How do you find weight with mass and density?

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:

1. Calculate Mass: Multiply the density of the object by its volume:

   • Mass (kg) = Density (kg/m³) * Volume (m³)

2. 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

1. Find Mass: Mass = 1000 kg/m³ * 0.1 m³ = 100 kg
2. Find Weight: Weight = 100 kg * 9.81 m/s² = 981 N

Therefore, the weight of the block is 981 Newtons.

Summary

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.