OCR FM1 AS 2021 June — Question 2 6 marks

Exam BoardOCR
ModuleFM1 AS (Further Mechanics 1 AS)
Year2021
SessionJune
Marks6
TopicWork done and energy
TypeParticle on smooth curved surface
DifficultyStandard +0.8 This is a standard energy conservation problem in circular motion with a rod, typical of FM1. Part (a) requires applying conservation of energy to find speed at a given angle (routine 4-mark calculation). Part (b) asks for the angle at instantaneous rest (straightforward 2-mark application). While it involves Further Maths content (making it harder than pure maths on an absolute scale), it's a textbook exercise requiring no novel insight—just direct application of mechanical energy principles.
Spec6.02i Conservation of energy: mechanical energy principle

A particle \(P\) of mass 5.6 kg is attached to one end of a light rod of length 2.1 m. The other end of the rod is freely hinged to a fixed point \(O\). The particle is initially at rest directly below \(O\). It is then projected horizontally with speed \(5 \text{ ms}^{-1}\). In the subsequent motion, the angle between the rod and the downward vertical at \(O\) is denoted by \(\theta\) radians, as shown in the diagram. \includegraphics{figure_2}
  1. Find the speed of \(P\) when \(\theta = \frac{1}{4}\pi\). [4]
  2. Find the value of \(\theta\) when \(P\) first comes to instantaneous rest. [2]

A particle $P$ of mass 5.6 kg is attached to one end of a light rod of length 2.1 m. The other end of the rod is freely hinged to a fixed point $O$.

The particle is initially at rest directly below $O$. It is then projected horizontally with speed $5 \text{ ms}^{-1}$. In the subsequent motion, the angle between the rod and the downward vertical at $O$ is denoted by $\theta$ radians, as shown in the diagram.

\includegraphics{figure_2}

\begin{enumerate}[label=(\alph*)]
\item Find the speed of $P$ when $\theta = \frac{1}{4}\pi$. [4]

\item Find the value of $\theta$ when $P$ first comes to instantaneous rest. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR FM1 AS 2021 Q2 [6]}}