Physics

5.4 - Mass, Weight & Gravity

8 min

Gravity and field strength

Weight and mass

What GPE is

Calculating GPE

note 1 of 4

Gravity is the force of attraction between masses

Everything with mass has a gravitational field around it, which attracts other masses.
Gravity is always attractive, and the more massive an object is, the stronger its gravitational field.
Gravity acts between any two masses, but the pull is only noticeable when at least one mass is very large, such as a planet or star.

Near the surface of a planet, gravity:

Makes objects fall towards the ground.
Gives every object a weight.

A standing person and a book on the ground joined by a dashed double arrow labelled weak gravity, beside a person falling towards a curved Earth with a double arrow labelled strong gravity.

note 2 of 4

Weight and mass are not the same

Mass - The amount of matter in an object. Measured in kilograms (kg). Mass doesn't depend on location, so an object has the same mass anywhere in the universe. It's a scalar quantity.
Weight - The force acting on an object due to gravity. Weight is a force, so it's measured in newtons (N) using a calibrated spring balance (a newtonmeter).
Weight acts as though it's concentrated at a single point on the object, called the centre of mass.

Why weight changes with location

Weight depends on the gravitational field strength where the object is.
An object has different weights in different places, even though its mass never changes.
A 1 kg mass weighs about 9.8 N on Earth but only about 1.6 N on the Moon, because the Moon's gravitational field strength is smaller.

A 1 kg mass shown three times: on Earth labelled strong gravity, weight = 9.8 N, on the Moon labelled weak gravity, weight = 1.6 N, and in space labelled very weak gravity, almost weightless.

note 3 of 4

Formula for weight

$W = m g$

Where:

$W$ = Weight, in newtons (N)
$m$ = Mass, in kilograms (kg)
$g$ = Gravitational field strength, in newtons per kilogram (N/kg)

Values of g

Gravitational field strength is the force per unit mass: the gravitational force on each kilogram of mass.
On Earth, $g$ is about 9.8 N/kg (sometimes rounded to 10 N/kg) - always use the value given in the question.
On the Moon, $g$ is about 1.6 N/kg, and it's different again on other planets.
Weight and mass are directly proportional ( $W \propto m$ ) for a given gravitational field strength.

A purple weight block marked 10 kg with a curly label reading mass (kg), and a red arrow pointing straight down from its base labelled weight (N).

note 4 of 4

Worked example - Weight of a suitcase

A 6.0 kg suitcase is on Earth, where the gravitational field strength is 9.8 N/kg. Calculate its weight.

Step 1 - Formula

$W = m g$

Step 2 - Substitution and calculation

$W = 6.0 \times 9.8 = 59 N (to 2 s.f.)$

Step 3 - Interpretation

Taken to the Moon ( $g$ = 1.6 N/kg), the same suitcase would weigh 6.0 × 1.6 = 9.6 N. Its mass stays 6.0 kg in both places; only the weight changes, because $g$ is different.

key terms

TermDefinition

Gravitational fieldA region around a mass where other masses experience a force of attraction.

MassThe amount of matter in an object, measured in kilograms.

WeightThe force acting on an object due to gravity, measured in newtons.

Centre of massThe point through which the whole weight of an object can be thought of as acting. It is also called the centre of gravity.

end of notes

Key points to remember

Gravity is the force of attraction between masses

Everything with mass has a gravitational field around it, which attracts other masses.

Gravity is always attractive, and the more massive an object is, the stronger its gravitational field.

Gravity acts between any two masses, but the pull is only noticeable when at least one mass is very large, such as a planet or star.

Near the surface of a planet, gravity:

Makes objects fall towards the ground.

Gives every object a weight.

Weight and mass are not the same

Mass - The amount of matter in an object. Measured in kilograms (kg). Mass doesn't depend on location, so an object has the same mass anywhere in the universe. It's a scalar quantity.

Weight - The force acting on an object due to gravity. Weight is a force, so it's measured in newtons (N) using a calibrated spring balance (a newtonmeter).

Weight acts as though it's concentrated at a single point on the object, called the centre of mass.

Why weight changes with location

Weight depends on the gravitational field strength where the object is.

An object has different weights in different places, even though its mass never changes.

A 1 kg mass weighs about 9.8 N on Earth but only about 1.6 N on the Moon, because the Moon's gravitational field strength is smaller.

Formula for weight

$W = m g$

Where:

W

= Weight, in newtons (N)

m

= Mass, in kilograms (kg)

g

= Gravitational field strength, in newtons per kilogram (N/kg)

Values of g

Gravitational field strength is the force per unit mass: the gravitational force on each kilogram of mass.

On Earth,

g

is about 9.8 N/kg (sometimes rounded to 10 N/kg) - always use the value given in the question.

On the Moon,

g

is about 1.6 N/kg, and it's different again on other planets.

Weight and mass are directly proportional (

W \propto m

) for a given gravitational field strength.

Worked example - Weight of a suitcase

A 6.0 kg suitcase is on Earth, where the gravitational field strength is 9.8 N/kg. Calculate its weight.

Step 1 - Formula

$W = m g$

Step 2 - Substitution and calculation

$W = 6.0 \times 9.8 = 59 N (to 2 s.f.)$

Step 3 - Interpretation

Taken to the Moon ( $g$ = 1.6 N/kg), the same suitcase would weigh 6.0 × 1.6 = 9.6 N. Its mass stays 6.0 kg in both places; only the weight changes, because $g$ is different.