| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2002 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Bead on straight wire vector force |
| Difficulty | Standard +0.8 This M5 question requires understanding that only the horizontal component of force does work (since the wire constrains motion), calculating work done via dot product of force and displacement vectors, then applying work-energy theorem. It combines vector mechanics with energy principles and requires insight about constraints, making it moderately harder than average A-level questions. |
| 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 \hspace{0pt} [In this question $\mathbf { i }$ and $\mathbf { j }$ are horizontal unit vectors.]
\end{enumerate}
A small smooth ring of mass 0.5 kg moves along a smooth horizontal wire. The only forces acting on the ring are its weight, the normal reaction from the wire, and a constant force ( $5 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$ ) N. The ring is initially at rest at the point with position vector $( \mathbf { i } + \mathbf { j } + \mathbf { k } ) \mathrm { m }$, relative to a fixed origin.
Find the speed of the ring as it passes through the point with position vector $( 3 \mathbf { i } + \mathbf { k } ) \mathrm { m }$.\\
\hfill \mbox{\textit{Edexcel M5 2002 Q1 [5]}}