#### Example 4.3.2. Verignon’s Theorem: Parallel and Perpendicular Components.

A gardener is moving soil with a wheelbarrow. The length of the handle from \(A\) to \(B\) is \(\inch{45}\text{,}\) and in the position shown, \(\theta\) is \(\ang{25}\text{.}\)

Find the moment created about axle \(A\) when she applies a vertical \(\lb{30}\) force at \(B\) by resolving force \(F\) into components parallel and perpendicular to the handle.

## Answer.

\begin{equation*}
M_A = \inlb{1224}
\end{equation*}

## Solution.

When the handle makes an angle of \(\theta\) with the horizontal axis, the perpendicular component of \(F\) makes the same angle with the vertical, so resolving \(F\) into perpendicular and parallel components gives:

\begin{align*}
F_\perp \amp = F \cos \theta = \lb{27.19} \amp F_\| \amp = F \sin \theta = \lb{12.68}
\end{align*}

Summing the moments of the components we find

\begin{equation*}
M_A = F_\perp (\inch{45}) + F_\| (0) = \inlb{1224}
\end{equation*}

Note that the parallel component does not contribute to the moment.