Mass & weight
Mass and weight
Mass and weight — definitions
Mass is the measure of the amount of matter in an object.
SI unit: kilogram (kg)
Mass is a scalar quantity. It is the same everywhere in the universe — it does not change with location.
SI unit: kilogram (kg)
Mass is a scalar quantity. It is the same everywhere in the universe — it does not change with location.
Weight is the gravitational force acting on an object due to a gravitational field.
SI unit: newton (N)
Weight is a vector quantity — it always acts downward towards the centre of the Earth (or towards the centre of whatever body creates the gravitational field).
SI unit: newton (N)
Weight is a vector quantity — it always acts downward towards the centre of the Earth (or towards the centre of whatever body creates the gravitational field).
Never confuse mass and weight. In everyday language people say "I weigh 60 kg" — but kg is a unit of mass, not weight. In physics: mass is in kg, weight is in N. A student with mass 60 kg has a weight of about 600 N on Earth.
Calculating weight
\[ W = mg \]
On Earth's surface: \( g \approx 10\,\text{N/kg} \)
| Symbol | Quantity | Unit |
|---|---|---|
| \( W \) | Weight (gravitational force) | newton, N |
| \( m \) | Mass | kilogram, kg |
| \( g \) | Gravitational field strength | N/kg |
Worked example — calculate weight on Earth
A bag has a mass of 4.5 kg. Calculate its weight on Earth (\( g = 10\,\text{N/kg} \)).
\( W = mg = 4.5 \times 10 = 45\,\text{N} \)
Worked example — find mass from weight
An object has a weight of 280 N on Earth. Find its mass.
Rearrange: \( m = \dfrac{W}{g} = \dfrac{280}{10} = 28\,\text{kg} \)
Mass vs weight — comparison
| Property | Mass | Weight |
|---|---|---|
| What it measures | Amount of matter | Gravitational force on the object |
| Unit | kilogram (kg) | newton (N) |
| Scalar or vector | Scalar | Vector (downward) |
| Changes with location? | No — constant everywhere | Yes — depends on \( g \) |
| On the Moon? | Same as on Earth | About ⅙ of Earth weight |
| In space (far from any planet)? | Unchanged | Zero (weightless) |
Measuring mass and weight
- Beam balance (equal-arm balance) — measures mass. It compares the object against known masses. It works on any planet (or the Moon) because gravity acts equally on both sides; the result is independent of \( g \).
- Spring balance (Newton meter) — measures weight (force in newtons). The spring extends in proportion to the gravitational force. The reading would be different on the Moon because \( g \) is different.
- Top-pan balance / digital scale — actually measures weight but is calibrated to display mass in kg (assuming Earth's \( g \)). It would give a wrong mass reading on the Moon.
In exam questions about the Moon or other planets: mass stays the same, but weight changes. Calculate the new weight using \( W = mg \) with the new value of \( g \). The beam balance reading stays the same on the Moon; the spring balance reading decreases.