# Convert each of the following and express the answer using an appropriate prefix: (a) 175 lb /...

## Question:

Convert each of the following and express the answer using an appropriate prefix:

(a) {eq}\displaystyle 175\ \frac {lb}{ft^3} {/eq} to {eq}\displaystyle \frac {kN}{m^3} {/eq}.

(b) {eq}\displaystyle 6\ \frac {ft} h {/eq} to {eq}\displaystyle \frac {mm} s {/eq}.

(c) {eq}\displaystyle 835\ lb \cdot ft {/eq} to {eq}kN \cdot m {/eq}.

## Unit Conversions:

The unit conversions are very important part of the statistics and physics as in the problems related to different units of the things, it requires to make the unit of the thing same to be able to comparable. For example, speed of a car in kilometer per hour can be converted in miles per hour.

a)

The 175 pounds per cubic foot can be converted in kilonewton per cubic meters as:

1 pound per cubic feet (lb/ft^3) is 0.15709 kilonewton per cubic meters.

Hence,

{eq}\begin{align*} 175\,\,\dfrac{{lb}}{{f{t^3}}} &= 0.15709\left( {175} \right)\,\,\dfrac{{kN}}{{{m^3}}}\\ &= 27.49075\,\,\dfrac{{kN}}{{{m^3}}} \end{align*} {/eq}

Therefore, the converted value is {eq}27.49075\,\,\dfrac{{kN}}{{{m^3}}}. {/eq}

b)

The 175 foot per hour can be converted in millimeter per second as:

1 foot per hour (ft/h) is 0.08467 millimeter per second.

Hence,

{eq}\begin{align*} 6\,\,\dfrac{{ft}}{h} &= 0.08467\left( 6 \right)\,\,\dfrac{{mm}}{s}\\ &= 0.50802\,\,\dfrac{{mm}}{s} \end{align*} {/eq}

Therefore, the converted value is {eq}0.50802\,\,\dfrac{{mm}}{s}. {/eq}

c)

The 835 pound force foot can be converted in kilonewton meter as:

1 pound force foot (lb.ft) is 0.00136 kilonewton meter.

Hence,

{eq}\begin{align*} 835\,\,{\mathop{\rm lb}\nolimits} \cdot ft &= 0.00136\left( {835} \right)\,\,kN \cdot m\\ &= 1.1356\,\,kN \cdot m \end{align*} {/eq}

Therefore, the converted value is {eq}1.1356\,\,kN \cdot m. {/eq} 