Distinguish mass from weight and use weight = mass times gravitational field strength

What this dot point is asking

SEAB wants you to tell mass from weight, to use the formula weight $=$ mass $\times$ gravitational field strength, and to explain why an object's weight changes on the Moon while its mass does not. The big idea is that mass is the amount of matter in an object, and weight is the force of gravity acting on that mass.

The answer

Mass

Mass is the amount of matter in an object. It is measured in kilograms ($\text{kg}$). Mass does not change when you move the object: a $3\ \text{kg}$ bag has a mass of $3\ \text{kg}$ on Earth, on the Moon, or floating in space. Mass is a scalar.

Mass also measures how hard it is to change an object's motion. A larger mass needs a larger force for the same acceleration, which is why a loaded trolley is harder to get moving.

Weight

Weight is the force on an object due to gravity. Because it is a force, it is measured in newtons ($\text{N}$) and it is a vector that always points downward, toward the centre of the planet.

Weight depends on where you are. The same object weighs less on the Moon than on Earth because the Moon's gravity is weaker.

Gravitational field strength

The gravitational field strength, $g$, is the gravitational force on each kilogram of mass. On Earth it is about $10\ \text{N kg}^{-1}$ (more precisely $9.81\ \text{N kg}^{-1}$, but $10$ is used for simple work). On the Moon it is only about $1.6\ \text{N kg}^{-1}$.

Weight and mass are linked by:

where $W$ is the weight in newtons, $m$ is the mass in kilograms, and $g$ is the gravitational field strength in $\text{N kg}^{-1}$.

Why weight changes but mass does not

Mass is a property of the object itself, so it is fixed. Weight is a force that depends on the strength of gravity where the object is. Move to a place with weaker gravity and the same mass has a smaller weight. This is why an astronaut can lift heavy equipment easily on the Moon, even though its mass (and so its resistance to being pushed) is unchanged.

Examples in context

Example 1. Weighing scales. A bathroom scale really measures the force you press on it (your weight) but is marked in kilograms by assuming Earth's gravity. On the Moon the same scale would read a much smaller number, even though your mass is unchanged, because your weight is smaller.

Example 2. Lifting on the Moon. Apollo astronauts could carry heavy equipment with ease because its weight was about one sixth of its Earth weight. However, the equipment's mass was the same, so once moving it was just as hard to stop or change direction, which made handling it tricky.

Try this

• Cue. A crate has a mass of $12\ \text{kg}$. Find its weight on Earth, where $g = 10\ \text{N kg}^{-1}$. [2 marks] $W = mg = 12 \times 10 = 120\ \text{N}$.

• Cue. Explain why an object has the same mass but a different weight on the Moon. [2 marks] Mass is the amount of matter, which is fixed; weight depends on gravity, which is weaker on the Moon, so the weight is less.

• Cue. An object weighs $80\ \text{N}$ on Earth, where $g = 10\ \text{N kg}^{-1}$. Find its mass. [2 marks] $m = \dfrac{W}{g} = \dfrac{80}{10} = 8.0\ \text{kg}$.