| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Connected particles with pulley |
| Difficulty | Standard +0.3 This is a standard connected particles problem using energy methods. Part (a) requires basic equations of motion with constant acceleration, while part (b) applies work-energy principle with friction - both are routine M1 techniques with straightforward multi-step application but no novel insight required. |
| Spec | 3.03o Advanced connected particles: and pulleys6.02b Calculate work: constant force, resolved component6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| 7(a) | EITHER Solution 1 \(T = 0.8a\) for \(0 \leq t \leq 0.2a\) \(0.2a - 0.2a = 0.05\text{m}^2\) \(a = 2 - 0.2a\) \(a = 2.5 = [(0.2, 0.8)]\) OR Solution 2 \(T = 0.2a\) \(0.2a = 0.2 + 0.05\) \(a = [-(0 + \sqrt{D})]\) Available marks | M1 M1 A1 M1 A1 M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 7(b) | \(T = 0.2a\) \(0.2a - [(0.2 \times 2) + 0.05]\) \(0.2a - [0.05 \times 0.05]\) \(t = 1.58s\) \(r = 1.58s\) | M1M1 A1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 7(c) | MI For applying Newton's 2nd law either to the system as whole or to particles individually Particle B or particle A or the system \(2.5 = (0 + \sqrt{D})\) Allow \(\sqrt{v_D}\) | M1 A1 |
**7(a)** | EITHER Solution 1 $T = 0.8a$ for $0 \leq t \leq 0.2a$ $0.2a - 0.2a = 0.05\text{m}^2$ $a = 2 - 0.2a$ $a = 2.5 = [(0.2, 0.8)]$ OR Solution 2 $T = 0.2a$ $0.2a = 0.2 + 0.05$ $a = [-(0 + \sqrt{D})]$ Available marks | M1 M1 A1 M1 A1 M1 |
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# Question 7(b):
**7(b)** | $T = 0.2a$ $0.2a - [(0.2 \times 2) + 0.05]$ $0.2a - [0.05 \times 0.05]$ $t = 1.58s$ $r = 1.58s$ | M1M1 A1 A1 |
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# Question 7(c):
**7(c)** | MI For applying Newton's 2nd law either to the system as whole or to particles individually Particle B or particle A or the system $2.5 = (0 + \sqrt{D})$ Allow $\sqrt{v_D}$ | M1 A1 |7\\
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Two particles $A$ and $B$, of masses 0.8 kg and 0.2 kg respectively, are connected by a light inextensible string. Particle $A$ is placed on a horizontal surface. The string passes over a small smooth pulley $P$ fixed at the edge of the surface, and $B$ hangs freely. The horizontal section of the string, $A P$, is of length 2.5 m (see diagram). The particles are released from rest with both sections of the string taut.\\
(a) Given that the surface is smooth, find the time taken for $A$ to reach the pulley.\\
(b) It is given instead that the surface is rough and that the speed of $A$ immediately before it reaches the pulley is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The work done against friction as $A$ moves from rest to the pulley is 2 J .
Use an energy method to find $v$.\\
\hfill \mbox{\textit{CAIE M1 2020 Q7 [9]}}