Section 6.1: Density
Density is a measure of how much mass is contained in a given volume. It is a fundamental property of matter and is defined as:
Definition and Formula
\[
\rho = \frac{m}{V}
\]
where:
\( \rho \) = density (kg/m³)
\( m \) = mass (kg)
\( V \) = volume (m³)
Higher density means more mass is packed into a unit volume. This concept is crucial in fluids, buoyancy, and material science.
Example 1
A block has a mass of 2 kg and a volume of 0.001 m³. Find its density.
\(\rho = \frac{m}{V} = \frac{2}{0.001} = 2000 \, \text{kg/m³}\)
The block has a density of 2000 kg/m³.
Example 2
An object displaces 0.003 m³ of water and has a mass of 2.4 kg. Calculate its density.
\(\rho = \frac{m}{V} = \frac{2.4}{0.003} = 800 \, \text{kg/m³}\)
The object’s density is 800 kg/m³.
Practice Problems
- A cube of side 0.5 m has a mass of 50 kg. Find its density.
- A metal cylinder has a mass of 5 kg and a volume of 0.0005 m³. Determine its density.
- An object floats in water with 60% of its volume submerged. If the density of water is 1000 kg/m³, find the object’s density.
- A balloon contains helium with a mass of 0.1 kg and volume 0.125 m³. Calculate its density.
- A liquid has a mass of 2 kg for a volume of 0.0025 m³. Find its density.