Weight, Mass & Gravity

Mass and Weight

Mass is the amount of matter in an object. It is measured in kilograms (kg) and is a scalar quantity, meaning it has magnitude only and no direction.

Weight is the force exerted on an object due to gravity. It depends on both the mass of the object and the gravitational field strength at the location. Weight is a vector quantity because it has both magnitude and direction (downwards towards the centre of the Earth).

Unlike mass, which remains constant regardless of location, weight can change if the gravitational field strength changes (for example, on the Moon or other planets).

Gravity and Gravitational Field Strength

Gravity is an attractive force that pulls objects towards each other. On Earth, it pulls objects towards the ground.

The gravitational field strength ($g$) at a point is the force per unit mass experienced by an object placed at that point. It varies slightly depending on location (e.g., altitude or planet).

On Earth, the average gravitational field strength is approximately $9.8\, \text{N/kg}$, but it can be rounded to $10\, \text{N/kg}$ for many GCSE calculations.

Weight is calculated by multiplying mass by gravitational field strength:

$$\text{Weight} = \text{mass} \times \text{gravitational field strength}$$

Weight is measured in newtons (N), mass in kilograms (kg), and gravitational field strength in newtons per kilogram (N/kg).

Calculating Weight

The formula to calculate weight is:

$$\text{Weight} (N) = \text{mass} (kg) \times \text{gravitational field strength} (N/kg)$$

It is important to use the correct units: mass in kilograms, gravitational field strength in newtons per kilogram, and weight in newtons.

Since weight depends on gravitational field strength, an object’s weight will be different on the Moon (where $g \approx 1.6\, \text{N/kg}$) compared to Earth.

For instance, if a person has a mass of 70 kg on Earth, their weight is:

$$\text{Weight} = 70 \times 9.8 = 686\, \text{N}$$

Example calculation inline: Calculate the weight of a 10 kg object on Earth using $g = 9.8\, \text{N/kg}$:

$\text{Weight} = 10 \times 9.8 = 98\, \text{N}$