SPS SPS FM Mechanics 2026 January — Question 6 8 marks

Exam BoardSPS
ModuleSPS FM Mechanics (SPS FM Mechanics)
Year2026
SessionJanuary
Marks8
TopicCircular Motion 1
TypeMultiple particles on string
DifficultyChallenging +1.2 This is a standard conical pendulum problem extended to two particles, requiring resolution of forces and circular motion equations. While it involves multiple particles and angles, the approach is methodical: resolve forces on each particle, apply F=mrω², and use geometry. The setup is more complex than a single conical pendulum but follows established techniques without requiring novel insight. The multi-part structure and need to work systematically through both particles places it above average difficulty.
Spec6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r
\includegraphics{figure_6} A particle \(P\) of mass 0.05 kg is attached to one end of a light inextensible string of length 1 m. The other end of the string is attached to a fixed point \(O\). A particle \(Q\) of mass 0.04 kg is attached to one end of a second light inextensible string. The other end of this string is attached to \(P\). The particle \(P\) moves in a horizontal circle of radius 0.8 m with angular speed \(\omega\) rad s\(^{-1}\). The particle \(Q\) moves in a horizontal circle of radius 1.4 m also with angular speed \(\omega\) rad s\(^{-1}\). The centres of the circles are vertically below \(O\), and \(O\), \(P\) and \(Q\) are always in the same vertical plane. The strings \(OP\) and \(PQ\) remain at constant angles \(\alpha\) and \(\beta\) respectively to the vertical (see diagram).
  1. Find the tension in the string \(OP\). [3]
  2. Find the value of \(\omega\). [3]
  3. Find the value of \(\beta\). [2]
\includegraphics{figure_6}

A particle $P$ of mass 0.05 kg is attached to one end of a light inextensible string of length 1 m. The other end of the string is attached to a fixed point $O$. A particle $Q$ of mass 0.04 kg is attached to one end of a second light inextensible string. The other end of this string is attached to $P$.

The particle $P$ moves in a horizontal circle of radius 0.8 m with angular speed $\omega$ rad s$^{-1}$. The particle $Q$ moves in a horizontal circle of radius 1.4 m also with angular speed $\omega$ rad s$^{-1}$. The centres of the circles are vertically below $O$, and $O$, $P$ and $Q$ are always in the same vertical plane. The strings $OP$ and $PQ$ remain at constant angles $\alpha$ and $\beta$ respectively to the vertical (see diagram).

\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string $OP$. [3]
\item Find the value of $\omega$. [3]
\item Find the value of $\beta$. [2]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM Mechanics 2026 Q6 [8]}}
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