Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (212 mN)2, (b) (52800 ms)2, and (c) [548(106)]1/2 ms.
Engineering Mechanics: Statics 14th Edition by RC Hibbeler, Problem 1-14
Solution:
Part A
\begin{align*}
\left( 212 \ \text{mN} \right)^2 & = \left[ 212\times 10^{-3} \ \text{N} \right]^2 \\
& = 0.0449 \ \text{N}^2 \\
& = 4.49\times 10^{-2} \ \text{N}^2\\
\end{align*}Part B
\begin{align*}
\left( 52800 \ \text{ms} \right)^2 & = \left[ 52800\times 10^{-3} \ \text{s} \right]^2 \\
& =2788 \ \text{s}^2 \\
& = 2.79 \times 10^3 \ \text{s}^2
\end{align*}Part C
\begin{align*}
\left[ 548\left( 10^6 \right) \right]^{1/2} \ \text{ms}& =23409 \ \text{ms}\\
& =23409\times 10^{-3}\ \text{s}\\
& = 23.4\times 10^3\times 10^{-3} \ \text{s}\\
& = 23.4 \ \text{s}
\end{align*}
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