| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2006 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Bead on straight wire vector force |
| Difficulty | Moderate -0.3 This is a straightforward application of work = F·d requiring students to find the direction vector of the wire, scale it to 6m displacement, then compute a dot product. It's slightly easier than average because it's a direct formula application with clear setup and no conceptual obstacles, though the vector manipulation requires care. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication6.02b Calculate work: constant force, resolved component |
\begin{enumerate}
\item A bead is threaded on a straight wire. The vector equation of the wire is
\end{enumerate}
$$\mathbf { r } = \mathbf { i } - 3 \mathbf { j } + \mathbf { k } + t ( 2 \mathbf { i } - \mathbf { j } + 2 \mathbf { k } )$$
where the unit of length is the metre. The bead is moved from a point $A$ on the wire through a distance of 6 m along the wire to a point $B$ by a force $\mathbf { F } = ( 7 \mathbf { i } + 4 \mathbf { j } - 2 \mathbf { k } ) \mathrm { N }$.
Find the magnitude of the work done by $\mathbf { F }$ in moving the bead from $A$ to $B$.\\
(Total 4 marks)\\
\hfill \mbox{\textit{Edexcel M5 2006 Q1 [4]}}