**Mass and Weight Theory**

**Mass**

This is the “stuff” something is made of. It is the matter of an object and is measured in kilo-grams, kg.

The symbol for mass is: m.

**Weight**

This is the force produced by an object when gravity acts on the object. The units for weight are Newtons, N. The symbol for weight force is: F_{w}

Mass and weight are linked by the following formula:

F_{w} = m . g

Where g is the acceleration due to gravity and a constant equal to 10 ms^{-2}.

Gravity is very noticeable for very large objects like planets. Because planets are different sizes the strength of gravity therefore changes, e.g. the gravity on the Moon is ^{1}/_{6}, that of Earth.

It is important to note that when you step on a set of bathroom scales you are measuring your mass and not your weight!

**Worked Example**

A Moon rock is brought to Earth. It has a mass of 600 grams. What is the weight of the Moon rock on the Earth and on the Moon?

F_{w} = mass x gravity

On Earth

F_{w} = 0.6 kg x 10 Nkg-1

F_{w} = 6N

On the Moon

F = 0.6 kg x ^{10}/_{6 } Nkg^{-1} (Gravity on the Moon is 1/6 as strong as the Earth’s gravity)

= 1N

This means the rock would feel lighter to pick up if you were an astronaut walking on the Moon. The size and shape of the rock would be the same on the Moon and the Earth.

**Density**

Density describes the amount of mass an object has per unit volume. A denser object weighs more than a less dense object but both objects can occupy the same amount of space.

Density = mass (kg)

Volume (m^{3})

Worked Example

A cubic centimetre of lead has a mass of 8 grams.

1cm x 1cm x 1cm

To determine the density:

ρ = m

*v*

ρ = 0.008 kg

0.000001 m^{3}

(1 cubic centimetre = 0.000001 m^{3})