| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Pulley at edge of table, specific geometry |
| Difficulty | Standard +0.3 This is a standard two-particle pulley system with sequential motion phases. Part (i) requires routine application of Newton's second law to connected particles. Parts (ii) and (iii) involve straightforward kinematics using SUVAT equations with given distances. While multi-step, each component uses well-practiced techniques without requiring novel insight or complex problem-solving. |
| Spec | 3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\quad\) | M1 | For applying Newton's 2nd law to \(A\) or to \(B\) |
| \(0.32g - T = 0.32a\) (or \(T = 0.48a\)) | A1 | |
| \(T = 0.48a\) (or \(0.32g - T = 0.32a\)) OR \(0.32g = (0.32 + 0.48)a\) | B1 | |
| \(\quad\) | M1 | For solving for \(a\) and \(T\) |
| Acceleration is 4 m s\(^{-2}\) and tension is 1.92 N | A1 | 5 marks total |
| (ii) \([0.98 = \frac{1}{2} \times 4t^2]\) | M1 | For using \(s = \frac{1}{2}at^2\) |
| Time taken is 0.7 s | A1 | 2 marks total |
| (iii) \(\quad\) | M1 | For using \(v = at\) for taut stage and \(t = d/v\) for slack stage |
| \(v = 4 \times 0.7\) and \(t = (1.4 - 0.98)/v\) (= 0.15) | A1ft | ft a from (i) and/or t from (ii) (\(a>0\), \(a \neq g\)) |
| Time taken is 0.85 s | A1 | 3 marks total |
**(i)** $\quad$ | M1 | For applying Newton's 2nd law to $A$ or to $B$
$0.32g - T = 0.32a$ (or $T = 0.48a$) | A1 |
$T = 0.48a$ (or $0.32g - T = 0.32a$) OR $0.32g = (0.32 + 0.48)a$ | B1 |
$\quad$ | M1 | For solving for $a$ and $T$
Acceleration is 4 m s$^{-2}$ and tension is 1.92 N | A1 | 5 marks total
**(ii)** $[0.98 = \frac{1}{2} \times 4t^2]$ | M1 | For using $s = \frac{1}{2}at^2$
Time taken is 0.7 s | A1 | 2 marks total
**(iii)** $\quad$ | M1 | For using $v = at$ for taut stage and $t = d/v$ for slack stage
$v = 4 \times 0.7$ and $t = (1.4 - 0.98)/v$ (= 0.15) | A1ft | ft a from (i) and/or t from (ii) ($a>0$, $a \neq g$)
Time taken is 0.85 s | A1 | 3 marks total7\\
\includegraphics[max width=\textwidth, alt={}, center]{631ddcd9-17c0-4a15-8671-40788c3a84d3-3_565_828_1402_660}
Particles $A$ and $B$ have masses 0.32 kg and 0.48 kg respectively. The particles are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the edge of a smooth horizontal table. Particle $B$ is held at rest on the table at a distance of 1.4 m from the pulley. $A$ hangs vertically below the pulley at a height of 0.98 m above the floor (see diagram). $A , B$, the string and the pulley are all in the same vertical plane. $B$ is released and $A$ moves downwards.\\
(i) Find the acceleration of $A$ and the tension in the string.\\
$A$ hits the floor and $B$ continues to move towards the pulley. Find the time taken, from the instant that $B$ is released, for\\
(ii) $A$ to reach the floor,\\
(iii) $B$ to reach the pulley.
\hfill \mbox{\textit{CAIE M1 2012 Q7 [10]}}