You can find weight using mass and density, but you'll need an extra step involving volume and the acceleration due to gravity. Here's how:
Calculating Weight
Weight is the force exerted on an object due to gravity. It's calculated using mass and the acceleration due to gravity (approximately 9.81 m/s² on Earth). The core formula is:
- Weight (N) = Mass (kg) * Acceleration due to gravity (m/s²)
This is highlighted in reference 3.
However, if you only have density and not mass, you can find the mass using density and volume as stated in reference 2:
- Density (kg/m³) = Mass (kg) / Volume (m³)
This formula can be rearranged to calculate mass:
- Mass (kg) = Density (kg/m³) * Volume (m³)
Combining the Formulas
So, to find weight when you have density and volume, you do the following steps as described in references 4 and 5:
-
Calculate Mass: Multiply the density of the object by its volume:
- Mass (kg) = Density (kg/m³) * Volume (m³)
-
Calculate Weight: Once you have the mass, multiply that result by the acceleration due to gravity (approx. 9.81 m/s²):
- Weight (N) = Mass (kg) * 9.81 m/s²
Example
Let's say you have a block of material with:
- Density = 1000 kg/m³
- Volume = 0.1 m³
- Find Mass: Mass = 1000 kg/m³ * 0.1 m³ = 100 kg
- Find Weight: Weight = 100 kg * 9.81 m/s² = 981 N
Therefore, the weight of the block is 981 Newtons.
Summary
| Step | Calculation | Formula |
|---|---|---|
| 1 | Find Mass | Mass (kg) = Density (kg/m³) * Volume (m³) |
| 2 | Find Weight | Weight (N) = Mass (kg) * 9.81 m/s² |
In short, reference 1 encourages you to think through the process which is: If you don't have the mass, you can derive it using the density and volume first, and then use the acceleration due to gravity with the mass to get the weight.
