A concrete column has a diameter of 350 mm and a length of 2 m. If the density (mass/volume) of concrete is 2.45 Mg/m³, determine the weight of the column in pounds.

_{Engineering Mechanics: Statics 14th Edition by RC Hibbeler, Problem 1-19}

Solution:

The density of any material is given by the formula

\text{density}=\frac{\text{mass}}{\text{volume}}

From there, we can compute for the mass as

\text{mass}=\text{density} \times \text{volume}

We can solve for mass by multiplying density by volume. The density is already given, and we can compute for the volume of the concrete column by the formula of a volume of a cylinder.

\begin{align*}
\text{V} & = \pi \text{r}^2 \text{h}\\
& =\pi \left( \frac{0.35\ \text{m}}{2} \right)^2 \left( 2 \ \text{m} \right)\\
& =0.1924 \ \text{m}^3
\end{align*}

Therefore, the mass of the concrete column is

\begin{align*}
\text{mass} & =\text{density} \times \text{volume}\\
& = \left( 2.45 \times 10^3 \ \text{kg/m}^3 \right)\times \left( 0.1924 \ \text{m}^3 \right)\\
& =471.44 \ \text{kg}\\
\end{align*}

Now, we can solve for the weight by multiplying the mass by the acceleration due to gravity, g.

\begin{align*}
\text{Weight} & = \text{mass} \times \text{acceleration due to gravity} \\
& = 471.44 \ \text{kg} \times 9.81 \ \text{m/s}^2 \\
& = 4624.78 \ \text{N}
\end{align*}

Finally, we can convert the weight in Newtons to weight in pounds.

\begin{align*}
4624.78\ \text{N} & = 4624.78\ \text{N}\times \frac{1\ \text{lb}}{4.4482\ \text{N}}\\
& = 1039.70\ \text{lb}\\
& = 1.04\times 10^3 \  \text{lb}\\
& = 1.04 \ \text{kip}
\end{align*}