| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Bead on straight wire vector force |
| Difficulty | Standard +0.3 This M5 question requires understanding that perpendicular forces do no work, calculating displacement vectors, applying work-energy theorem, and solving for an unknown. While it involves 3D vectors and multiple forces, the method is standard: find displacement, use W = F·s for each force, apply ΔKE = total work. The conceptual part (a) is straightforward, and part (b) follows a routine procedure with no novel insight required, making it slightly easier than average. |
| Spec | 6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02i Conservation of energy: mechanical energy principle |
\begin{enumerate}
\item A bead of mass 0.5 kg is threaded on a smooth straight wire. The forces acting on the bead are a constant force $( 2 \mathbf { i } + 3 \mathbf { j } + \chi \mathbf { k } ) \mathrm { N }$, its weight $( - 4.9 \mathbf { k } ) \mathrm { N }$, and the reaction on the bead from the wire.\\
(a) Explain why the reaction on the bead from the wire does no work as the bead moves along the wire.
\end{enumerate}
The bead moves from the point $A$ with position vector $( \mathbf { i } + \mathbf { j } - 3 \mathbf { k } ) \mathrm { m }$ relative to a fixed origin $O$ to the point $B$ with position vector $( 3 \mathbf { i } - \mathbf { j } + 2 \mathbf { k } ) \mathrm { m }$. The speed of the bead at $A$ is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the speed of the bead at $B$ is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(b) Find the value of $x$.\\
\hfill \mbox{\textit{Edexcel M5 Q1 [7]}}