| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Vertical elastic string: projected vertically or mid-motion analysis |
| Difficulty | Standard +0.3 This is a standard Hooke's law and energy conservation problem with straightforward application of formulas. Part (i) requires simple equilibrium (T=mg), part (ii)(a) uses T=λx/l directly, and part (ii)(b) applies energy conservation with elastic PE. All steps are routine for M2 students with no novel insight required, making it slightly easier than average. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
A particle $P$ of mass $0.3$ kg is attached to one end of a light elastic string of natural length $0.9$ m and modulus of elasticity $18$ N. The other end of the string is attached to a fixed point $O$ which is $3$ m above the ground.
\begin{enumerate}[label=(\roman*)]
\item Find the extension of the string when $P$ is in the equilibrium position. [2]
\end{enumerate}
$P$ is projected vertically downwards from the equilibrium position with initial speed $6$ m s$^{-1}$. At the instant when the tension in the string is $12$ N the string breaks. $P$ continues to descend vertically.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item \begin{enumerate}[label=(\alph*)]
\item Calculate the height of $P$ above the ground at the instant when the string breaks. [2]
\item Find the speed of $P$ immediately before it strikes the ground. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2015 Q5 [8]}}