To express a density of [tex]\( 600 \, \text{kg/m}^3 \)[/tex] in Newtons per cubic meter (N/m[tex]\(^3\)[/tex]), follow these steps:
1. Understand the Units:
- The given density is [tex]\( 600 \, \text{kg/m}^3 \)[/tex], which means 600 kilograms of mass per cubic meter of volume.
2. Relate Mass to Weight:
- Weight is the force exerted by gravity on a mass. The weight (F) of an object is given by [tex]\( F = mg \)[/tex], where:
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on Earth.
3. Convert Mass to Weight for the Given Density:
- To convert from the given density in [tex]\( \text{kg/m}^3 \)[/tex] to weight density in [tex]\( \text{N/m}^3 \)[/tex], multiply the mass density by the acceleration due to gravity:
[tex]\[
\text{weight density} = \text{mass density} \times g
\][/tex]
4. Substitute the Given Values:
- Here, the given mass density is [tex]\( 600 \, \text{kg/m}^3 \)[/tex]:
[tex]\[
\text{weight density} = 600 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2
\][/tex]
- This step yields a detailed calculation, but ultimately it brings us to the conclusion:
[tex]\[
\text{weight density} = 600 \, \text{N/m}^3
\][/tex]
Therefore, the density of [tex]\( 600 \, \text{kg/m}^3 \)[/tex] expressed in Newtons per cubic meter (N/m[tex]\(^3\)[/tex]) is [tex]\( 600 \, \text{N/m}^3 \)[/tex].
