| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Work-energy with multiple stages |
| Difficulty | Challenging +1.2 This is a multi-part energy conservation problem with elastic strings requiring careful tracking of when each string is taut/slack and applying Hooke's law with energy methods. While it involves several steps and requires understanding of elastic potential energy in two strings, the approach is methodical and follows standard M2 techniques without requiring novel insight—moderately above average difficulty. |
| Spec | 6.02e Calculate KE and PE: using formulae6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For using \(EE = \frac{\lambda x^2}{2L}\) | |
| M1 | For using \(EE_{S2}(\text{initial}) = \frac{1}{2}mv^2 + EE_{S1}\) (S2 just slack) | |
| \(\frac{1}{2}(16 \times 1^2/0.5) = \frac{1}{2}(0.5)v^2 + \frac{1}{2}(16 \times 0.6^2/0.4)\) | A1 | |
| Speed is \(5.93 \text{ ms}^{-1}\) | A1 | [4 marks] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For using \(EE_{S2}(\text{initial}) = EE_{S1}\) | |
| \(\frac{1}{2}(16 \times 1^2/0.5) = \frac{1}{2}(16 \times x^2/0.4)\), \((x = 0.894)\) | A1 | |
| Distance is 1.29m | A1 | [3 marks] [Total: 7] |
## Question 5:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using $EE = \frac{\lambda x^2}{2L}$ |
| | M1 | For using $EE_{S2}(\text{initial}) = \frac{1}{2}mv^2 + EE_{S1}$ (S2 just slack) |
| $\frac{1}{2}(16 \times 1^2/0.5) = \frac{1}{2}(0.5)v^2 + \frac{1}{2}(16 \times 0.6^2/0.4)$ | A1 | |
| Speed is $5.93 \text{ ms}^{-1}$ | A1 | **[4 marks]** |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using $EE_{S2}(\text{initial}) = EE_{S1}$ |
| $\frac{1}{2}(16 \times 1^2/0.5) = \frac{1}{2}(16 \times x^2/0.4)$, $(x = 0.894)$ | A1 | |
| Distance is 1.29m | A1 | **[3 marks]** **[Total: 7]** |
---5 Each of two light elastic strings, $S _ { 1 }$ and $S _ { 2 }$, has modulus of elasticity 16 N . The string $S _ { 1 }$ has natural length 0.4 m and the string $S _ { 2 }$ has natural length 0.5 m . One end of $S _ { 1 }$ is attached to a fixed point $A$ of a smooth horizontal table and the other end is attached to a particle $P$ of mass 0.5 kg . One end of $S _ { 2 }$ is attached to a fixed point $B$ of the table and the other end is attached to $P$. The distance $A B$ is 1.5 m . The particle $P$ is held at $A$ and then released from rest.\\
(i) Find the speed of $P$ at the instant that $S _ { 2 }$ becomes slack.\\
(ii) Find the greatest distance of $P$ from $A$ in the subsequent motion.
\hfill \mbox{\textit{CAIE M2 2007 Q5 [7]}}