| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Elastic string on smooth inclined plane |
| Difficulty | Standard +0.8 This is a multi-stage mechanics problem requiring equilibrium analysis with Hooke's law, conservation of momentum for collision, energy conservation with elastic potential energy, and finding maximum speed conditions. While each individual technique is standard M2 content, the combination of collision dynamics, elastic strings, and energy methods across three connected parts with 11 total marks requires sustained problem-solving and careful tracking of the system state through multiple phases. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.03b Conservation of momentum: 1D two particles6.03l Newton's law: oblique impacts |
A particle $P$ is attached to one end of a light elastic string of natural length $1.2 \text{ m}$ and modulus of elasticity $12 \text{ N}$. The other end of the string is attached to a fixed point $O$ on a smooth plane inclined at an angle of $30°$ to the horizontal. $P$ rests in equilibrium on the plane, $1.6 \text{ m}$ from $O$.
\begin{enumerate}[label=(\roman*)]
\item Calculate the mass of $P$. [2]
\end{enumerate}
A particle $Q$, with mass equal to the mass of $P$, is projected up the plane along a line of greatest slope. When $Q$ strikes $P$ the two particles coalesce. The combined particle remains attached to the string and moves up the plane, coming to instantaneous rest after moving $0.2 \text{ m}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Show that the initial kinetic energy of the combined particle is $1 \text{ J}$. [4]
\end{enumerate}
The combined particle subsequently moves down the plane.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Calculate the greatest speed of the combined particle in the subsequent motion. [5]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2016 Q7 [11]}}