Chapter 4 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

S3.7.4 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

  • Explain the difference between mass in kilograms and weight in newtons
  • Explain why your weight would be less on the Moon

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.

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.