| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | November |
| Marks | 7 |
| 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 This is a standard elastic string energy problem requiring conservation of energy with gravitational PE and elastic PE. Part (i) needs identifying that maximum speed occurs when forces balance (mg = λx/l), then applying energy conservation. Part (ii) is straightforward energy conservation to find maximum extension. The setup is routine for M2 level with clear methodology, though requires careful bookkeeping of energy terms across multiple steps. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| 3(i) | 20e/0.5 = 0.4g | M1 |
| e = 0.1 | A1 | |
| 0.4v2/2 = 0.4g(0.5 + 0.1) – 20×0.12/(2×0.5) | M1 | Attempt to set up a 3 term energy equation |
| v = 11 = 3.32 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(ii) | 0.4g(5 + x) = 20x2/(2×0.5) | M1 |
| [0 = 20x2 – 4x – 2] [ x = 0.432] | M1 | Attempt to solve a 3 term quadratic equation |
| Distance below O = (0.5 + 0.432) = 0.932 m | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(i) ---
3(i) | 20e/0.5 = 0.4g | M1 | Use T = λx/L
e = 0.1 | A1
0.4v2/2 = 0.4g(0.5 + 0.1) – 20×0.12/(2×0.5) | M1 | Attempt to set up a 3 term energy equation
v = 11 = 3.32 | A1
4
--- 3(ii) ---
3(ii) | 0.4g(5 + x) = 20x2/(2×0.5) | M1 | Attempt to set up a 2 term energy equation
[0 = 20x2 – 4x – 2] [ x = 0.432] | M1 | Attempt to solve a 3 term quadratic equation
Distance below O = (0.5 + 0.432) = 0.932 m | A1
3
Question | Answer | Marks | GuidanceA particle $P$ of mass $0.4\text{ kg}$ is attached to a fixed point $O$ by a light elastic string of natural length $0.5\text{ m}$ and modulus of elasticity $20\text{ N}$. The particle $P$ is released from rest at $O$.
\begin{enumerate}[label=(\roman*)]
\item Find the greatest speed of $P$ in the subsequent motion. [4]
\item Find the distance below $O$ of the point at which $P$ comes to instantaneous rest. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2018 Q3 [7]}}