Curriculum

SQA National 5 Physics

1. Dynamics

0/22

2. Space

0/12

3. Electricity

0/16

4. Properties of Matter

0/11

5. Waves

0/8

6. Radiation

0/14

Text lesson

2.1.7 Calculating Weight across the Universe

2.1.7 Calculating Weight across the Universe: Use W = mg to calculate the weight of an object on different planets and moons, and explain why mass stays the same while weight changes.

Although everyday speech mixes the two ideas, physics treats them as different quantities.

Mass

The amount of matter in an object, measured in kilograms; it is the same everywhere in the universe.

Weight

The force of gravity acting on an object's mass, measured in newtons, so it depends on where the object is.

Gravitational field strength

The force exerted on each kilogram of mass, measured in newtons per kilogram (N/kg), written g.

Scale and unit

A balance compares masses in kg, while a newtonmeter measures weight in N because it responds to a force.

Quantity	Symbol	Unit	Changes with location?
Mass	m	kg	No
Weight	W	N	Yes
Gravitational field strength	g	N/kg	Yes

The weight of an object is found by multiplying its mass by the local gravitational field strength.

The Relationship W = mg

Equation

W = mg, where W is weight in newtons, m is mass in kilograms and g is field strength in N/kg.

Rearranged forms

m = W ÷ g finds mass from weight, and g = W ÷ m finds the field strength of a planet.

Direction

Weight acts downwards, towards the centre of the planet or moon that is attracting the object.

Proportionality

On any one planet, doubling the mass doubles the weight because g is fixed there.

A larger, denser body usually has a stronger gravitational field at its surface.

Earth

Has g = 9.8 N/kg, so every kilogram of mass weighs 9.8 N at the surface.

Moon

Has g = 1.6 N/kg, so objects weigh roughly one sixth of their Earth weight and astronauts bounce easily.

Mars

Has g = 3.7 N/kg, which is a little over a third of the value on Earth.

Jupiter

Has g = 23 N/kg, so a person there would feel more than twice as heavy as on Earth.

Body	g (N/kg)	Weight of a 1.0 kg mass (N)
Moon	1.6	1.6
Mars	3.7	3.7
Earth	9.8	9.8
Jupiter	23	23

Follow the same order each time to avoid losing marks.

Write down the known quantities and check that mass is in kilograms before doing anything else.

Choose the correct field strength for the planet named in the question, using the data sheet if needed.

Write the relationship W = mg (or its rearrangement) and substitute the numbers with units.

Calculate the result and give a unit of newtons for weight or kilograms for mass.

If the object moves to another planet, remember that mass is unchanged and only g needs replacing.

Question: A probe weighs 740 N on Mars where g = 3.7 N/kg. Calculate its mass and its weight on Earth (g = 9.8 N/kg).

Rearrange W = mg to give m = W ÷ g.
m = 740 ÷ 3.7 = 200 kg.
Mass does not change, so on Earth W = mg = 200 × 9.8 = 1960 N.

Answer: Mass = 200 kg and weight on Earth = 1960 N (about 2.0 × 10³ N).

2.1.7 – Key Points for the Exam

Weight: The force of gravity on an object, found from W = mg.
Mass: The quantity of matter in an object; independent of location.
Gravitational field strength: Force per unit mass, measured in N/kg.
Newton: The unit of force, used for weight.

Common Mistakes

Saying that an astronaut's mass is smaller on the Moon; only the weight is smaller.
Quoting weight in kilograms; weight is a force and must be given in newtons.
Using 9.8 for every planet instead of the g value for the body in the question.
Forgetting to convert grams to kilograms before substituting into W = mg.