Density

Density is a key property of matter that affects whether objects float or sink. In this section, we will learn how to calculate the density of different types of materials, and how to use density data to determine the buoyancy of objects or liquids.

Defining density

Density is defined as the mass per unit volume of a substance. It tells us how much mass is packed into a given volume and is represented by the symbol ρ (rho).

• The formula for calculating density is:

• Where:

  • ρ is the density (in kilograms per cubic meter, kg/m³).

  • m is the mass (in kilograms, kg).

  • V is the volume (in cubic meters, m³).

Determining density

To determine the density of a substance, it is important to measure both its mass and its volume accurately. The procedure for determining the density depends on whether the material is a liquid, a regular solid, or an irregular solid.

(a) Density of a Liquid:

• To determine the density of a liquid, you first measure its mass using a balance.

• Then, measure the volume of the liquid using a measuring cylinder or similar container.

• Finally, use the density formula ρ=mV​ to calculate the density.

(b) Density of a Regularly Shaped Solid:

• For a solid with a regular shape, such as a cube or cylinder, calculate the volume using geometrical formulas (e.g., V = length × width × height for a cube).

• Measure the mass of the solid using a balance.

• Use the density formula to calculate the density.

(c) Density of an Irregularly Shaped Solid:

• For an irregularly shaped solid, measure its mass using a balance.

• Determine the volume using the displacement method:

  • Fill a measuring cylinder with a known volume of water.

  • Carefully submerge the solid in the water and measure the new volume.

  • The difference between the initial and final volume is the volume of the solid.

  • Use the density formula to find the density.

Determining bouyancy

Buoyancy refers to whether an object will float or sink in a fluid. Whether an object floats or sinks depends on its density relative to the density of the fluid it is placed in:

• If an object’s density is less than the density of the fluid, the object will float.

• If an object’s density is greater than the density of the fluid, the object will sink.

For example:

• If a wooden block (density less than water) is placed in water, it will float.

• If a metal block (density greater than water) is placed in water, it will sink.

Density and liquid layers