Weight and Mass

• The precise scientific distinction between mass and weight
• How to calculate weight on different planets
• What "weightlessness" actually means (hint: you're not outside gravity's reach)
• Common everyday confusions this topic clears up

Mass Mass is the measure of the total amount of matter contained in an object. It is a scalar quantity (no direction) measured in kilograms (kg). Mass is intrinsic — it does not change based on where the object is. Your mass on Earth, on the Moon, in deep space, or at the top of Mount Everest is exactly the same.

Mass is also a measure of inertia — the resistance an object has to a change in its state of motion. A truck is harder to get moving than a bicycle because it has more mass (more inertia).

Weight Weight is the force of gravity pulling on an object. It is a vector quantity (directed toward the centre of the gravitational body) measured in Newtons (N). The formula is:

W = m × g

where m is mass in kg and g is the local gravitational acceleration in m/s².

Weight depends entirely on the local value of g. Since g varies from planet to planet (and even slightly across Earth's surface — it is marginally higher at the poles than at the equator due to Earth's shape), weight is not constant.

Values of g on different bodies

Note: "You weigh 16 kg on the Moon" is an informal way of saying your Moon-weight equals what 16 kg-force feels like on Earth (since 1/6 × 60 ≈ 10 kg; the exact fraction gives ~10 kg-equivalent). In precise scientific terms, your weight on the Moon is about 98 N, not 16 kg — kg is a unit of mass, not weight.

Weightlessness Astronauts in the International Space Station (ISS) orbit about 400 km above Earth. At that altitude, g is still about 8.7 m/s² — they are definitely not outside Earth's gravity. They feel weightless because they and the station are both in free fall — accelerating toward Earth at the same rate. There is no surface beneath them pushing up, so they experience no normal force. This state is called microgravity or apparent weightlessness.

True weightlessness (zero gravity) only exists at a theoretical point infinitely far from all masses.

Why the distinction matters in physics problems In Newton's Second Law, F = ma, the m is mass. When calculating friction (f = μN) on a horizontal surface, N = mg = weight. Mixing up units or swapping mass for weight leads to wrong answers. Always check: is the quantity in kg (mass) or N (force/weight)?

Problem: A person has a mass of 60 kg. Calculate their weight on Earth (g = 9.8 m/s²), on the Moon (g = 1.63 m/s²), and on Jupiter (g = 24.8 m/s²).

Solution:

Weight on Earth: W = mg = 60 × 9.8 = 588 N

Weight on Moon: W = mg = 60 × 1.63 = 97.8 N

Weight on Jupiter: W = mg = 60 × 24.8 = 1488 N

The person's mass remains 60 kg everywhere. On Jupiter they would feel nearly 2.5 times heavier than on Earth and could not stand up — their muscles and bones are adapted to Earth's g. On the Moon they would feel about 1/6 as heavy and could jump roughly 6 times higher.

• Saying "I weigh 60 kg" is scientifically wrong. You mean you have a mass of 60 kg. Your weight is 588 N. In everyday language this is fine, but in physics exams it costs marks.
• Claiming you lose mass on a diet. You do lose mass (and weight changes with it on Earth). But the two are different things. Saying "I lost weight" is imprecise — you lost mass, and that caused a reduction in your Earth-weight.
• Thinking weightlessness means zero gravity. Gravity extends infinitely (it weakens with distance but never becomes zero). Weightlessness is about the absence of a support force, not the absence of gravity.
• Using weight (N) where mass (kg) is required in F = ma. If a problem gives you weight and asks for acceleration, first convert: m = W/g.

1. A rock has a mass of 2 kg on Earth. What is its mass on Mars?
2. Calculate the weight of a 50 kg student on Earth (g = 9.8 m/s²) and on the Moon (g = 1.63 m/s²).
3. Why do astronauts in the ISS float, even though Earth's gravity still acts on them?