with the label water surface. In the first picture one hole near the top, labelled high, sends a short jet. In the second picture a middle hole, labelled mid, sends a longer jet. In the third picture a low hole, labelled low, sends the longest jet. Labels: water surface, high, mid, low.water surfacehighmidlow

    3 Add a hole 16 cm below the surface. Its jet lands farthest of all.

The deepest hole has the biggest pressure behind it, so its water leaves fastest. The bottle must stand high up. Then the water has a long way to fall, and a faster jet lands farther out.

If the bottle stood on the ground, the lowest jet would have almost no height to fall. It would land close, even though its pressure is the biggest. So stand the bottle on something high.

See it three ways

As a picture

A table with the columns hole, depth and lands. Hole high: depth 4 cm, lands 22 cm. Hole mid: depth 10 cm, lands 32 cm. Hole low: depth 16 cm, lands 38 cm.holedepthlandshigh4 cm22 cmmid10 cm32 cmlow16 cm38 cm

In words

A deeper hole has a bigger water pressure. The water leaves faster and lands farther out, as long as the bottle stands high.

In symbols

Depth 4 cm: lands about 22 cm out. Depth 16 cm: lands about 38 cm out.

The push of the air is air pressure. The air above us is very deep, so it pushes on everything. We do not feel it, because our bodies push out from inside just as hard.

A cup of water with a straw. Three arrows push down on the water outside the straw, labelled air pushes. The water stands higher inside the straw, where the label says less air pressure. Labels: air pushes, less air pressure.air pushesless air pressure
Air pushes down on the water in the cup. When you drink, you lower the air pressure in the straw. The air outside pushes the water up.

When you drink through a straw, you lower the air pressure in your mouth and in the straw. The air pressing on the drink outside is now stronger. It pushes the drink up the straw. You do not pull the drink up.

Water also pushes up on anything in it. The water below a thing is deeper. It pushes up harder than the water or air above pushes down. The difference is the upthrust.

A boat, drawn as a box, sits half in water that is shown with dots. An arrow starts in the water under the boat and points up at it, labelled upthrust 5 N. An arrow of the same length starts in the middle of the boat and points down to its bottom, labelled weight 5 N. Labels: upthrust 5 N, weight 5 N.weight 5 Nupthrust 5 N
A boat with a mass of 0.5 kg weighs 5 N. It floats when the upthrust is also 5 N. The two forces are balanced.

A thing floats when the upthrust equals its weight. It settles into the water until the water pushes up as hard as gravity pulls down. If the water can never push up that hard, the thing sinks.

A stone, drawn as a plain box, under water that is shown with dots. A long arrow points down from the middle of the stone, labelled weight 6 N. A short arrow starts under the stone and points up at it, labelled upthrust 2 N. Labels: weight 6 N, upthrust 2 N.weight 6 Nupthrust 2 N
This stone weighs 6 N, but the water pushes up with only 2 N. The arrows are not equal, so the stone sinks. Arrows are drawn to the same scale as the boat.

Try it

Make a bottle with holes

You need: a tall plastic bottle, filled with water, a nail, and an adult to push it through the plastic, tape, a stool or box about 30 cm high, a string or ruler, and stones to mark where the water lands.

Be safe: An adult must push the nail through the plastic. Never heat the nail. Push away from your hand.

  1. Ask an adult to push the nail through the plastic. Make three holes in a line down one side, well spaced. Put one long strip of tape over all three holes.
  2. Stand the bottle on the stool near the edge, outside or over a sink. Face the holes out. Fill the bottle.
  3. Pull the strip off in one go. Watch the jets.
  4. Put a stone where each jet lands. Measure each distance from the bottle with the string.
  5. Refill the bottle and stand it on the ground instead. Where does the lowest jet land now?

What you will see: The jet from the lowest hole leaves fastest and lands farthest. The top jet lands closest. Our marks were 22, 32, 38 cm, from top to bottom. Real jets land a little closer than a perfect jet would. They land closer still as the water runs down. Yours will differ. On the ground the lowest jet has little height to fall, so it no longer lands the farthest.

If you cannot try it, this is what happens.
A table of one learner's marks with the columns hole, depth and lands. Hole high: depth 4 cm, lands 22 cm. Hole mid: depth 10 cm, lands 32 cm. Hole low: depth 16 cm, lands 38 cm.holedepthlandshigh4 cm22 cmmid10 cm32 cmlow16 cm38 cm

A wrong idea many people have

When you drink through a straw, you pull the drink up with your mouth.

Why it feels right: It feels as if you are pulling, because your cheeks work to drink.

The test that breaks it: Ask an adult to snip a small hole near the top of a straw. Now try to drink with the straw in a cup. It is much harder, or does not work at all, because air comes in at the hole.

What is true: Your mouth lowers the air pressure in the straw. The air outside is at a higher pressure, and it pushes the drink up.

Key words

water pressure
the push of water in every direction. It grows with depth.
depth
how far a point is below the surface.
air pressure
the push of the air on everything it touches.
upthrust
the push up that water gives a thing in it.

Back to your guess

The answer is A: Deeper water has more water above it pushing down, so the pressure is bigger.

The deeper the water, the more water is above it. That makes the pressure bigger. A bigger pressure pushes the water out faster.

Check yourself

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

  1. A bottle of water stands on a tall block. It has three holes, 4, 10, 16 cm below the surface. Which hole's jet lands farthest from the bottle?

    Tap your answer.

    1. Not this one. The top hole has the least water above it, so the smallest pressure. Its jet lands closest. Go to S3.7.8. Try another.

    2. Yes, that is right. Water pressure grows with depth. The lowest hole has the biggest pressure, so its jet leaves fastest and lands farthest.

    3. Not this one. The middle hole is deeper than the top one, but not as deep as the lowest. Look at which jet goes farthest. Go to S3.7.8. Try another.

    See the answer

    The hole 16 cm down

    Water pressure grows with depth. The lowest hole has the biggest pressure, so its jet leaves fastest and lands farthest.

    • If you chose A: The top hole has the least water above it, so the smallest pressure. Its jet lands closest. Go to S3.7.8.
    • If you chose C: The middle hole is deeper than the top one, but not as deep as the lowest. Look at which jet goes farthest. Go to S3.7.8.

  2. Kofi swims down to the bottom of a deep pool. What does the water do to his body?

    Tap your answer.

    1. Not this one. Water pressure pushes in every direction, not just down. It pushes on his sides and from below too. Go to S3.7.8. Try another.

    2. Not this one. The deeper he goes, the more water is above him. That makes the pressure bigger, not the same. Go to S3.7.8. Try another.

    3. Not this one. It is the water above him that makes the pressure. More water above means more pressure, so it grows with depth. Go to S3.7.8. Try another.

    4. Yes, that is right. Water pushes in every direction. The deeper he goes, the more water is above him, so the pressure grows.

    See the answer

    It pushes on him from every side, and it pushes harder the deeper he goes.

    Water pushes in every direction. The deeper he goes, the more water is above him, so the pressure grows.

    • If you chose A: Water pressure pushes in every direction, not just down. It pushes on his sides and from below too. Go to S3.7.8.
    • If you chose B: The deeper he goes, the more water is above him. That makes the pressure bigger, not the same. Go to S3.7.8.
    • If you chose C: It is the water above him that makes the pressure. More water above means more pressure, so it grows with depth. Go to S3.7.8.

  3. You drink through a straw. What pushes the drink up the straw?

    Tap your answer.

    1. Not this one. Your mouth only lowers the pressure inside the straw. Something else does the pushing. Go to S3.7.8. Try another.

    2. Not this one. A straw is only a tube. It does not squeeze. The push comes from the air. Go to S3.7.8. Try another.

    3. Yes, that is right. You lower the air pressure in the straw. The air outside is at a higher pressure, so it pushes the drink up.

    See the answer

    The air pressing on the drink outside the straw.

    You lower the air pressure in the straw. The air outside is at a higher pressure, so it pushes the drink up.

    • If you chose A: Your mouth only lowers the pressure inside the straw. Something else does the pushing. Go to S3.7.8.
    • If you chose B: A straw is only a tube. It does not squeeze. The push comes from the air. Go to S3.7.8.

  4. A toy boat has a mass of 2 kg and floats at rest. How big is the upthrust on it?

    Tap your answer.

    1. Not this one. You used the mass in kilograms as if it were newtons. First find the weight: each kilogram weighs about 10 N. Go to S3.7.4. Try another.

    2. Not this one. A floating boat still has gravity pulling it down. The water pushes up to hold it, so the upthrust is not zero. Go to S3.7.8. Try another.

    3. Not this one. The upthrust does not need to be bigger. When it equals the weight, the forces are balanced and the boat stays at rest. Go to S3.7.3. Try another.

    4. Yes, that is right. The weight is 2 × 10 = 20 N. The boat floats at rest, so the forces are balanced. The upthrust is also 20 N.

    See the answer

    20 N

    The weight is 2 × 10 = 20 N. The boat floats at rest, so the forces are balanced. The upthrust is also 20 N.

    • If you chose A: You used the mass in kilograms as if it were newtons. First find the weight: each kilogram weighs about 10 N. Go to S3.7.4.
    • If you chose B: A floating boat still has gravity pulling it down. The water pushes up to hold it, so the upthrust is not zero. Go to S3.7.8.
    • If you chose C: The upthrust does not need to be bigger. When it equals the weight, the forces are balanced and the boat stays at rest. Go to S3.7.3.

  5. A stone weighs 30 N. The most the water can push up on it is 12 N. What is the overall force on the stone as you let it go in the water?

    See the answer

    18 N downwards. It sinks.

    The forces are opposite, so take one from the other. 30 − 12 = 18 N. The weight is bigger, so the overall force points down and the stone sinks.

  6. In the bottle test, why must the bottle stand high up?

    Tap your answer.

    1. Yes, that is right. On the ground the lowest jet has hardly any height to fall, so it lands close. A tall stand lets the faster jet reach farther.

    2. Not this one. The pressure depends on depth, not on how high the bottle stands. The height gives the water room to fall and spread out. Go to S3.7.8. Try another.

    3. Not this one. The holes stay the same size. The height is about how far the water falls. Go to S3.7.8. Try another.

    See the answer

    The water then has a long way to fall, so a faster jet lands farther out.

    On the ground the lowest jet has hardly any height to fall, so it lands close. A tall stand lets the faster jet reach farther.

    • If you chose B: The pressure depends on depth, not on how high the bottle stands. The height gives the water room to fall and spread out. Go to S3.7.8.
    • If you chose C: The holes stay the same size. The height is about how far the water falls. Go to S3.7.8.

  7. From an earlier chapter

    Review: a force of 80 N pushes on an area of 20 cm². What is the pressure?

    Tap your answer.

    1. Not this one. You added the two numbers. Pressure is force divided by area. Go to S3.7.7. Try another.

    2. Yes, that is right. Pressure = force ÷ area = 80 ÷ 20 = 4 N/cm².

    3. Not this one. You divided area by force. Put the force first: force ÷ area. Go to S3.7.7. Try another.

    See the answer

    4 N/cm²

    Pressure = force ÷ area = 80 ÷ 20 = 4 N/cm².

    • If you chose A: You added the two numbers. Pressure is force divided by area. Go to S3.7.7.
    • If you chose C: You divided area by force. Put the force first: force ÷ area. Go to S3.7.7.

Keep it

Copy this into your exercise book.

Water pressure grows with depth and pushes in every direction. Air pressure pushes a drink up a straw. A thing floats when the upthrust equals its weight.

Draw: A bottle on a tall block with three holes. Draw the longest jet from the lowest hole.

Key words, A to Z

Every key word in this book, what it means, and the chapter that teaches it.

air pressure
the push of the air on everything it touches. S3.7.8
area
how much surface a force touches. We measure it in cm². S3.7.7
average speed
the total distance divided by the total time. S3.7.1
balanced
two forces that are equal and opposite. The overall force is zero. S3.7.3
depth
how far a point is below the surface. S3.7.8
distance
how far a thing goes, measured in metres. S3.7.1
distance and time graph
a graph with time across and distance from home up. S3.7.2
effort
the force you use to move a load. S3.7.6
kilogram
the unit of mass. We write kg. S3.7.4
lever
a stiff bar that turns about a pivot. S3.7.6
load
the weight hanging on a band or spring. S3.7.5
mass
how much stuff is in a thing. It is measured in kilograms. S3.7.4
metres per second
the unit of speed. We write m/s. S3.7.1
newton
the unit of force and of weight. We write N. S3.7.4
original length
how long a band or spring is with no stones, only the empty bag. S3.7.5
overall force
all the forces on a thing added up into one. S3.7.3
pascal
the unit of pressure in N/m². We write Pa. S3.7.7
pivot
the point a lever turns about. S3.7.6
pressure
the force on each unit of area, such as each square centimetre: force ÷ area. S3.7.7
speed
how far a thing goes in one second. S3.7.1
steeper
climbing more quickly. A steeper line means a faster speed. S3.7.2
still
not moving. The graph line is flat. S3.7.2
stretch
how much longer it gets: new length minus original length. S3.7.5
turning effect
force × distance from the pivot. S3.7.6
unbalanced
forces that are not equal. There is an overall force. S3.7.3
upthrust
the push up that water gives a thing in it. S3.7.8
water pressure
the push of water in every direction. It grows with depth. S3.7.8
weight
the pull of gravity on a thing. It is measured in newtons. S3.7.4