| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2003 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Bead on straight wire vector force |
| Difficulty | Challenging +1.2 This M5 question requires work-energy theorem with 3D vectors and constraint forces. Students must identify that only the component of force parallel to the wire does work, resolve vectors correctly, and apply energy conservation. While requiring multiple steps and vector manipulation, it follows a standard M5 template without requiring novel geometric insight. |
| 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 In this question $\mathbf { i }$ and $\mathbf { j }$ are perpendicular unit vectors in a horizontal plane and $\mathbf { k }$ is a unit vector vertically upwards.
\end{enumerate}
A small smooth ring of mass 0.1 kg is threaded onto a smooth horizontal wire which is parallel to $( \mathbf { i } + 2 \mathbf { j } )$. The only forces acting on the ring are its weight, the normal reaction from the wire and a constant force $( \mathbf { i } + 2 \mathbf { j } - 2 \mathbf { k } )$ N. The ring starts from rest at the point $A$ on the wire, whose position vector relative to a fixed origin is $( 2 \mathbf { i } - 2 \mathbf { j } - 3 \mathbf { k } ) \mathrm { m }$, and passes through the point $B$ with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find the position vector of $B$.\\
(6)\\
\hfill \mbox{\textit{Edexcel M5 2003 Q1 [6]}}