| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Marks | 5 |
| Paper | 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 the applied force does work (since the wire constrains vertical motion), calculating the displacement vector, applying work-energy theorem, and handling 3D vectors with constraints. It's above average difficulty due to the constraint analysis and 3D vector manipulation, but follows a standard work-energy approach once the constraint is recognized. |
| Spec | 1.10e Position vectors: and displacement1.10g Problem solving with vectors: in geometry6.02e Calculate KE and PE: using formulae |
\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 $( 5 \mathbf { i } + \mathbf { j } - 3 \mathbf { k } ) \mathrm { N }$. 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 Q1 [5]}}