| 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 Hooke's law, energy conservation, collision dynamics (coalescence), and analysis of motion with varying elastic forces. Part (i) is routine equilibrium. Part (ii) requires careful energy accounting through extension changes (working backwards from given answer). Part (iii) demands finding maximum speed during oscillatory motion by identifying the equilibrium position and applying energy methods. The combination of elastic strings, inclined planes, and inelastic collisions with multiple energy transformations makes this significantly harder than standard M2 questions, though the structured parts provide guidance. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings6.03b Conservation of momentum: 1D two particles |
A particle $P$ is attached to one end of a light elastic string of natural length $1.2$ m and modulus of elasticity $12$ 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, $1.6$ 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 $0.2$ m.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Show that the initial kinetic energy of the combined particle is $1$ 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]}}