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Forces and Motion - Density

Grade 9IB

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

🔑Concepts

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Density is a measure of how much mass is contained within a given volume of a substance, defined by the ratio ρ=mV\rho = \frac{m}{V}.

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The SI unit for density is kilograms per cubic meter (kg/m3kg/m^3), but it is frequently measured in grams per cubic centimeter (g/cm3g/cm^3).

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Conversion between units: 1 g/cm3=1000 kg/m31 \text{ g/cm}^3 = 1000 \text{ kg/m}^3.

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For regular solids, volume VV can be calculated using geometric formulas (e.g., V=l×w×hV = l \times w \times h). For irregular solids, the displacement method (using a Eureka can or measuring cylinder) is used.

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The density of pure water is approximately 1000 kg/m31000 \text{ kg/m}^3 or 1 g/cm31 \text{ g/cm}^3. Objects with a density less than the fluid they are in will float, while those with a higher density will sink.

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Density is an intensive property, meaning it does not change regardless of the amount of the substance present, provided temperature and pressure remain constant.

📐Formulae

ρ=mV\rho = \frac{m}{V}

m=ρ×Vm = \rho \times V

V=mρV = \frac{m}{\rho}

💡Examples

Problem 1:

An irregular piece of rock is placed into a displacement can filled with water. The volume of water displaced is 45 cm345 \text{ cm}^3. If the mass of the rock is 121.5 g121.5 \text{ g}, calculate the density of the rock in g/cm3\text{g/cm}^3.

Solution:

Given: Mass m=121.5 gm = 121.5 \text{ g} Volume V=45 cm3V = 45 \text{ cm}^3

Using the formula: ρ=mV\rho = \frac{m}{V} ρ=121.545\rho = \frac{121.5}{45} ρ=2.7 g/cm3\rho = 2.7 \text{ g/cm}^3

Explanation:

The volume of the displaced water is equal to the volume of the submerged object. Dividing the mass by this volume gives the density.

Problem 2:

A wooden block has a density of 0.6 g/cm30.6 \text{ g/cm}^3 and a volume of 250 cm3250 \text{ cm}^3. Calculate the mass of the block.

Solution:

Given: Density ρ=0.6 g/cm3\rho = 0.6 \text{ g/cm}^3 Volume V=250 cm3V = 250 \text{ cm}^3

Using the formula: m=ρ×Vm = \rho \times V m=0.6×250m = 0.6 \times 250 m=150 gm = 150 \text{ g}

Explanation:

To find the mass, rearrange the density formula to multiply the density by the volume.

Problem 3:

A liquid has a mass of 400 g400 \text{ g} and a density of 0.8 g/cm30.8 \text{ g/cm}^3. What is the volume of the liquid?

Solution:

Given: Mass m=400 gm = 400 \text{ g} Density ρ=0.8 g/cm3\rho = 0.8 \text{ g/cm}^3

Using the formula: V=mρV = \frac{m}{\rho} V=4000.8V = \frac{400}{0.8} V=500 cm3V = 500 \text{ cm}^3

Explanation:

The volume is calculated by dividing the mass of the substance by its density.