Determining the mass (\(m\)) of an object is fundamental in physics and engineering. The mass can be calculated using the formula:
\[ m = \rho \cdot V \]
Where:
- \(m\) is the mass of the object (in kilograms, kg)
- \(\rho\) is the density of the object (in kilograms per cubic meter, kg/m³)
- \(V\) is the volume of the object (in cubic meters, m³)
Example 1: Determining the Mass of a Steel Rod
Problem: A steel rod has a density of 7850 kg/m³ and a volume of 0.002 m³. What is the mass of the steel rod?
Calculation:
Given:
- \(\rho = 7850 \, \text{kg/m}^3\)
- \(V = 0.002 \, \text{m}^3\)
Using the formula:
\[ m = \rho \cdot V = 7850 \cdot 0.002 = 15.7 \, \text{kg} \]
Answer: The mass of the steel rod is 15.7 kg.
Example 2: Determining the Mass of an Aluminum Can
Problem: An aluminum can has a density of 2700 kg/m³ and a volume of 0.0003 m³. What is the mass of the aluminum can?
Calculation:
Given:
- \(\rho = 2700 \, \text{kg/m}^3\)
- \(V = 0.0003 \, \text{m}^3\)
Using the formula:
\[ m = \rho \cdot V = 2700 \cdot 0.0003 = 0.81 \, \text{kg} \]
Answer: The mass of the aluminum can is 0.81 kg.
Example 3: Determining the Mass of a Water Container
Problem: A water container has a density of 1000 kg/m³ and a volume of 0.05 m³. What is the mass of the water container?
Calculation:
Given:
- \(\rho = 1000 \, \text{kg/m}^3\)
- \(V = 0.05 \, \text{m}^3\)
Using the formula:
\[ m = \rho \cdot V = 1000 \cdot 0.05 = 50 \, \text{kg} \]
Answer: The mass of the water container is 50 kg.
