How to solve

Units Focus Homework

Problem $1(4$ pts$)$

Convert the quantities in the left column to the units shown in the right column, making sure to show

each step. There is a document titled "NCEES fe$-$handbook$-10-0-1$ Unit Conversion" on Canvas for

reference. For example if asked to convert $10$ miles $\frac{?}{hr}$ to $k\frac{m}{m}in$ you would show the following:

$10\frac{\text{m}\text{i}\text{l}\text{e}\text{s}}{hr}x|\frac{5280ft}{1\text{m}\text{i}\text{l}\text{e}}||\frac{1(m)}{3\mathrm{.}281ft}||\frac{1(km)}{1000(m)}||\frac{1hr}{60(min)}|=0\mathrm{.}268\frac{(km)}{\text{m}\text{i}\text{n}}$

Problem $2(3$ pts$)$

Which of the following equations is dimensionally homogeneous $($i$.$e$.$ the units of each term agree$)?$ Show

your proof for each case below. $[$The units for each variable are listed below problem$]$

a$)F=m{V}^2$

b$)E^2=(m{c}^2{)}^2+(pc{)}^2$

c$)F=m\frac{v^3}{r}$

Where:

$t=$ time $(s)$

$F=$ force $($ N $)$

$m=$ mass $($ kg $)$

$V=$ velocity $(\frac{m}{s})$

$E=$ energy $($J$)$

$c=$ speed of light $(\frac{m}{s})$

$p=$ momentum $(k{g}^{**}\frac{m}{s})$

$r=$radius$(m)$