| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2020 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Vertical elastic string: released from rest, string starts taut |
| Difficulty | Standard +0.3 This is a straightforward application of Hooke's law and energy conservation. Part (a) requires simple force balance (T = λx/a, then F=ma), while part (b) uses standard elastic potential energy formula with conservation of energy. Both parts follow textbook methods with no novel insight required, making it slightly easier than average despite being Further Maths content. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
One end of a light elastic spring, of natural length $a$ and modulus of elasticity $5mg$, is attached to a fixed point $A$. The other end of the spring is attached to a particle $P$ of mass $m$. The spring hangs with $P$ vertically below $A$. The particle $P$ is released from rest in the position where the extension of the spring is $\frac{3}{5}a$.
\begin{enumerate}[label=(\alph*)]
\item Show that the initial acceleration of $P$ is $\frac{3}{5}g$ upwards. [3]
\item Find the speed of $P$ when the spring first returns to its natural length. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q3 [7]}}