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Motion, Forces and Energy - Mass, weight and density

Grade 11IGCSEPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

Mass (mm) is a measure of the quantity of matter in an object at rest relative to the observer. It is measured in kilograms (kgkg) and remains constant regardless of location.

Weight (WW) is the gravitational force acting on an object that has mass. It is measured in Newtons (NN) and changes depending on the gravitational field strength (gg).

The gravitational field strength (gg) is the force per unit mass, expressed as g=Wmg = \frac{W}{m}. On Earth, gg is approximately 9.8 N/kg9.8 \text{ N/kg} (or 10 N/kg10 \text{ N/kg} for some IGCSE syllabus variations).

Density (ρ\rho) is defined as the mass per unit volume of a substance. The standard SI unit is kg/m3kg/m^3, but g/cm3g/cm^3 is frequently used in laboratory experiments (1 g/cm3=1000 kg/m31 \text{ g/cm}^3 = 1000 \text{ kg/m}^3).

To determine the density of an irregularly shaped solid, the displacement method is used: the volume of the solid is equal to the volume of liquid it displaces in a measuring cylinder.

Objects float in a fluid if their density is less than the density of the fluid (ρobject<ρfluid\rho_{object} < \rho_{fluid}) and sink if their density is greater.

📐Formulae

W=mgW = m \cdot g

ρ=mV\rho = \frac{m}{V}

Virregular=VfinalVinitialV_{irregular} = V_{final} - V_{initial}

💡Examples

Problem 1:

A piece of rock has a mass of 450 g450 \text{ g} and a volume of 150 cm3150 \text{ cm}^3. Calculate its density in kg/m3kg/m^3.

Solution:

First, calculate density in g/cm3g/cm^3: ρ=450 g150 cm3=3 g/cm3\rho = \frac{450 \text{ g}}{150 \text{ cm}^3} = 3 \text{ g/cm}^3. Convert to kg/m3kg/m^3: 3×1000=3000 kg/m33 \times 1000 = 3000 \text{ kg/m}^3.

Explanation:

Density is found by dividing mass by volume. To convert from g/cm3g/cm^3 to kg/m3kg/m^3, we multiply by 10001000 because there are 1000 g1000 \text{ g} in a kgkg and 1,000,000 cm31,000,000 \text{ cm}^3 in a m3m^3.

Problem 2:

An object weighs 200 N200 \text{ N} on Earth (g=10 N/kgg = 10 \text{ N/kg}). What is its mass, and how much would it weigh on Mars where g=3.7 N/kgg = 3.7 \text{ N/kg}?

Solution:

Mass on Earth: m=Wg=200 N10 N/kg=20 kgm = \frac{W}{g} = \frac{200 \text{ N}}{10 \text{ N/kg}} = 20 \text{ kg}. Weight on Mars: W=mgmars=20 kg×3.7 N/kg=74 NW = m \cdot g_{mars} = 20 \text{ kg} \times 3.7 \text{ N/kg} = 74 \text{ N}.

Explanation:

The mass of the object is constant (20 kg20 \text{ kg}) across the universe. The weight changes because the gravitational field strength gg is different on Mars compared to Earth.

Mass, weight and density - Revision Notes & Key Formulas | IGCSE Grade 11 Physics