What you'll learn
This topic establishes the fundamental difference between mass and weight, two terms often confused in everyday language but distinct in physics. You will master the relationship between mass, weight and gravitational field strength, learn how to calculate density for regular and irregular objects, and apply these concepts to solve quantitative problems that appear frequently in CIE IGCSE Physics Paper 2 and Paper 4.
Key terms and definitions
Mass — the amount of matter in an object, measured in kilograms (kg). Mass remains constant regardless of location in the universe.
Weight — the force of gravity acting on an object's mass, measured in newtons (N). Weight varies depending on the gravitational field strength.
Gravitational field strength (g) — the force per unit mass experienced by an object in a gravitational field, measured in newtons per kilogram (N/kg) or metres per second squared (m/s²).
Density — the mass per unit volume of a substance, measured in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³).
Centre of mass — the point at which the entire mass of an object can be considered to be concentrated.
Centre of gravity — the point at which the entire weight of an object appears to act.
Uniform gravitational field — a region where the gravitational field strength has the same magnitude and direction at all points.
Core concepts
Understanding mass
Mass is a scalar quantity that measures the amount of matter in an object. Key properties include:
- Mass is measured using a balance or electronic scales
- The SI unit is the kilogram (kg)
- Mass does not change with location — an astronaut has the same mass on Earth, the Moon, or in deep space
- Mass is related to an object's inertia — its resistance to changes in motion
- Smaller units include grams (g): 1 kg = 1000 g
In CIE IGCSE Physics examinations, you must distinguish clearly between mass and weight. Many exam questions specifically test whether students understand this difference.
Understanding weight
Weight is a vector quantity representing the gravitational force acting on a mass. Critical aspects include:
- Weight is measured using a newton meter (spring balance)
- The SI unit is the newton (N)
- Weight changes depending on the strength of the gravitational field
- Weight always acts vertically downward toward the centre of the gravitating body
- Weight can be zero in locations with no gravitational field, but mass cannot
The relationship between mass and weight is expressed by the equation:
W = m × g
Where:
- W = weight (N)
- m = mass (kg)
- g = gravitational field strength (N/kg)
Gravitational field strength values
Gravitational field strength varies across different celestial bodies:
- Earth: g ≈ 10 N/kg (more precisely 9.8 N/kg or 9.81 N/kg)
- Moon: g ≈ 1.6 N/kg
- Mars: g ≈ 3.7 N/kg
- Jupiter: g ≈ 25 N/kg
CIE IGCSE Physics papers typically use g = 10 N/kg for simplicity in calculations unless otherwise stated. The value of 9.8 N/kg or 9.81 N/kg may appear in data sheets or specific questions requiring greater precision.
An object with a mass of 5 kg has a weight of 50 N on Earth (5 × 10 = 50 N) but only 8 N on the Moon (5 × 1.6 = 8 N). The mass remains 5 kg in both locations.
Centre of mass and centre of gravity
For objects in a uniform gravitational field (like near Earth's surface), the centre of mass and centre of gravity coincide at the same point. This point represents:
- The balance point of the object
- Where the resultant weight force acts
- The point about which the object will rotate if thrown
For symmetrical objects with uniform density:
- A sphere: centre of mass is at the geometric centre
- A rectangular block: centre of mass is at the intersection of the diagonals
- A uniform rod: centre of mass is at the midpoint
For irregular shapes, the centre of mass can be found experimentally by:
- Suspending the object from one point and drawing a vertical line downward
- Suspending the object from a different point and drawing another vertical line
- The centre of mass lies at the intersection of these lines
Understanding density
Density describes how tightly matter is packed within a substance. The density equation is:
ρ = m / V
Where:
- ρ (rho) = density (kg/m³ or g/cm³)
- m = mass (kg or g)
- V = volume (m³ or cm³)
This equation can be rearranged:
- m = ρ × V
- V = m / ρ
The density triangle helps remember these arrangements: place m at the top, ρ and V at the bottom.
Typical density values
Knowing approximate densities helps check answer reasonableness:
Solids:
- Lead: 11,300 kg/m³
- Copper: 8,900 kg/m³
- Iron/Steel: 7,800 kg/m³
- Aluminium: 2,700 kg/m³
- Ice: 920 kg/m³
Liquids:
- Mercury: 13,600 kg/m³
- Water: 1,000 kg/m³ (or 1 g/cm³)
- Ethanol: 790 kg/m³
Gases (at atmospheric pressure):
- Air: 1.3 kg/m³
- Oxygen: 1.4 kg/m³
- Hydrogen: 0.09 kg/m³
Solids and liquids are typically thousands of times denser than gases because particles are much more closely packed.
Measuring density of regular objects
For objects with regular geometric shapes:
- Measure mass: Place the object on an electronic balance and record mass in grams or kilograms
- Calculate volume: Use appropriate geometric formulae:
- Cube/cuboid: V = length × width × height
- Cylinder: V = π × r² × h
- Sphere: V = (4/3) × π × r³
- Calculate density: Use ρ = m / V with consistent units
Measuring density of irregular objects
For irregularly shaped objects (like a stone or metal lump):
- Measure mass: Use an electronic balance
- Measure volume using the displacement method:
- Fill a displacement can (eureka can) until water just begins to pour out the spout
- Wait for dripping to stop
- Place a measuring cylinder under the spout
- Carefully lower the object into the water
- Collect the displaced water in the measuring cylinder
- The volume of displaced water equals the volume of the object
- Calculate density: Use ρ = m / V
Alternative displacement method:
- Partially fill a measuring cylinder with water and record the volume (V₁)
- Carefully lower the object into the water
- Record the new volume reading (V₂)
- Volume of object = V₂ - V₁
Measuring density of liquids
- Measure the mass of an empty measuring cylinder
- Pour a known volume of liquid into the measuring cylinder (e.g., 50 cm³)
- Measure the combined mass of cylinder and liquid
- Calculate the liquid's mass: mass of liquid = combined mass - cylinder mass
- Calculate density: ρ = m / V
Worked examples
Example 1: Mass and weight calculations
Question: An astronaut has a mass of 80 kg.
(a) Calculate the astronaut's weight on Earth where g = 10 N/kg. [2]
(b) Calculate the astronaut's weight on Mars where g = 3.7 N/kg. [2]
(c) Explain why the astronaut's mass remains constant but weight changes. [2]
Solution:
(a) W = m × g [1 mark for equation]
W = 80 × 10 = 800 N [1 mark for answer]
(b) W = m × g [1 mark for equation]
W = 80 × 3.7 = 296 N [1 mark for answer]
(c) Mass is the amount of matter in the astronaut, which does not change with location. [1 mark]
Weight is the force of gravity acting on the mass, and gravitational field strength is weaker on Mars than Earth, so weight decreases. [1 mark]
Example 2: Density calculation for a regular object
Question: A rectangular metal block has dimensions 5.0 cm × 4.0 cm × 2.0 cm. The block has a mass of 432 g.
(a) Calculate the volume of the block in cm³. [2]
(b) Calculate the density of the metal in g/cm³. [2]
(c) Suggest which metal the block is made from. [1]
Solution:
(a) Volume = length × width × height [1 mark for method]
V = 5.0 × 4.0 × 2.0 = 40 cm³ [1 mark for answer]
(b) ρ = m / V [1 mark for equation]
ρ = 432 / 40 = 10.8 g/cm³ [1 mark for answer]
(c) The metal is likely silver (density ≈ 10.5 g/cm³) or lead (density ≈ 11.3 g/cm³). [1 mark for reasonable suggestion]
Example 3: Density using displacement method
Question: A student investigates the density of an irregular stone.
- Mass of stone = 156 g
- Initial water volume in measuring cylinder = 50 cm³
- Final water volume with stone submerged = 80 cm³
(a) Calculate the volume of the stone. [1]
(b) Calculate the density of the stone in g/cm³. [2]
(c) Convert this density to kg/m³. [2]
Solution:
(a) Volume = final volume - initial volume = 80 - 50 = 30 cm³ [1 mark]
(b) ρ = m / V [1 mark for equation]
ρ = 156 / 30 = 5.2 g/cm³ [1 mark for answer]
(c) To convert g/cm³ to kg/m³, multiply by 1000 [1 mark for method]
ρ = 5.2 × 1000 = 5200 kg/m³ [1 mark for answer]
Common mistakes and how to avoid them
Confusing mass and weight in everyday language: Many students write that "weight is measured in kilograms" because bathroom scales show kg. Weight is always measured in newtons; bathroom scales actually measure the force you exert and convert it to mass. Always use kg for mass and N for weight in physics.
Forgetting to convert units: Mixing centimetres with metres or grams with kilograms produces incorrect answers. When using ρ = m / V, ensure consistent units: either g and cm³ (giving g/cm³) or kg and m³ (giving kg/m³). Remember: 1 g/cm³ = 1000 kg/m³.
Rearranging equations incorrectly: Students often struggle to rearrange ρ = m / V. Use the density triangle or remember: multiply when the unknown is on top alone (m = ρ × V), divide when the unknown is on the bottom (V = m / ρ).
Stating that mass changes with location: Mass never changes regardless of gravitational field strength. Only weight changes. An object with 60 kg mass on Earth still has 60 kg mass on the Moon, in space, or on Jupiter.
Reading measuring cylinders incorrectly: Always read the bottom of the meniscus (curved water surface) at eye level. Reading from above or below introduces parallax error. In displacement experiments, ensure no air bubbles are trapped under the object.
Using the wrong value for g: CIE IGCSE Physics papers typically use g = 10 N/kg for calculations. Some students use 9.8 N/kg or 9.81 N/kg without checking the question or data sheet. Always use the value given in the question or provided in the data sheet.
Exam technique for Mass, Weight and Density
Command words matter: "Define" requires a precise statement (e.g., "mass is the amount of matter in an object"). "Calculate" requires showing the equation, substitution with units, and final answer with units. "Explain" requires reasoning with physics principles, not just stating facts. Questions asking you to "distinguish" or "compare" mass and weight appear frequently.
Show all working for calculations: Even if your final answer is incorrect, you can earn method marks by writing the correct equation and showing substitution. Always include units in your final answer. For 3-mark calculations, typically 1 mark for equation, 1 mark for substitution, 1 mark for answer with unit.
Experimental questions: Paper 4 (Alternative to Practical) and Paper 6 (Alternative to Coursework) frequently test density measurements. Know the complete method for measuring density of regular solids, irregular solids using displacement, and liquids. Be able to identify sources of error (e.g., water clinging to object, parallax error, trapped air bubbles) and suggest improvements (e.g., dry object before weighing, read at eye level, tap object to release bubbles).
Graph and data analysis: Questions may provide mass-volume data and ask you to calculate density from the gradient of a mass-volume graph. Remember: density = gradient when mass is plotted on the y-axis and volume on the x-axis. Alternatively, you may need to calculate individual densities and find a mean value.
Quick revision summary
Mass (kg) is the amount of matter in an object and never changes. Weight (N) is the gravitational force on that mass, calculated using W = m × g, where g = 10 N/kg on Earth. Weight varies with location. Density (kg/m³ or g/cm³) measures how much mass occupies a given volume, calculated using ρ = m / V. Regular objects use geometric formulae for volume; irregular objects use water displacement. Always show equations, substitute values with units, and check unit consistency in calculations.