| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with force at angle to slope |
| Difficulty | Standard +0.3 This is a standard M1 friction problem with two parts: (i) finding coefficient of friction from constant speed motion (routine equilibrium on slope), and (ii) resolving forces with an applied force at an angle. Part (ii) requires careful resolution in two directions and understanding that friction acts down the slope, but follows standard M1 techniques without requiring novel insight. The 7 marks for part (ii) reflect multiple resolution steps rather than conceptual difficulty. |
| Spec | 3.03e Resolve forces: two dimensions3.03f Weight: W=mg3.03m Equilibrium: sum of resolved forces = 03.03r Friction: concept and vector form3.03v Motion on rough surface: including inclined planes |
A block $B$ of weight $10$ N is projected down a line of greatest slope of a plane inclined at an angle of $20°$ to the horizontal. $B$ travels down the plane at constant speed.
\begin{enumerate}[label=(\roman*)]
\item \begin{enumerate}[label=(\alph*)]
\item Find the components perpendicular and parallel to the plane of the contact force between $B$ and the plane. [2]
\item Hence show that the coefficient of friction is $0.364$, correct to $3$ significant figures. [2]
\end{enumerate}
\item
\includegraphics{figure_6}
$B$ is in limiting equilibrium when acted on by a force of $T$ N directed towards the plane at an angle of $45°$ to a line of greatest slope (see diagram). Given that the frictional force on $B$ acts down the plane, find $T$. [7]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 2009 Q6 [11]}}