To find mass when you know the mass density, you need to use the relationship between mass, density, and volume. The formula to calculate mass, given density and volume, is:
Understanding the Relationship
Mass density, or simply density, describes how much "stuff" is packed into a given space. It is the amount of mass per unit of volume.
The key is the formula which relates mass (m), density (ρ), and volume (V). This formula can be expressed in three different ways, depending on which variable you want to calculate:
| Variable to Find | Formula |
|---|---|
| Mass (m) | m = ρ × V |
| Density (ρ) | ρ = m ÷ V |
| Volume (V) | V = m ÷ ρ |
Calculating Mass
The formula Mass = Density x Volume is used to calculate mass when density and volume are known. Let's break down the process:
- Identify the density (ρ): This is given in units like grams per cubic centimeter (g/cm³), kilograms per cubic meter (kg/m³), or pounds per cubic foot (lb/ft³).
- Identify the volume (V): The volume is expressed in units such as cubic centimeters (cm³), cubic meters (m³), or cubic feet (ft³), depending on the unit of density. Ensure that the units of density and volume are consistent.
- Multiply density and volume: Multiply the numerical values of density and volume together.
- Include appropriate units: The units of mass depend on the units of density and volume used in the calculation. For instance, if density is in g/cm³ and volume is in cm³, the resulting mass will be in grams (g). If density is in kg/m³ and volume is in m³, the resulting mass will be in kilograms (kg).
Example
Let's say you have a material with a density of 2 g/cm³ and a volume of 10 cm³. To find the mass, you multiply these two values:
- Mass = 2 g/cm³ × 10 cm³
- Mass = 20 g
Therefore, the mass of the material is 20 grams.
Key Takeaways
- The relationship between mass, density, and volume is a fundamental concept in physics.
- You can calculate the mass by multiplying the density by the volume of an object.
- Ensure the units of density and volume are consistent to obtain the correct units for mass.
