The elements of a wheel$-$height adjuster for a lawn mower are shown. The wheel $($partial outline shown dashed for clarity$)$ bolts

through the hole at $A,$ which goes through the bracket but not the housing $H.$ A pin fixed to the back of the bracket at $B$ fits into one of

the seven elongated holes of the housing. For the position shown, determine the magnitude of the force at the pin $B$ and the magnitude

of the reaction at the pivot $O.$ The wheel supports a force of magnitude $\frac{W}{4},$ where $W$ is the weight of the entire mower.

Answers:

$F_B=$

$F_O=,W$