## Question:

The loading on the bookshelf is distributed as shown. Determine the magnitude of the equivalent resultant location, measured from point $O$.

Given:

${ w }_{ 1 }$ = $2\frac { Ib }{ ft }$

${ w }_{ 2 }$ = $3.5\frac { Ib }{ ft }$

$a$ = $2.75$ $ft$

$b$ = $4$ $ft$

$c$ = $1.5$ $ft$

## Step-by-step

Guesses$\quad \quad R=1Ib\quad \quad d$ = $1$ $ft$

Given $\quad \quad { w }_{ 1 }b+{ w }_{ 2 }c\quad$ = $R$

$\quad \quad\quad { w }_{ 1 }b\left( a-\frac { b }{ 2 } \right)$ $– { w }_{ 2 }c\left( \frac { c }{ 2 } +b-a \right)$ = $-dR$

$\left( \begin{matrix} R \\ d \end{matrix} \right)$ = $Find (R,d)$ $\quad \quad R$ = $13.25$ $Ib$ $\quad \quad d$ = $0.34$ $ft$