QuestionJuly 10, 2025

1-2. Represent each of the following combinations of units in the correct SI form:(a) kN/mu s (b) Mg/mN and (c) MN/(kgcdot ms)

1-2. Represent each of the following combinations of units in the correct SI form:(a) kN/mu s (b) Mg/mN and (c) MN/(kgcdot ms)
1-2. Represent each of the following combinations of units in the correct SI form:(a) kN/mu s (b) Mg/mN and (c) MN/(kgcdot ms)

Solution
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Answer

(a) 10^9 \text{ N/s}, (b) 10^9 \text{ kg/N}, (c) 10^9 \text{ N/(kg \cdot s)} Explanation 1. Convert Units to Base SI Units (a) kN/\mu s: Convert kN to N and \mu s to s. 1 \text{ kN} = 10^3 \text{ N}, 1 \mu s = 10^{-6} \text{ s}. (b) Mg/mN: Convert Mg to kg and mN to N. 1 \text{ Mg} = 10^6 \text{ kg}, 1 \text{ mN} = 10^{-3} \text{ N}. (c) MN/(kg\cdot ms): Convert MN to N and ms to s. 1 \text{ MN} = 10^6 \text{ N}, 1 \text{ ms} = 10^{-3} \text{ s}. 2. Simplify the Expressions (a) kN/\mu s = \frac{10^3 \text{ N}}{10^{-6} \text{ s}} = 10^9 \text{ N/s}. (b) Mg/mN = \frac{10^6 \text{ kg}}{10^{-3} \text{ N}} = 10^9 \text{ kg/N}. (c) MN/(kg\cdot ms) = \frac{10^6 \text{ N}}{1 \text{ kg} \cdot 10^{-3} \text{ s}} = 10^9 \text{ N/(kg \cdot s)}.

Explanation

1. Convert Units to Base SI Units<br /> (a) $kN/\mu s$: Convert $kN$ to $N$ and $\mu s$ to $s$. $1 \text{ kN} = 10^3 \text{ N}$, $1 \mu s = 10^{-6} \text{ s}$.<br /> (b) $Mg/mN$: Convert $Mg$ to $kg$ and $mN$ to $N$. $1 \text{ Mg} = 10^6 \text{ kg}$, $1 \text{ mN} = 10^{-3} \text{ N}$.<br /> (c) $MN/(kg\cdot ms)$: Convert $MN$ to $N$ and $ms$ to $s$. $1 \text{ MN} = 10^6 \text{ N}$, $1 \text{ ms} = 10^{-3} \text{ s}$.<br /><br />2. Simplify the Expressions<br /> (a) $kN/\mu s = \frac{10^3 \text{ N}}{10^{-6} \text{ s}} = 10^9 \text{ N/s}$.<br /> (b) $Mg/mN = \frac{10^6 \text{ kg}}{10^{-3} \text{ N}} = 10^9 \text{ kg/N}$.<br /> (c) $MN/(kg\cdot ms) = \frac{10^6 \text{ N}}{1 \text{ kg} \cdot 10^{-3} \text{ s}} = 10^9 \text{ N/(kg \cdot s)}$.
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