Edexcel M3 2005 January — Question 1 7 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2005
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeConical pendulum – horizontal circle in free space (no surface)
DifficultyModerate -0.3 This is a standard conical pendulum problem requiring resolution of forces and application of circular motion formulas (T cos θ = mg, T sin θ = mrω²). While it involves multiple steps and simultaneous equations, it follows a well-established method taught directly in M3 with no novel problem-solving required, making it slightly easier than average.
Spec6.05c Horizontal circles: conical pendulum, banked tracks

A particle \(P\) of mass 0.5 kg is attached to one end of a light inextensible string of length 1.5 m. The other end of the string is attached to a fixed point \(A\). The particle is moving, with the string taut, in a horizontal circle with centre \(O\) vertically below \(A\). The particle is moving with constant angular speed 2.7 rad s\(^{-1}\). Find
  1. the tension in the string, [4]
  2. the angle, to the nearest degree, that \(AP\) makes with the downward vertical. [3]

A particle $P$ of mass 0.5 kg is attached to one end of a light inextensible string of length 1.5 m. The other end of the string is attached to a fixed point $A$. The particle is moving, with the string taut, in a horizontal circle with centre $O$ vertically below $A$. The particle is moving with constant angular speed 2.7 rad s$^{-1}$. Find

\begin{enumerate}[label=(\alph*)]
\item the tension in the string, [4]
\item the angle, to the nearest degree, that $AP$ makes with the downward vertical. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3 2005 Q1 [7]}}