Question $5$: $10$ points

The cable structure shown in Figure carries a triangular load that is zero at the left$-$hand support and increases to $w_o\frac{N}{m}$ at the right$-$hand support.

Minir

$[5$a$]$ Starting from first principles $($i$.$e$.,$ the differential equation$),$ show that cable profile is given by the equation

$y(x)=\frac{w_o{x}^3}{180H}+(1-\frac{5w_o}{H})x$

Now let us assume that the minumum value of the cable profile occurs at $x=10.$

$[5$b$]$ Show that the horizontal cable force is:

$H=\frac{20w_o}{6}$

$[5$c$]$ Draw and label a diagram showing the horizontal and vertical components of reaction force at the leftand right$-$hand cable supports.