GCSE · Physics · Edexcel · Spec 1PH0

Weight equation W = mg

On the Moon you would weigh less — yet you would be made of exactly the same atoms. So weight and mass cannot be the same thing.

Physics · Weight

Near the Earth, every kilogram is pulled with about 10 newtons

the mass: 1/10. Mass 1 kg. Weight near the Earth's surface 10 N. Newtons for each kilogram (g) 10 N/kg

Mass1 kgWeight near the Earth's surface10 NNewtons for each kilogram (g)10 N/kg

Near the Earth's surface the gravitational field strength, g, is about 10 N/kg: each kilogram of mass is pulled down with about 10 N. Drag the bar to change the mass and watch the weight keep pace.

Watch out: Weight is a force, so it is measured in newtons (N), never in kilograms. Kilograms are for mass.

Mass versus weight

MassvsWeight

Start with the top row — it is the difference people most often get wrong.

Focus

Take the object to the Moon

Mass

Exactly the same

Weight

Less than on Earth

The insight

The object still contains the same number of atoms, so its mass cannot change. The Moon's gravitational field strength is lower than the Earth's, so each kilogram is pulled less and the weight goes down.

Take it into deep space, far from all planets and stars

Mass

Still exactly the same

Weight

Zero — it has no weight

What it actually is

Mass

The amount of material in the object

Weight

The gravitational force acting on the object

Unit

Mass

kilograms (kg)

Weight

newtons (N)

How you notice it

Mass

Not a force — it is the material that gets pulled on

Weight

It is the force the object presses down on a support with, and the force you need to hold it still or lift it

Physics · Rearranging

Running the equation backwards

A suitcase has a weight of 180 N near the Earth's surface, where g = 10 N/kg. What is its mass?

Known: W = 180 N and g = 10 N/kg. Unknown: the mass, m.Before you touch the numbers, decide which quantity you are finding. Here it is the mass.
Start from W = m × g.Always start from the equation you know, then rearrange it.
missing step

Which line is step 3?

Divide both sides by g: m = W ÷ gMultiply both sides by g: m = W × gDivide g by W: m = g ÷ W

Physics · Spot the slip

Find the line where this answer goes wrong

An apple has a mass of 250 g. Calculate its weight near the Earth's surface, where g = 10 N/kg.

A student's answer — which line goes wrong?

m = 250 g, g = 10 N/kg
W = m × g
W = 250 × 10
W = 2500 N

Physics · What do you think?

Where does weight actually change?

A person carries a 2 kg bag of shopping from the ground floor to the roof of a tall building. Later, an astronaut takes the same kind of bag to the Moon.

Which of these ideas is closest to what you think right now?

The bag weighs noticeably less on the roof, because gravity gets weaker the higher you go.On the Moon the bag has less mass, as well as less weight.Weight and mass are the same thing — the bag weighs 2 kg.The bag's weight only changes if the field it is in changes, and its mass never changes.

How sure are you?

I'm sureI think soI'm guessing

The bag weighs noticeably less on the roof, because gravity gets weaker the higher you go.

This is a common misconception

Half right, which is why it is so convincing. The Earth's gravitational field does get weaker further from the Earth — but near the surface, up to tens of kilometres above it, it is effectively constant. A tall building is nowhere near that high, so the bag still weighs about 20 N on the roof.

On the Moon the bag has less mass, as well as less weight.

This is a common misconception

The weight part is right: the Moon's gravitational field strength is lower, so the bag weighs less there. But the mass is the amount of material, and the bag still has the same number of atoms. It is still 2 kg.

Weight and mass are the same thing — the bag weighs 2 kg.

This is a common misconception

This is the one to shake off. 2 kg is the bag's mass. Its weight is a force, measured in newtons: near the Earth's surface W = 2 × 10 = 20 N.

The bag's weight only changes if the field it is in changes, and its mass never changes.

This matches the evidence

Exactly. W = m × g, and m is fixed. On the roof g is effectively the same as on the ground, so the weight hardly changes. On the Moon g is lower, so the weight falls — and the mass stays 2 kg throughout.

Mass goes wherever the object goes, unchanged. Weight follows the field: it changes on the Moon or in deep space, but not noticeably as you climb near the Earth's surface.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Your mass stays put. Your weight depends on where you are.

What you need to know

Mass is the amount of material in an object, in kilograms. It does not change when the object moves somewhere else.
Weight is the gravitational force on an object, in newtons. It depends on the gravitational field the object is in.
W = m × g links them: weight (N) = mass (kg) × gravitational field strength (N/kg).

The big picture

Mass is how much material an object contains, in kilograms, and it stays the same wherever the object goes. Weight is the gravitational force on that material, in newtons, and it depends on the field the object is in. The link is W = m × g, where g is the gravitational field strength in newtons per kilogram — about 10 N/kg near the Earth's surface. Rearrange it to find m = W ÷ g or g = W ÷ m, and always turn grams into kilograms first.

Key points

1Weight is the gravitational force on an object, measured in newtons (N).

2Mass is the amount of material in an object, measured in kilograms (kg), and it is the same everywhere.

3W = m × g, where g is the gravitational field strength in N/kg — the force on each kilogram.

4Near the Earth's surface g is about 10 N/kg, so every kilogram weighs about 10 N.

5Rearranged: m = W ÷ g and g = W ÷ m.

6Convert grams to kilograms (divide by 1000) before using the equation.

7Weight changes from place to place because the field changes: less on the Moon, zero in deep space. Near the Earth's surface it does not noticeably change with height.

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Worked example

Problem

The weight of a 400 g block is 4.0 N. Calculate the gravitational field strength where the block is.

⚠ Watch out

Giving a weight in kilograms. Kilograms measure mass; weight is a force, so its unit is the newton. A 60 kg person does not 'weigh 60 kg' in physics — near the Earth's surface their weight is 60 × 10 = 600 N.

🧠

Memory hook

g means 'newtons per kilogram'. Count the kilograms, give each one about 10 newtons, and you have the weight.

✓

Check yourself

Without looking back: what does a 5 kg bag weigh near the Earth's surface? On the Moon, what is its mass — and is its weight more, less or the same?

Flashcards

(13)

What is weight?

The gravitational force acting on an object.

What is mass?

The amount of material in an object, measured in kilograms (kg).

What is the unit of weight, and why?

The newton (N), because weight is a force.

What does gravitational field strength (g) mean?

The gravitational force on each kilogram of mass. Its unit is newtons per kilogram (N/kg).

About how big is g near the Earth's surface?

About 10 N/kg — so a 1 kg mass is pulled down with about 10 N.

Write the weight equation with its units.

W = m × g: weight in N, mass in kg, gravitational field strength in N/kg.

Rearranging: how do you find the mass, and how do you find g?

Mass: divide the weight by g. To find g: divide the weight by the mass.

A mass is given in grams. What must you do before using the weight equation?

Convert it to kilograms by dividing by 1000 (1 kg = 1000 g).

Why does an object's mass stay the same on the Moon?

It still contains the same number of atoms — the same amount of material.

Why does an object weigh less on the Moon?

The Moon's gravitational field strength is lower than the Earth's, and the mass is unchanged.

Far from all planets and stars, what happens to an object's weight and mass?

It has no weight, but it keeps all of its mass.

Does your weight change noticeably at the top of a tall building?

No. Near the Earth's surface (up to tens of kilometres up) the field is effectively constant.

Weight is the force you need to do what to an object?

To hold it still or lift it — it is also the force the object presses down on a support with.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Running the equation backwards

Find the line where this answer goes wrong

Where does weight actually change?

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