| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2003 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough horizontal surface, particle hanging |
| Difficulty | Moderate -0.3 This is a standard two-particle pulley system problem requiring Newton's second law applied to both particles, solving simultaneous equations for tension and acceleration, then using constant acceleration kinematics. While it involves multiple steps and careful sign conventions, it follows a well-established method taught in M1 with no novel insight required. The friction component is straightforward. Slightly easier than average due to being a textbook application. |
| Spec | 3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| For applying Newton's second law to A or to B (3 terms needed) | M1 | |
| \(T - 0.6 = 0.4a\) or \(0.1g - T = 0.1a\) | A1 | |
| For a second of the above 2 equations or for \(0.1g - 0.6 = 0.5a\) | B1 | (Can be scored in part (ii)) |
| (Sign of a must be consistent with that in first equation) | ||
| Tension is 0.92 N | A1 | 4 marks |
| \(a = 0.8\) | B1 | |
| For using \(v = at\) | M1 | |
| Speed = 1.2 m s\(^{-1}\) | A1 | 3 marks |
For applying Newton's second law to A or to B (3 terms needed) | M1 |
$T - 0.6 = 0.4a$ or $0.1g - T = 0.1a$ | A1 |
For a second of the above 2 equations or for $0.1g - 0.6 = 0.5a$ | B1 | (Can be scored in part (ii))
(Sign of a must be consistent with that in first equation) | |
Tension is 0.92 N | A1 | 4 marks
$a = 0.8$ | B1 |
For using $v = at$ | M1 |
Speed = 1.2 m s$^{-1}$ | A1 | 3 marks
---5\\
\includegraphics[max width=\textwidth, alt={}, center]{5cba3e17-3979-4c22-a415-2cdd60f09289-3_300_792_274_680}
Particles $A$ and $B$, of masses 0.4 kg and 0.1 kg respectively, are attached to the ends of a light inextensible string. Particle $A$ is held at rest on a horizontal table with the string passing over a smooth pulley at the edge of the table. Particle $B$ hangs vertically below the pulley (see diagram). The system is released from rest. In the subsequent motion a constant frictional force of magnitude 0.6 N acts on $A$. Find\\
(i) the tension in the string,\\
(ii) the speed of $B 1.5 \mathrm {~s}$ after it starts to move.
\hfill \mbox{\textit{CAIE M1 2003 Q5 [7]}}