OCR M1 — Question 7 15 marks

Exam BoardOCR
ModuleM1 (Mechanics 1)
Marks15
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMotion on a slope
TypeMotion up then down slope
DifficultyStandard +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.
Spec3.02d 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 \(0.6\).
  1. Show that the magnitude of the frictional force acting on \(P\) is \(2.25\) N, correct to 3 significant figures. [3]
  2. Find the acceleration of \(P\) when it is moving
    1. up the plane,
    2. down the plane.
    [4]
  3. When \(P\) is moving up the plane, it passes through a point \(A\) with speed \(4\) m s\(^{-1}\).
    1. Find the length of time before \(P\) reaches its highest point.
    2. Find the total length of time for \(P\) to travel from the point \(A\) to its highest point and back to \(A\).
    [8]

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]}}