Determining the density (\(\rho\)) of an object is crucial in various fields such as materials science, engineering, and everyday life applications. The density can be calculated using the formula:
\[ \rho = \dfrac{m}{V} \]
Where:
- \(\rho\) is the density of the object (in kilograms per cubic meter, kg/m³)
- \(m\) is the mass of the object (in kilograms, kg)
- \(V\) is the volume of the object (in cubic meters, m³)
Example 1: Determining the Density of a Metal Cube
Problem: A metal cube has a mass of 2 kg and a volume of 0.001 m³. What is the density of the metal?
Calculation:
Given:
- \(m = 2 \, \text{kg}\)
- \(V = 0.001 \, \text{m}^3\)
Using the formula:
\[ \rho = \dfrac{m}{V} = \dfrac{2}{0.001} = 2000 \, \text{kg/m}^3 \]
Answer: The density of the metal is 2000 kg/m³.
Example 2: Determining the Density of a Wooden Block
Problem: A wooden block has a mass of 0.5 kg and a volume of 0.0025 m³. What is the density of the wood?
Calculation:
Given:
- \(m = 0.5 \, \text{kg}\)
- \(V = 0.0025 \, \text{m}^3\)
Using the formula:
\[ \rho = \dfrac{m}{V} = \dfrac{0.5}{0.0025} = 200 \, \text{kg/m}^3 \]
Answer: The density of the wood is 200 kg/m³.
Example 3: Determining the Density of a Plastic Bottle
Problem: A plastic bottle has a mass of 0.1 kg and a volume of 0.0002 m³. What is the density of the plastic?
Calculation:
Given:
- \(m = 0.1 \, \text{kg}\)
- \(V = 0.0002 \, \text{m}^3\)
Using the formula:
\[ \rho = \dfrac{m}{V} = \dfrac{0.1}{0.0002} = 500 \, \text{kg/m}^3 \]
Answer: The density of the plastic is 500 kg/m³.
