Mass and WeightCambridge IGCSE Physics: Revision notes
Section 1
What is mass?
Mass is a measure of the quantity of matter in an object at rest relative to the observer. It is an intrinsic property of an object, meaning it does not change regardless of location or gravitational field strength.
- Mass is measured in kilograms (kg)
- Mass remains constant whether an object is on Earth, the Moon, or in space
- Mass is a scalar quantity (has magnitude only, no direction)
- Mass is determined by the number and type of atoms that make up an object
Think of mass as the amount of 'stuff' in an object – like the number of grains in a sack of sugar. Whether the sack is on Earth or the Moon, it always contains the same number of grains (same mass).
Section 2
What is weight?
Weight is the gravitational force exerted on an object that has mass. Weight is not an intrinsic property; it depends on the gravitational field where the object is located.
- Weight is measured in newtons (N)
- Weight is a vector quantity (has both magnitude and direction – always acts downwards towards the centre of the Earth or other celestial body)
- Weight changes depending on gravitational field strength
- An object with the same mass will weigh less on the Moon than on Earth because the Moon's gravitational field is weaker
- Weight acts at the centre of mass of an object
Examiners expect you to state that weight is a force and specify that it is a gravitational force. Simply saying 'weight is mass times gravity' loses marks if you do not identify it as a force.
Students often confuse mass and weight or use them interchangeably. Remember: mass is constant everywhere; weight changes with gravitational field strength.
Section 3
What is gravitational field strength?
Gravitational field strength is defined as the gravitational force per unit mass. It is represented by the symbol g and is measured in N/kg (newtons per kilogram).
The equation is:
g = W/m
Where:
- g = gravitational field strength (N/kg)
- W = weight (N)
- m = mass (kg)
Gravitational field strength is also equivalent to the acceleration of free fall (measured in m/s²). This means:
g = a (when an object falls freely under gravity alone)
- On Earth's surface, g ≈ 10 N/kg (or 9.8 N/kg for more precision)
- On the Moon's surface, g ≈ 1.6 N/kg
- Gravitational field strength is a vector quantity (always directed towards the centre of mass creating the field)
Examiners test whether you can rearrange g = W/m to find any of the three quantities. Learn the triangle method: W at the top, m and g at the bottom. Cover the quantity you need to find.
A 5 kg object on Earth experiences a weight of 50 N. Calculate g: g = W/m = 50/5 = 10 N/kg. The same object on the Moon (where g ≈ 1.6 N/kg) would weigh: W = m × g = 5 × 1.6 = 8 N.
Section 4
How do we compare masses and weights?
Balances are used to compare masses and weights:
| Type of Balance | What it Measures | How it Works | Affected by Gravity? |
|---|---|---|---|
| Beam/Lever Balance | Mass | Uses a pivot; object balanced against standard masses | No – compares mass directly |
| Spring Scale | Weight | Uses a spring that stretches; marked in newtons or grams | Yes – reading depends on g |
Key points:
- A beam balance directly compares masses and is not affected by gravitational field strength. The same balance reading on Earth will occur on the Moon
- A spring scale measures weight (the force stretching the spring) and will give different readings in different gravitational fields
- To find mass using a spring scale, you must divide the weight reading by the local gravitational field strength: m = W/g
Examiners often ask which type of balance to use for accurate mass measurement. The answer is always a beam/lever balance because it is independent of gravity. Spring scales are unreliable for mass in different locations.
Section 5
How does a gravitational field affect mass?
Weight is the effect of a gravitational field on a mass. An object with mass placed in a gravitational field experiences a downward force (weight) towards the source of the field.
Key concept:
- Any object with mass creates its own weak gravitational field around it
- A stronger gravitational field (like Earth's) exerts a greater force on a given mass, resulting in greater weight
- The relationship between mass, gravitational field strength, and weight is linear: W = mg
Practical understanding:
- A 1 kg mass on Earth (g = 10 N/kg) weighs 10 N
- The same 1 kg mass on the Moon (g = 1.6 N/kg) weighs 1.6 N
- The mass has not changed; only the gravitational field strength (and therefore weight) has changed
- Weight always acts vertically downwards towards the centre of the Earth (or other massive body)
Imagine mass as an object and gravitational field strength as the 'pull' of a magnet. The stronger the magnet (stronger field), the greater the pull (weight) on the same metal object (mass).
Must Know
- Mass is the quantity of matter in an object; it is constant everywhere and measured in kg
- Weight is a gravitational force measured in newtons (N); it changes with gravitational field strength
- Gravitational field strength (g) is force per unit mass, calculated using g = W/m, measured in N/kg, and is equivalent to acceleration of free fall
- The relationship W = mg connects mass, weight, and gravitational field strength; rearrange as needed: g = W/m or m = W/g
- Beam/lever balances measure mass and are unaffected by gravity; spring scales measure weight and vary with gravitational field
- Weight is the effect of a gravitational field on mass; stronger fields produce greater weight for the same mass
That's the notes covered.
Carry on to the next subtopic.