| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion up then down slope |
| Difficulty | Standard +0.3 This is a standard M1 inclined plane problem with friction, requiring resolution of forces, Newton's second law, and kinematics with constant acceleration. All steps follow routine procedures: calculating friction force using F=μR, finding accelerations in both directions, and applying suvat equations. The multi-part structure and 15 marks indicate moderate length, but no novel problem-solving or geometric insight is required—slightly easier than the typical average A-level question. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03f Weight: W=mg3.03r Friction: concept and vector form3.03v Motion on rough surface: including inclined planes |
A particle $P$ of mass $0.5$ kg moves upwards along a line of greatest slope of a rough plane inclined at an angle of $40°$ to the horizontal. $P$ reaches its highest point and then moves back down the plane. The coefficient of friction between $P$ and the plane is $0.6$.
\begin{enumerate}[label=(\roman*)]
\item Show that the magnitude of the frictional force acting on $P$ is $2.25$ N, correct to 3 significant figures. [3]
\item Find the acceleration of $P$ when it is moving
\begin{enumerate}[label=(\alph*)]
\item up the plane,
\item down the plane.
\end{enumerate}
[4]
\item When $P$ is moving up the plane, it passes through a point $A$ with speed $4$ m s$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Find the length of time before $P$ reaches its highest point.
\item Find the total length of time for $P$ to travel from the point $A$ to its highest point and back to $A$.
\end{enumerate}
[8]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q7 [15]}}