1.4.3 Mass and Weight

1.4.3 Mass and Weight: Distinguish between mass and weight, and use W = m g with gravitational field strength to calculate weight on different planets.

In everyday language we use the two words as if they mean the same, but in physics they are different quantities.

Mass

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

Weight

Weight is the force of gravity on an object, measured in newtons, so it is a vector pointing towards the centre of the planet.

Variation

Weight changes from place to place, because the strength of gravity depends on the planet or moon the object is on.

Measuring

Mass is measured with a balance, while weight is measured with a newton balance (a spring balance).

Gravitational Field Strength

Definition

Gravitational field strength g is the weight in newtons of each kilogram of mass, measured in N/kg.

Equation

Weight is calculated using W = m g, where W is weight in N, m is mass in kg and g is gravitational field strength in N/kg.

On Earth

Near the surface of the Earth g is 9.8 N/kg, so every kilogram of mass weighs 9.8 N.

Elsewhere

On the Moon g is about 1.6 N/kg, so objects weigh roughly one sixth of their weight on Earth.

Place	g (N/kg)	Weight of 60 kg person (N)
Earth	9.8	588
Moon	1.6	96

Identify which quantity is asked for: weight, mass or gravitational field strength.

Make sure the mass is in kilograms; convert grams by dividing by 1000.

Substitute into W = m g, rearranging as m = W ÷ g or g = W ÷ m if needed.

State the answer with the correct unit, newtons for weight and kilograms for mass.

Remember that weightlessness in orbit does not mean zero mass; the astronaut still has the same mass.

Question: Calculate the weight of a 60 kg astronaut on Earth (g = 9.8 N/kg) and on the Moon (g = 1.6 N/kg). What is the mass of an object that weighs 49 N on Earth?

Earth: W = m g = 60 × 9.8 = 588 N.
What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg⁻¹ on Earth)
Moon: W = 60 × 1.6 = 96 N; the mass is still 60 kg.
Object: m = W ÷ g = 49 ÷ 9.8 = 5.0 kg.

Answer: 588 N on Earth, 96 N on the Moon; the object has mass 5.0 kg.

1.4.3 – Key Points for the Exam

Mass: The quantity of matter in an object, in kg.
Weight: The force of gravity acting on a mass, in N.
Gravitational field strength: The force per kilogram exerted by gravity, in N/kg.
Newton balance: A spring balance that measures force in newtons.

Common Mistakes

Quoting weight in kilograms instead of newtons.
Saying an astronaut's mass changes on the Moon, when only their weight changes.
Forgetting to convert grams into kilograms before using W = m g.
Using g = 9.8 m/s² as a unit instead of N/kg when asked for field strength.