# Mass and Weight

## Mass

**Mass** is defined as the quantity of matter in a substance.

- The mass of an object is the same everywhere.

The unit of mass is kilogram [kg].

#### Instrument for measuring mass is:

Beam balance

## Weight

**Weight** is defined as the attractive force exerted on an object by gravity

- The weight of an object varies from place to place. (e.g. from the earth to the moon)

The unit of weight is Newton [N].

#### Instrument for measuring weight

Spring balance

Bathroom scale

#### Relationship between mass and weight

The weight of an object is directly proportional to its mass.

##### Formula

$W=\mathrm{mg}$

w: weight [N]

m: mass [kg]

g: acceleration due to gravity[m/s2]

- Gravity on earth is 10m/s2

- Gravity of the moon is only about 1/6 that of the earth.

g = 10×16m/s2 (≈ 1.67 m/s2) on the moon

- No gravity in outer space.

g = 0 m/s2 in the outer space

The following table shows the changes to the mass and weight of an astronaut when he travels from the earth to the moon in a spacecraft.

$\begin{array}{|llll|}\hline \mathrm{}& \mathrm{Earth}& \mathrm{Moon}& \mathrm{Outer\; Space}\\ \mathrm{Mass}& \mathrm{60kg}& \mathrm{60kg}& \mathrm{60kg}\\ \mathrm{Weight}& \mathrm{600N}& \mathrm{100N}& \mathrm{0N}\\ \hline\end{array}$The mass of a man is 70kg. What is his weight on the earth?

Solution

given that

m = 70kg

g = 10m/s2

W = ?

$W=\mathrm{mg}$

$W=70\times 10$

$W=\mathrm{700N}$

Answer: $W=\mathrm{700N}$

#### Centre of gravity

** The center of gravity ** of a body is defined as the point through which its whole weight appears to act.

below is the diagram that illustrate the center of gravity

#### Stability

**The stability ** of an object is defined as the ability of an object to regain its original position after it has been displaced slightly.

The position of centre of gravity affects the stability of a body.

##### Example 1

Which is more stable? from the objects below

(1) is more stable than (2) because it has a lower centre of gravity.

##### Example 2

Which is more stable? from the objects below

(2) is more stable than (1) because it has a larger base area.

##### To increase the stability of an object,

the centre of gravity should be as low as possible.

the base area should be as large as possible.