Hibbeler Statics 14E P1.14 — Evaluation of expression to correct SI Units

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

(212 mN)2=[212×10−3 N]2=0.0449 N2=4.49×10−2 N2\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

(52800 ms)2=[52800×10−3 s]2=2788 s2=2.79×103 s2\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

[548(106)]1/2 ms=23409 ms=23409×10−3 s=23.4×103×10−3 s=23.4 s\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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