| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Variable mass or unknown mass |
| Difficulty | Standard +0.3 This is a standard two-particle pulley problem requiring application of Newton's second law and kinematics. Students must set up equations for both masses, use v²=u²+2as to find acceleration, then solve simultaneous equations for tension and mass. While it involves multiple steps, the approach is routine for M1 students and requires no novel insight—slightly easier than average. |
| Spec | 3.03k Connected particles: pulleys and equilibrium6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.6^2 = 0 + 2a \times 0.8\) | M1 | For use of \(v^2 = u^2 + 2as\) |
| \(a = 0.225\) | A1 | |
| \(T - 0.3g = 0.3a\) | M1 | For using Newton's second law for the 0.3 kg particle |
| \(T = 3.07\text{ N}\ (3.0675\text{ N})\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(mg - T = ma,\ m(10 - 0.225) = 3.0675\) | M1 | For using Newton's second law applied to the \(m\) kg particle |
| \(m = 0.314\text{ kg}\ (0.31381\ldots)\) | A1 |
## Question 4(i):
| $0.6^2 = 0 + 2a \times 0.8$ | M1 | For use of $v^2 = u^2 + 2as$ |
|---|---|---|
| $a = 0.225$ | A1 | |
| $T - 0.3g = 0.3a$ | M1 | For using Newton's second law for the 0.3 kg particle |
| $T = 3.07\text{ N}\ (3.0675\text{ N})$ | A1 | |
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## Question 4(ii):
| $mg - T = ma,\ m(10 - 0.225) = 3.0675$ | M1 | For using Newton's second law applied to the $m$ kg particle |
|---|---|---|
| $m = 0.314\text{ kg}\ (0.31381\ldots)$ | A1 | |
---4 Two particles $A$ and $B$, of masses $m \mathrm {~kg}$ and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley and the particles hang freely below it. The system is released from rest, with both particles 0.8 m above horizontal ground. Particle $A$ reaches the ground with a speed of $0.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Find the tension in the string during the motion before $A$ reaches the ground.\\
(ii) Find the value of $m$.\\
\hfill \mbox{\textit{CAIE M1 2018 Q4 [6]}}