Weight, mass and gravity: the difference between mass and weight, the weight equation W = mg, gravitational field strength, and weight measured with a calibrated balance.

What this dot point is asking

Edexcel wants you to distinguish mass from weight, to recall and use the weight equation $W = mg$, to understand gravitational field strength and how it differs on other bodies, to recall that weight acts at the centre of mass, and to know that weight is measured with a calibrated spring balance (newtonmeter).

Mass versus weight

The crucial distinction is that mass does not change when you move an object to the Moon or into space, but weight does, because weight depends on the local gravitational field. A $1\,\text{kg}$ bag of sugar has the same mass on Earth and the Moon, but it weighs about six times less on the Moon because the Moon's gravitational field is weaker.

The weight equation

Because $W = mg$, weight and mass are directly proportional at a given location, so a graph of weight against mass is a straight line through the origin with gradient $g$. The weight of an object acts at a single point called the centre of mass, which is where you can treat all the weight as acting.

Measuring weight

A spring balance works because the extension of the spring is proportional to the force pulling on it (Hooke's law), so a scale marked in newtons can be read directly. Kitchen and bathroom scales often display a mass in kilograms, but they actually sense weight and convert it using the local value of $g$, which is why a set of bathroom scales calibrated on Earth would read incorrectly on the Moon even though your mass is unchanged.

How Edexcel examines this

Weight questions appear on both tiers, most often as a two or three mark calculation using $W = mg$, frequently set on another planet or the Moon to test whether you understand that mass stays the same while weight changes. The mark scheme rewards selecting the equation, substituting the correct value of $g$ for the body named in the question, and quoting the answer in newtons, so never carry over Earth's $g$ when a different value is given. A favourite extended-response style asks you to "explain how the mass and weight of an object change" when it is moved between two locations; the full-mark answer states clearly that mass is unchanged (because it is the amount of matter) and that weight changes in proportion to $g$, ideally backed by a calculation of the two weights. Because weight against mass is a straight line through the origin with gradient $g$, Edexcel may give a graph and ask you to find $g$ from its gradient, linking this dot point to the graph skills used elsewhere in the topic. Keep the language precise: write "gravitational field strength" for $g$ in $\text{N/kg}$, and remember it is numerically equal to the acceleration of free fall in $\text{m/s}^2$.

Try this

Q1. State the unit of weight. [1 mark]

• Cue. The newton ($\text{N}$).

Q2. Calculate the weight of a $25\,\text{kg}$ mass on Earth ($g = 10\,\text{N/kg}$). [2 marks]

• Cue. $W = mg = 25 \times 10 = 250\,\text{N}$.