OCR H240/03 2021 November — Question 10 6 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2021
SessionNovember
Marks6
PaperDownload PDF ↗
TopicForces, equilibrium and resultants
TypeMaximum/minimum force for equilibrium
DifficultyStandard +0.3 This is a standard A-level mechanics equilibrium problem requiring resolution of forces and application of friction law F ≤ μR. Part (a) is trivial force diagram drawing. Part (b) involves resolving horizontally and vertically, finding the normal reaction R = 50 - 15sin(θ), then applying F ≤ μR to get the required inequality. The steps are routine and follow a standard textbook approach with no novel insight required, making it slightly easier than average.
Spec3.03m Equilibrium: sum of resolved forces = 0

\includegraphics{figure_10} A block \(D\) of weight 50 N lies at rest in equilibrium on a fixed rough horizontal surface. A force of magnitude 15 N is applied to \(D\) at an angle \(\theta\) to the horizontal (see diagram).
  1. Complete the diagram in the Printed Answer Booklet showing all the forces acting on \(D\). [1]
It is given that \(D\) remains at rest and the coefficient of friction between \(D\) and the surface is 0.2.
  1. Show that $$15\cos\theta - 3\sin\theta \leqslant 10.$$ [5]

\includegraphics{figure_10}

A block $D$ of weight 50 N lies at rest in equilibrium on a fixed rough horizontal surface. A force of magnitude 15 N is applied to $D$ at an angle $\theta$ to the horizontal (see diagram).

\begin{enumerate}[label=(\alph*)]
\item Complete the diagram in the Printed Answer Booklet showing all the forces acting on $D$. [1]
\end{enumerate}

It is given that $D$ remains at rest and the coefficient of friction between $D$ and the surface is 0.2.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that
$$15\cos\theta - 3\sin\theta \leqslant 10.$$ [5]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/03 2021 Q10 [6]}}