| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Particle on rough horizontal, string over pulley |
| Difficulty | Moderate -0.8 This is a standard two-particle pulley system requiring straightforward application of Newton's second law to each particle separately. The acceleration is given, making it a routine calculation problem with no problem-solving insight needed—just F=ma applied twice and solving for two unknowns across approximately 4-5 marks of work. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| \([0.2g - T = 0.2 \times 1.6]\) | M1 | For applying Newton's 2nd law to B |
| Tension is 1.68 N | A1 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(T - F = 0.3 \times 1.6\) | M1 | For applying Newton's 2nd law to A |
| \(T - F = 0.3 \times 1.6\) | A1 | |
| Frictional force is 1.2 N | A1 ft | 3 |
**(i)**
$[0.2g - T = 0.2 \times 1.6]$ | M1 | For applying Newton's 2nd law to B
Tension is 1.68 N | A1 | 2
**(ii)**
$T - F = 0.3 \times 1.6$ | M1 | For applying Newton's 2nd law to A
$T - F = 0.3 \times 1.6$ | A1 |
Frictional force is 1.2 N | A1 ft | 3 | If T = 0.482\\
\includegraphics[max width=\textwidth, alt={}, center]{2bb3c9bb-60f0-440d-a148-b4db3478ca31-2_212_625_528_761}
Particles $A$ and $B$, of masses 0.3 kg and 0.2 kg respectively, are attached to the ends of a light inextensible string. $A$ is held at rest on a rough horizontal table with the string passing over a small smooth pulley at the edge of the table. $B$ hangs vertically below the pulley (see diagram). The system is released and $B$ starts to move downwards with acceleration $1.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. Find\\
(i) the tension in the string after the system is released,\\
(ii) the frictional force acting on $A$.
\hfill \mbox{\textit{CAIE M1 2012 Q2 [5]}}