Standard +0.8 This M5 question requires multiple coordinated steps: finding the direction vector AB, determining the force vector from the given line equation, computing the displacement, and applying the work formula W = F·d. While each individual step uses standard techniques (vectors, dot product), the combination of geometric setup, vector decomposition, and careful coordinate work makes this moderately challenging for A-level, though still within expected M5 scope.
A small bead is threaded on a smooth, straight horizontal wire which passes through the point \(A(-3, 1)\) and the point \(B(2, 5)\) in the \(x\)-\(y\) plane. The bead moves under the action of a horizontal force \(\mathbf{F}\) of magnitude \(8.5\) N whose line of action is parallel to the line with equation \(15x - 8y + 4 = 0\). The unit on both the \(x\) and \(y\) axes has length one metre. Find the work done by \(\mathbf{F}\) as it moves the bead from \(A\) to \(B\).
[8]
A small bead is threaded on a smooth, straight horizontal wire which passes through the point $A(-3, 1)$ and the point $B(2, 5)$ in the $x$-$y$ plane. The bead moves under the action of a horizontal force $\mathbf{F}$ of magnitude $8.5$ N whose line of action is parallel to the line with equation $15x - 8y + 4 = 0$. The unit on both the $x$ and $y$ axes has length one metre. Find the work done by $\mathbf{F}$ as it moves the bead from $A$ to $B$.
[8]
\hfill \mbox{\textit{Edexcel M5 2014 Q1 [8]}}