| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Elastic string with variable force |
| Difficulty | Standard +0.3 This is a straightforward elastic string problem requiring standard mechanics techniques: (i) uses F=ma with weight only (string slack), (ii) uses energy conservation with elastic PE. Both parts are direct applications of standard M2 formulas with clear setup and minimal problem-solving insight required. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(T = 19.2 \times (2.7 - 1.2)/1.2\) | B1 | \(T = 24\) N |
| \(0.4a = 0.4g + T\) | M1 | Newton's Second Law with 3 terms |
| \(a = 70 \text{ ms}^{-2}\) | A1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(19.2(2.7-1.2)^2/(2 \times 1.2)\) | B1 | Initial EE = 18 |
| M1 | For a 3 term energy equation | |
| \(0.4v^2/2 = 0.4g \times 2.7 + 19.2 \times (2.7-1.2)^2/(2 \times 1.2)\) | A1 | |
| \(v = 12 \text{ ms}^{-1}\) | A1 [4] |
## Question 2:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $T = 19.2 \times (2.7 - 1.2)/1.2$ | B1 | $T = 24$ N |
| $0.4a = 0.4g + T$ | M1 | Newton's Second Law with 3 terms |
| $a = 70 \text{ ms}^{-2}$ | A1 [3] | |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $19.2(2.7-1.2)^2/(2 \times 1.2)$ | B1 | Initial EE = 18 |
| | M1 | For a 3 term energy equation |
| $0.4v^2/2 = 0.4g \times 2.7 + 19.2 \times (2.7-1.2)^2/(2 \times 1.2)$ | A1 | |
| $v = 12 \text{ ms}^{-1}$ | A1 [4] | |
**Total: [7]**
---2 A particle $P$ of mass 0.4 kg is attached to one end of a light elastic string of natural length 1.2 m and modulus of elasticity 19.2 N . The other end of the string is attached to a fixed point $A$. The particle $P$ is released from rest at the point 2.7 m vertically above $A$. Calculate\\
(i) the initial acceleration of $P$,\\
(ii) the speed of $P$ when it reaches $A$.
\hfill \mbox{\textit{CAIE M2 2013 Q2 [7]}}