Edexcel M5 — Question 1 5 marks

Exam BoardEdexcel
ModuleM5 (Mechanics 5)
Marks5
PaperDownload PDF ↗
TopicAdvanced work-energy problems
TypeBead on straight wire vector force
DifficultyStandard +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.
Spec1.10e Position vectors: and displacement1.10g Problem solving with vectors: in geometry6.02e Calculate KE and PE: using formulae

  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors.]
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 \(( 3 \mathbf { i } + \mathbf { k } ) \mathrm { m }\).

\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]}}