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SingaporePhysicsSyllabus dot point

What is the difference between the mass of an object and its weight?

Distinguish mass from weight, relate weight to gravitational field strength, and explain why weight varies with location

A focused answer to the O-Level Physics outcome on mass and weight. Mass as the amount of matter, weight as the gravitational force, the relationship W equals mg, gravitational field strength, and why weight changes with location.

Generated by Claude Opus 4.87 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this dot point is asking
  2. The answer
  3. Examples in context
  4. Try this

What this dot point is asking

SEAB wants you to distinguish mass from weight clearly, to use the relationship W=mgW = mg, to understand gravitational field strength gg, and to explain why weight changes from place to place while mass does not. The big idea is that mass is a fixed property of an object, but weight is a force that depends on the gravity where the object is.

The answer

Mass

Mass is the amount of matter in an object. It is a scalar, measured in kilograms (kg\text{kg}), and it does not change when the object is moved to the Moon, into space, or up a mountain. Mass also measures inertia, the reluctance of an object to change its motion.

Weight

Weight is the gravitational force acting on an object. It is a vector pointing downward (toward the centre of the Earth), measured in newtons (N\text{N}):

W=mgW = mg

Here mm is the mass in kilograms and gg is the gravitational field strength.

Gravitational field strength

The gravitational field strength gg is the force of gravity on each kilogram of mass:

g=Wmg = \frac{W}{m}

Its unit is newtons per kilogram (N kg−1\text{N kg}^{-1}). On Earth g≈10 N kg−1g \approx 10\ \text{N kg}^{-1} (the O-Level value), on the Moon about 1.6 N kg−11.6\ \text{N kg}^{-1}. Numerically gg as a field strength equals gg as the acceleration of free fall.

Why weight varies but mass does not

Move an object to the Moon and its mass is unchanged, but the Moon's gg is about one sixth of Earth's, so its weight is about one sixth. Even on Earth, weight is slightly smaller up a high mountain because gg falls a little with distance from the Earth's centre. Mass, the amount of matter, never changes with location.

Examples in context

Example 1. A bathroom scale. A bathroom scale really measures the force you press on it, your weight, then displays a mass by dividing by Earth's gg. On the Moon the same scale would read about one sixth, even though your body contains exactly the same amount of matter, because it has been calibrated for Earth's gravity.

Example 2. Spacecraft and fuel. Engineers care about a spacecraft's mass when working out how much force is needed to accelerate it (because F=maF = ma uses mass), but about its weight when it sits on the launch pad under Earth's gravity. The same object has a fixed mass but a weight that drops to nearly zero far from any planet.

Try this

Q1. State the difference between mass and weight, including their units. [2 marks]

  • Cue. Mass is the amount of matter in kilograms; weight is the gravitational force in newtons, equal to mgmg.

Q2. A box has a mass of 12 kg12\ \text{kg}. Find its weight on Earth, where g=10 N kg−1g = 10\ \text{N kg}^{-1}. [2 marks]

  • Cue. W=mg=12×10=120 NW = mg = 12 \times 10 = 120\ \text{N}.

Q3. Explain why an astronaut weighs less on the Moon than on Earth but has the same mass. [3 marks]

  • Cue. Mass is the unchanged amount of matter; weight is mgmg, and the Moon's smaller gg means a smaller weight for the same mass.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marksAn astronaut has a mass of 80 kg80\ \text{kg}. (a) Find her weight on Earth, where g=10 N kg−1g = 10\ \text{N kg}^{-1}. (b) Find her weight on the Moon, where g=1.6 N kg−1g = 1.6\ \text{N kg}^{-1}. (c) State what happens to her mass on the Moon.
Show worked answer →

(a) Weight on Earth: W=mg=80×10=800 NW = mg = 80 \times 10 = 800\ \text{N}.

(b) Weight on the Moon: W=mg=80×1.6=128 NW = mg = 80 \times 1.6 = 128\ \text{N}.

(c) Her mass stays 80 kg80\ \text{kg}, because mass is the amount of matter and does not depend on location; only the weight changes because gg is smaller on the Moon.

Markers reward W=mgW = mg used twice with the right gg each time, and the key point that mass is unchanged while weight is smaller on the Moon.

Original3 marks(a) Define the weight of an object. (b) Explain, using physics, why an object weighs slightly less at the top of a tall mountain than at sea level.
Show worked answer →

(a) The weight of an object is the gravitational force acting on it, W=mgW = mg, measured in newtons.

(b) At the top of a mountain the object is further from the centre of the Earth, so the gravitational field strength gg is slightly smaller. Since W=mgW = mg and the mass is unchanged, a smaller gg gives a slightly smaller weight.

Markers reward weight defined as the gravitational force (W=mgW = mg), and the explanation that greater distance from the Earth's centre means a smaller gg and so a smaller weight for the same mass.

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