Chapter 3 of 8

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

S3.7.3 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

  • Draw force arrows on an object and find the overall force
  • Explain why balanced forces do not change speed or direction

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.

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

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