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1.2.5Forces and Motion

Weight

5 min read 9 parts Lesson 1 of 26 Unit quiz

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Section 1 of 9Mass and weight

Mass is the amount of matter in an object. It is a scalar, measured in kilograms (kg) and does not change with place. Weight is the gravitational force acting on a mass. It is a vector pointing towards the centre of the Earth and is measured in newtons (N).

Section 2 of 9Gravitational field strength

A gravitational field is a region where a mass experiences a force. The gravitational field strength g tells how many newtons act on each kilogram:

W = m g

What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg−1 on Earth)

W is weight in N, m is mass in kg and g is gravitational field strength in N/kg. On the surface of the Earth g is about 9.8 N/kg (often taken as 10 N/kg in some questions). On the Moon it is about 1.6 N/kg and on Jupiter about 25 N/kg.

g also equals the acceleration of free fall in m/s2 when air resistance is ignored, so N/kg and m/s2 are equivalent units.

Different bodies have different g because g depends on the mass of the body and its radius.

Gravitational field strength
A more massive planet pulls harder, while a larger radius spreads the same pull further from the centre and reduces it.
On the Earth's surface g also decreases with height, though only by a tiny amount on a mountain.
In a question, always use the value of g given on the paper.

Section 3 of 9Mass stays, weight changes

Mass stays, weight changes
An astronaut of mass 80 kg has the same mass on the Moon as on Earth but a much smaller weight, because the Moon has a smaller g.
  • Weight also changes slightly with location on Earth, being a little greater at the poles than at the equator.
Mass is measured with a balance, which compares masses, while weight is measured with a newton meter (a spring balance).
Comparing weight and mass: if two objects of masses 2 kg and 6 kg are weighed on Earth they give 19.6 N and 58.8 N, in the ratio 1 : 3, the same ratio as the masses.
Mass stays, weight changes
A balance reads the same on any planet because the same comparison happens, but a spring balance would give different readings.
That is why the astronaut's mass is quoted in kg and not in newtons.

Section 4 of 9Centre of gravity and direction

The weight of an object seems to act from a single point, its centre of gravity. Weight always acts vertically downwards, so on a slope the weight arrow still points straight down, not into the slope.

Section 5 of 9Free fall and weight

All objects near the Earth's surface fall with the same acceleration g when air resistance is negligible, because the larger force on a heavier object is exactly shared out over its larger mass: a = W/m = mg/m = g. In air, a feather falls slower than a stone because drag matters more for it, but in a vacuum they fall together.

A graph of weight against mass is a straight line through the origin with gradient g.

Free fall and weight
Measuring the gradient of such a graph, using a newton meter and a set of known masses, is a good way to determine g in the laboratory.
The line should pass through the origin: if it has a positive intercept, the newton meter has a zero error.

Section 6 of 9Apparent weight

The reading on a scale is the contact force from the scale, not the weight. In a lift accelerating upwards the contact force is greater than the weight and you feel heavier; in free fall it is zero and you feel weightless, although the weight still acts.

An easy way to remember

  • mass is "how much stuff", weight is "how hard gravity pulls on that stuff".
  • If a question asks for the "weight in kg", it is using everyday language;
    • in physics, use kg for mass and N for weight, and convert with W = mg when the question needs a force.

Section 7 of 9Worked examples

  1. Find the weight of a 65 kg student on Earth (g = 9.8 N/kg).

  2. A rock weighs 24 N on the Moon where g = 1.6 N/kg. Find its mass and its weight on Earth.

  3. An object of mass 2.5 kg is lifted on a planet where its weight is 20 N. Find g for that planet.

Section 8 of 9Key terms

TermMeaning
MassAmount of matter in an object, in kg.
WeightGravitational force on a mass, in N.
Gravitational field strength (g)Force per unit mass; 9.8 N/kg on Earth.
Free fallMotion under gravity alone.
Centre of gravityThe point where the weight appears to act.

Section 9 of 9Exam technique

1
Saying mass is measured in newtons.
2
Thinking an astronaut in orbit has no weight: gravity still acts on them, they are in free fall.
3
Mixing up kg and N when substituting into W = mg.
4
Drawing weight perpendicular to a slope.
5
Thinking heavier objects fall faster in a vacuum.
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