Weight density is the weight per unit volume of a substance, while mass density is the mass per unit volume; therefore, weight density is the mass density multiplied by the acceleration due to gravity.
Here's a breakdown of the relationship:
Understanding Mass Density
Mass density (often represented by the Greek letter ρ, rho) is a fundamental property of a material that describes how much mass is packed into a given volume. It is defined as:
ρ = m/V
Where:
- ρ = mass density
- m = mass
- V = volume
The SI unit for mass density is kilograms per cubic meter (kg/m³).
Understanding Weight Density
Weight density (often represented by the Greek letter γ, gamma) is the weight per unit volume of a substance. Since weight is the force of gravity acting on an object (w = mg), weight density is given by:
γ = w/V = mg/V
Where:
- γ = weight density
- w = weight
- V = volume
- m = mass
- g = acceleration due to gravity
The SI unit for weight density is Newtons per cubic meter (N/m³).
The Relationship Explained
Comparing the two formulas, we can see a direct relationship:
γ = mg/V = (m/V) g = ρ g
Therefore, weight density is equal to mass density multiplied by the acceleration due to gravity (g). The value of 'g' is approximately 9.81 m/s² on the Earth's surface.
Examples
Let's consider water as an example:
- Mass density of water (ρ): Approximately 1000 kg/m³
- Acceleration due to gravity (g): Approximately 9.81 m/s²
- Weight density of water (γ): γ = ρ g = 1000 kg/m³ 9.81 m/s² = 9810 N/m³
Table Summarizing the Difference
| Feature | Mass Density (ρ) | Weight Density (γ) |
|---|---|---|
| Definition | Mass per unit volume | Weight per unit volume |
| Formula | ρ = m/V | γ = w/V = ρg |
| SI Unit | kg/m³ | N/m³ |
| Dependence | Mass and Volume | Mass, Volume, Gravity |
In summary, weight density is directly related to mass density through the acceleration due to gravity. It represents the force exerted by gravity on a unit volume of a substance.
