OCR M1 — Question 3 8 marks

Exam BoardOCR
ModuleM1 (Mechanics 1)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFriction
TypeConnected particles with friction
DifficultyStandard +0.3 This is a standard M1 equilibrium problem with friction requiring straightforward application of Newton's laws and friction formulae. Part (i) involves resolving forces and using F=μR in limiting equilibrium (routine 5-mark question). Part (ii) adds a horizontal force but uses the same principles. The problem requires no novel insight—just systematic application of standard mechanics techniques with clear force diagrams.
Spec3.03k Connected particles: pulleys and equilibrium3.03r Friction: concept and vector form3.03u Static equilibrium: on rough surfaces

\includegraphics{figure_3} A block \(B\) of mass \(0.4\) kg and a particle \(P\) of mass \(0.3\) kg are connected by a light inextensible string. The string passes over a smooth pulley at the edge of a rough horizontal table. \(B\) is in contact with the table and the part of the string between \(B\) and the pulley is horizontal. \(P\) hangs freely below the pulley (see diagram).
  1. The system is in limiting equilibrium with the string taut and \(P\) on the point of moving downwards. Find the coefficient of friction between \(B\) and the table. [5]
  2. A horizontal force of magnitude \(X\) N, acting directly away from the pulley, is now applied to \(B\). The system is again in limiting equilibrium with the string taut, and with \(P\) now on the point of moving upwards. Find the value of \(X\). [3]

\includegraphics{figure_3}

A block $B$ of mass $0.4$ kg and a particle $P$ of mass $0.3$ kg are connected by a light inextensible string. The string passes over a smooth pulley at the edge of a rough horizontal table. $B$ is in contact with the table and the part of the string between $B$ and the pulley is horizontal. $P$ hangs freely below the pulley (see diagram).

\begin{enumerate}[label=(\roman*)]
\item The system is in limiting equilibrium with the string taut and $P$ on the point of moving downwards. Find the coefficient of friction between $B$ and the table. [5]
\item A horizontal force of magnitude $X$ N, acting directly away from the pulley, is now applied to $B$. The system is again in limiting equilibrium with the string taut, and with $P$ now on the point of moving upwards. Find the value of $X$. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR M1  Q3 [8]}}