| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2020 |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Vertical elastic string: released from rest at natural length or above (string initially slack) |
| Difficulty | Standard +0.3 Part (a) is a direct application of Hooke's law at equilibrium (T = λx/a = 2mg), giving x = a immediately. Part (b) requires energy conservation with elastic potential energy (½λx²/a) equated to gravitational potential energy loss, leading to a quadratic equation. While this involves multiple steps and careful energy accounting, it follows a standard mechanics problem template with no novel insights required. The 8 total marks reflect routine further maths mechanics content that's slightly above average difficulty due to the energy method and algebraic manipulation, but well within expected techniques. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
A light elastic string of natural length $a$ and modulus of elasticity $2mg$. One end of the string is attached to a fixed point $A$. The other end of the string is attached to a particle of mass $2m$.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $a$, the extension of the string when the particle hangs freely in equilibrium below $A$. [2]
\item The particle is released from rest at $A$.
Find, in terms of $a$, the distance of the particle below $A$ when it first comes to instantaneous rest. [6]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q2 [8]}}