| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Particle on inclined plane with friction |
| Difficulty | Moderate -0.3 This is a straightforward M2 mechanics question testing standard impulse-momentum and energy methods. Part (i) is direct application of impulse = change in momentum; part (ii) uses conservation of energy with no friction; part (iii) applies work-energy theorem with friction. All parts follow textbook procedures with no novel problem-solving required, though the multi-step nature and need to apply multiple mechanics principles makes it slightly more substantial than the most basic recall questions. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes6.02d Mechanical energy: KE and PE concepts6.02i Conservation of energy: mechanical energy principle6.03e Impulse: by a force6.03f Impulse-momentum: relation |
A particle of mass 0.5 kg is held at rest at a point $P$, which is at the bottom of an inclined plane. The particle is given an impulse of 1.8 N s directed up a line of greatest slope of the plane.
\begin{enumerate}[label=(\roman*)]
\item Find the speed at which the particle starts to move. [2]
\end{enumerate}
The particle subsequently moves up the plane to a point $Q$, which is 0.3 m above the level of $P$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Given that the plane is smooth, find the speed of the particle at $Q$. [4]
\end{enumerate}
It is given instead that the plane is rough. The particle is now projected up the plane from $P$ with initial speed 3 ms$^{-1}$, and comes to rest at a point $R$ which is 0.2 m above the level of $P$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Given that the plane is inclined at 30° to the horizontal, find the magnitude of the frictional force on the particle. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR M2 2013 Q6 [10]}}