GCSE · Physics · Edexcel · Spec 1PH0

Weight and gravitational field strength relationship

Pick up your bag. That tug on your arm isn't how much stuff is inside — it's gravity pulling on that stuff. Physics keeps those two ideas apart.

Physics · Weight

Drag the mass. Watch the weight keep pace.

mass: 1/10. Mass 1 kg. Weight (g = 9.8 N/kg) 9.8 N. Weight (g = 10 N/kg) 10 N. Gravitational field strength, g about 9.8 N/kg (≈ 10) — the same at every mass

Mass1 kgWeight (g = 9.8 N/kg)9.8 NWeight (g = 10 N/kg)10 NGravitational field strength, gabout 9.8 N/kg (≈ 10) — the same at every mass

The bar is the object's mass, from 0 kg to 10 kg. The readouts show its weight near the Earth's surface: once with g = 9.8 N/kg, and once with the rounded value g = 10 N/kg that calculations often use. Notice which readout never moves.

Watch out: The bar is mass, in kilograms. The readouts are weight, in newtons. Same object — two different quantities, with two different units.

Your turn · Running it backwards

From weight back to mass

A sack of potatoes has a weight of 250 N on Earth. Taking g = 10 N/kg, what is its mass?

Write down what you know: W = 250 N, g = 10 N/kg. We want m.Units tell you what each number is: N is a force (the weight), N/kg is the field strength.
Start from the equation that links them: W = m × gOn the bar, each kilogram brought its newtons with it: weight was mass multiplied by g. This time you know the newtons, so you work backwards.
missing step

Which line is step 3?

Rearrange for mass: m = W × gRearrange for mass: m = W ÷ gRearrange for mass: m = g ÷ W

What do you really think?

A trip to the Moon

An astronaut packs a bag on Earth and takes it to the Moon. The gravitational field strength on the Moon is lower than on Earth. Nothing is added to or taken out of the bag.

When the bag arrives on the Moon, which of these is closest to what you think?

Its mass gets smaller too — less gravity means less mass.Its mass stays the same, but its weight gets smaller, because g is lower on the Moon.Nothing changes. It's the same bag, so it has the same weight everywhere.It weighs fewer kilograms on the Moon.

How sure are you?

I'm sureI think soI'm guessing

Its mass gets smaller too — less gravity means less mass.

This is a common misconception

Mass is how much stuff is in the bag, and nobody took anything out. The same stuff is there on the Moon, so the mass is the same. Gravity doesn't make the stuff; it pulls on the stuff.

Its mass stays the same, but its weight gets smaller, because g is lower on the Moon.

This matches the evidence

Spot on. Mass is the amount of stuff, so it doesn't change. Weight is W = m × g: same m, smaller g, so smaller W. Fewer newtons for each kilogram.

Nothing changes. It's the same bag, so it has the same weight everywhere.

This is a common misconception

The mass is the same everywhere — that part is right. But weight isn't a fixed label on the bag. It's the pull of the field the bag is in, and the Moon's field pulls each kilogram less strongly than the Earth's does.

It weighs fewer kilograms on the Moon.

This is a common misconception

Kilograms measure mass, and the mass hasn't changed. Weight is a force, so it's measured in newtons. What does get smaller on the Moon is the number of newtons.

Mass goes with the object: same kilograms anywhere. Weight goes with the place: it depends on g, so it's measured in newtons and it changes when g changes.

Lifting at a steady pace

Tap each arrow. The two arrows are drawn the same length on purpose.

Tap a force to see what it does.

Spot the slip

Where does this answer go wrong?

An apple has a mass of 400 g. Taking g = 10 N/kg, calculate its weight.

A student's answer — which line goes wrong?

m = 400 g, g = 10 N/kg
W = m × g
W = 400 × 10
W = 4000
Weight = 4000 N

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

W = m × g

Weight is the pull of a gravitational field on your mass — and g tells you how many newtons of pull each kilogram gets.

What you need to know

Weight is the gravitational force acting on an object in a gravitational field, so it is measured in newtons (N).
Mass is the amount of matter in an object, measured in kilograms (kg); it is the same wherever the object is.
Gravitational field strength, g, is the force per kilogram, in N/kg: about 9.8 N/kg near the Earth's surface, often rounded to 10 N/kg.
Weight = mass × gravitational field strength: W = m × g, with W in N, m in kg and g in N/kg.

The big picture

Mass is how much stuff an object is made of, measured in kilograms. Weight is the gravitational force on that stuff, so it is a force, measured in newtons. Gravitational field strength, g, links them: it is the force on each kilogram, in N/kg. Near the Earth's surface g is about 9.8 N/kg (10 N/kg for calculations), and W = m × g. Mass stays the same wherever an object goes, but its weight changes with g.

Key points

1Weight is a force, so it is measured in newtons (N); mass is measured in kilograms (kg).

2g is the force on each kilogram: about 9.8 N/kg near the Earth's surface, or 10 N/kg for calculations.

3W = m × g. For the same g, weight is directly proportional to mass — double the mass, double the weight.

4Rearranged, m = W ÷ g. Convert grams to kilograms before substituting.

5Mass stays the same everywhere; weight depends on g, so an object weighs less on the Moon, where g is lower.

6The force needed to lift an object steadily is equal in size to its weight.

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Worked example

Problem

A student has a mass of 60 kg. Using g = 9.8 N/kg, calculate the student's weight on Earth.

⚠ Watch out

Giving weight in kilograms. Kilograms are for mass; weight is a force, so it is always in newtons. If your answer to 'calculate the weight' ends in kg, go back and check.

🧠

Memory hook

Mass is what you've GOT, weight is what you GET. Your kilograms go everywhere with you; the newtons you get for them depend on the local exchange rate, g.

✓

Check yourself

A 7 kg bag of rice sits on Earth (g = 10 N/kg). What is its weight? Taken to the Moon, would its mass change? (Answer: 70 N. No — still 7 kg.)

Flashcards

(11)

What is weight?

The gravitational force acting on an object in a gravitational field.

What unit is weight measured in, and why?

Newtons (N), because weight is a force.

What unit is mass measured in?

Kilograms (kg).

What does g stand for, and what is its unit?

Gravitational field strength: the force per kilogram, in newtons per kilogram (N/kg).

What is g near the Earth's surface?

About 9.8 N/kg (9.81 N/kg), often rounded to 10 N/kg in calculations.

Write the equation linking weight, mass and g.

W = m × g (weight = mass × gravitational field strength).

In the same place, an object's mass is doubled. What happens to its weight?

It doubles: for a given g, weight is directly proportional to mass.

How do you find mass if you know weight and g?

Divide: m = W ÷ g, giving the mass in kg.

An object is moved to a place where g is lower. What happens to its mass and its weight?

Its mass stays the same; its weight gets smaller.

How big is the force needed to lift an object steadily?

Equal in size to the object's weight.

A mass is given in grams. What must you do before using W = m × g?

Convert it to kilograms (divide by 1000), because g is in N per kg.

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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From weight back to mass

A trip to the Moon

Where does this answer go wrong?

More Edexcel GCSE Physics topics