| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| 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 three-part elastic string problem requiring Hooke's law for equilibrium (part i), energy conservation for projection speed (part ii), and energy methods for maximum extension (part iii). While it involves multiple steps and careful consideration of when the string is taut vs slack, these are routine M2 techniques with no novel insight required—slightly above average due to the multi-stage energy analysis. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5 = 0.2\lambda/0.4\) | M1 | Tension \(= \lambda\text{ext}/l\) |
| \(\lambda = 10\) N | A1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| B1\(\checkmark\) | Correct EE term | |
| \(10(0.2^2/(2 \times 0.4)) + (5/g)v^2/2 = 0.3 \times 5\) | M1 | PE/KE/EE 3 terms |
| \(v = 2\) m s\(^{-1}\) | A1 (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| B1\(\checkmark\) | Correct EE term | |
| \(10e^2/(2 \times 0.4) = 5(e + 0.1)\) | M1 | Energy equation |
| \(e = 0.483\) | A1 (3) |
## Question 2:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5 = 0.2\lambda/0.4$ | M1 | Tension $= \lambda\text{ext}/l$ |
| $\lambda = 10$ N | A1 (2) | |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| | B1$\checkmark$ | Correct EE term |
| $10(0.2^2/(2 \times 0.4)) + (5/g)v^2/2 = 0.3 \times 5$ | M1 | PE/KE/EE 3 terms |
| $v = 2$ m s$^{-1}$ | A1 (3) | |
### Part (iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| | B1$\checkmark$ | Correct EE term |
| $10e^2/(2 \times 0.4) = 5(e + 0.1)$ | M1 | Energy equation |
| $e = 0.483$ | A1 (3) | |
---2 One end of a light elastic string of natural length 0.4 m is attached to a fixed point $O$. The other end of the string is attached to a particle of weight 5 N which hangs in equilibrium 0.6 m vertically below $O$.\\
(i) Find the modulus of elasticity of the string.
The particle is projected vertically upwards from the equilibrium position and comes to instantaneous rest after travelling 0.3 m upwards.\\
(ii) Calculate the speed of projection of the particle.\\
(iii) Calculate the greatest extension of the string in the subsequent motion.
\hfill \mbox{\textit{CAIE M2 2016 Q2 [8]}}