Fluid mechanics density problem

[velocityay]

Homework Statement

If the density of iron is 7.8x10³kg/m³, what is the highest possible height of a square based column of sides=40cm and mass of 1,000kg?

Homework Equations

$$\rho$$=m/v
Fg=$$\rho$$vg (I think?)

The Attempt at a Solution

I took the length of the side of the square and used it to find a volume which I got to be .064m³, I'm really not sure where to go from here or if I understand what the question is asking

 

[rl.bhat]

Find the area of the base.
Volume of the column = Area* height.
Density = mass /volume.

 

[tomcue]

.I would approach this problem by first understanding the concept of density and how it relates to the given information. Density is defined as the mass of a substance per unit volume. In other words, it is how much matter is packed into a given space.

In this problem, we are given the density of iron (7.8x103 kg/m3), the mass of the column (1,000 kg), and the length of one side of the square base (40 cm or 0.4 m). The goal is to find the maximum height of the column.

To solve this problem, we can use the formula for density: ρ = m/v, where ρ is the density, m is the mass, and v is the volume. We already know the density and mass, so we can rearrange the equation to solve for the volume: v = m/ρ. Plugging in the values, we get v = 1,000 kg / 7.8x103 kg/m3 = 0.128 m3.

Next, we need to find the volume of the square base. Since it is a square, we can use the formula for volume of a cube: v = s3, where s is the length of one side. Plugging in the value for s (0.4 m), we get v = (0.4 m)3 = 0.064 m3.

Now, we can use the formula for volume of a cylinder to find the maximum height of the column: V = πr2h, where V is the volume, r is the radius of the base, and h is the height. Since we know the volume of the base (0.064 m3) and the radius (0.2 m, half of the side length), we can solve for the height: h = V / (πr2) = 0.064 m3 / (π(0.2 m)2) ≈ 1.02 m.

Therefore, the highest possible height of the column is approximately 1.02 meters.

As for the equation Fg = ρvg, it is the equation for calculating the force of gravity (Fg) on an object with a certain mass (m) and volume (v) due to the acceleration of gravity (g), which is approximately 9.8 m/s2 on Earth. This equation is not directly related to the