| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Atwood machine, vertical strings |
| Difficulty | Moderate -0.8 This is a standard two-particle pulley system requiring straightforward application of Newton's second law to find acceleration and tension, followed by basic kinematics. The setup is routine with clear given values, requiring only F=ma for each particle, solving simultaneous equations, and using s=ut+½at². No novel insight or complex problem-solving needed—slightly easier than average A-level mechanics. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| M1 | For applying Newton's second law to P or to Q (3 terms) | |
| \(0.6g - T = 0.6a\) | A1 | |
| \(T - 0.2g = 0.2a\) | A1 | Allow B1 for \(0.6g - 0.2g = (0.6 + 0.2)a\) as an alternative for either of the above A marks |
| Acceleration is \(5\ \text{ms}^{-2}\) | B1 | |
| Tension is 3 N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \([0.9 = \frac{1}{2} \cdot 5t^2]\) | M1 | For using \(s = ut + \frac{1}{2}at^2\) |
| Time taken is 0.6 s | A1ft | ft \(\sqrt{1.8/a}\) |
## Question 4:
### Part (i):
| Working/Answer | Mark | Guidance |
|---|---|---|
| | M1 | For applying Newton's second law to P or to Q (3 terms) |
| $0.6g - T = 0.6a$ | A1 | |
| $T - 0.2g = 0.2a$ | A1 | Allow B1 for $0.6g - 0.2g = (0.6 + 0.2)a$ as an alternative for either of the above A marks |
| Acceleration is $5\ \text{ms}^{-2}$ | B1 | |
| Tension is 3 N | A1 | |
### Part (ii):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $[0.9 = \frac{1}{2} \cdot 5t^2]$ | M1 | For using $s = ut + \frac{1}{2}at^2$ |
| Time taken is 0.6 s | A1ft | ft $\sqrt{1.8/a}$ |
---4\\
\includegraphics[max width=\textwidth, alt={}, center]{f7a22c07-44e3-4891-be60-cbab772f45df-3_702_709_269_719}
Particles $P$ and $Q$, of masses 0.6 kg and 0.2 kg respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed peg. The particles are held at rest with the string taut. Both particles are at a height of 0.9 m above the ground (see diagram). The system is released and each of the particles moves vertically. Find\\
(i) the acceleration of $P$ and the tension in the string before $P$ reaches the ground,\\
(ii) the time taken for $P$ to reach the ground.
\hfill \mbox{\textit{CAIE M1 2007 Q4 [7]}}