| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Particle leaving a surface |
| Difficulty | Standard +0.3 This is a standard Hooke's law problem with equilibrium and energy conservation. Part (i) requires simple force balance, part (ii) involves recognizing that the particle leaves when the normal force becomes zero, and part (iii) applies conservation of energy. While it requires multiple steps and careful setup, the techniques are routine for M2 students with no novel insights needed—slightly easier than average. |
| Spec | 3.03n Equilibrium in 2D: particle under forces6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
A particle $P$ of mass $0.2\,\text{kg}$ is attached to one end of a light elastic string of natural length $0.75\,\text{m}$ and modulus of elasticity $21\,\text{N}$. The other end of the string is attached to a fixed point $A$ which is $0.8\,\text{m}$ vertically above a smooth horizontal surface. $P$ rests in equilibrium on the surface.
\begin{enumerate}[label=(\roman*)]
\item Find the magnitude of the force exerted on $P$ by the surface. [2]
\end{enumerate}
$P$ is now projected horizontally along the surface with speed $3\,\text{m s}^{-1}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Calculate the extension of the string at the instant when $P$ leaves the surface. [3]
\item Hence find the speed of $P$ at the instant when it leaves the surface. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2015 Q5 [8]}}