Mass vs weight — two-element definitions
Mass is the quantity of matter — a scalar in kg, unchanged by location. Weight is the force on an object due to a gravitational field — a vector in N, given by , and it changes with location. The two elements the mark scheme needs for weight: (1) it is a force, (2) due to a gravitational field (or gravity); "pull of gravity" or "how heavy it is" scores zero. Mini-example: a 70 kg astronaut weighs N on Earth.
W = mg and g = 10 N/kg
Gravitational field strength is the force per unit mass; on Earth Cambridge uses N/kg. From , weight is proportional to mass. Rearrange: and . Unit check: N/kg = m/s², so both are accepted for . Mini-example: a 1.5 kg bag weighs N, and a 350 N rock has mass kg. (E) Define as force per unit mass () to explain why differs between planets.
Measuring mass vs weight
A newton-meter (spring balance) measures weight — a force, in N — from how far a spring extends; a balance (beam or electronic) measures mass, in kg, by comparison. A newton-meter's scale may be marked in kg, but it still measures a force: take it to the Moon and its reading falls, while a balance reads the same because it compares masses. So on the Moon, weight is smaller but mass is unchanged.
Drawn from real examiner reports.
Weight is not "force per unit mass"
Writing "weight is the gravitational force per unit mass" defines gravitational field strength (N/kg), not weight. Weight is the total gravitational force on the object, (N), and depends on the object's mass. "Pull of gravity" is also too vague — the word "force" must appear. Correct mark-scheme form: "the force on an object due to a gravitational field".
June 2024 Paper 0625/13 Q4: "Many incorrectly believed that weight is the gravitational force per unit mass rather than the gravitational force on an object, so chose option A."
Mass in kg, weight in N — do not swap
Given mass 60 kg and weight 590 N, candidates label them the wrong way round. The rule: if the unit is kg it is a mass; if the unit is N it is a force (weight, thrust, friction). Weight in N is larger than mass in kg whenever N/kg, so if your "weight" is the smaller number you have either swapped the labels or divided by mistake.
November 2023 Paper 0625/22 Q4: "Many candidates knew the relationship between 590 N and 60 kg, but misidentified the former as the mass and the latter as the weight."
Weight is m × g, not m ÷ g
To find weight, multiply: . Weaker candidates divide (), giving a tiny answer with the wrong meaning. Check the magnitude: on Earth a weight in N is about ten times the mass in kg. If your weight is smaller than the mass number, you have divided instead of multiplied. Always write first.
June 2024 Paper 0625/23 Q3: "Some weaker candidates could not recall the correct equation to calculate weight and instead divided the mass by the gravitational field strength."
Mass does not change on the Moon
Mass is invariant — an object has the same mass on Earth, the Moon or in space, because it is the quantity of matter. Only weight changes, because is smaller on the Moon (about 1.6 N/kg). In a "state the mass on the Moon" part, just quote the Earth value; if you calculated a new mass, you have made an error. Weight changes with location; mass does not.
A weight must be given in newtons
Weight is a force, so its unit is the newton (N) — never kg. "The weight is 3 kg" scores zero; 3 kg is the mass, and the weight is N. For "define weight", both elements are needed: it is a force, and it is due to gravity / a gravitational field. On a force diagram the weight arrow points downward from the centre of gravity.
Give both elements in a definition
For "define weight", write two elements: (1) a force, (2) due to a gravitational field / gravity — "Weight is the force on an object due to gravity, measured in N." The word "force" and the word "gravitational" must both appear; "pull of gravity" alone earns nothing.
For another planet, find the mass first
For "weight on another planet" questions, find the mass first ( on Earth), because mass is invariant, then apply the new value: . Jumping straight from one weight to another with a ratio is risky unless Earth's is exactly 10 N/kg.
Write W = mg before substituting
Write the formula (, or , or ) before you substitute — Cambridge gives the method (C1) mark for this even if the arithmetic is wrong. Check units: mass in kg, in N/kg, weight in N. Then write the answer with the correct unit.
| Quantity | Symbol | Formula | Unit |
|---|---|---|---|
| Weight | newton, N | ||
| Mass | kilogram, kg | ||
| Gravitational field strength | N/kg (= m/s²) |
On Earth: (Cambridge standard — use this value unless the question specifies otherwise).
Full symbol definitions:
(E) Extended definition of gravitational field strength: The gravitational field strength at a point is the force per unit mass experienced by a small test mass placed at that point: .
What are the two key differences between mass and weight?
A parcel has a mass of 2.5 kg.
Calculate the weight of the parcel on the surface of the Earth.
(Gravitational field strength on Earth N/kg)
Give the unit of your answer.
