| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Force on pulley from string |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem requiring resolution of forces at the pulley, equilibrium equations, and friction at limiting equilibrium. The three parts involve straightforward application of T = 4N from pulley geometry, friction F = μR, and then F = ma for the accelerating system. Slightly above average due to the pulley force resolution in part (i), but otherwise routine mechanics. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03m Equilibrium: sum of resolved forces = 03.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(T = 4\sqrt{2}\cos 45° = 4\) N | B1 | 2 |
| Mass of \(Q\) is \(0.4\) kg | B1 | |
| (ii) \(4 = 0.8 \times m_P \times 10\) | M1 | For using \(F = T\), \(F = \mu R\) (or \(m_Q g = \mu R\)) and \(R = mg\) |
| Mass of \(P\) is \(0.5\) kg | A1 | 2 |
| (iii) | M1 | For applying Newton's second law to \(P\) or to \(Q\) |
| \(T - 0.8 \times 0.5g = 0.5a\) | A1 ft | |
| \(0.5g - T = 0.5a\) | ||
| Alternative to either of the two A1 marks above: | ||
| Tension is \(4.5\) N | A1 | 4 |
**(i)** $T = 4\sqrt{2}\cos 45° = 4$ N | B1 | 2 |
Mass of $Q$ is $0.4$ kg | B1 | |
**(ii)** $4 = 0.8 \times m_P \times 10$ | M1 | For using $F = T$, $F = \mu R$ (or $m_Q g = \mu R$) and $R = mg$ |
| | |
Mass of $P$ is $0.5$ kg | A1 | 2 |
**(iii)** | M1 | For applying Newton's second law to $P$ or to $Q$ |
$T - 0.8 \times 0.5g = 0.5a$ | A1 ft | |
$0.5g - T = 0.5a$ | | |
| | Alternative to either of the two A1 marks above: |
Tension is $4.5$ N | A1 | 4 | $5 - 4 = (0.5 + 0.5)a$ ... B1 |
---5\\
\includegraphics[max width=\textwidth, alt={}, center]{b5873699-d207-4cad-9518-1321dc429c15-3_305_599_1717_774}
Particles $P$ and $Q$ are attached to opposite ends of a light inextensible string. $P$ is at rest on a rough horizontal table. The string passes over a small smooth pulley which is fixed at the edge of the table. $Q$ hangs vertically below the pulley (see diagram). The force exerted on the string by the pulley has magnitude $4 \sqrt { } 2 \mathrm {~N}$. The coefficient of friction between $P$ and the table is 0.8 .\\
(i) Show that the tension in the string is 4 N and state the mass of $Q$.\\
(ii) Given that $P$ is on the point of slipping, find its mass.
A particle of mass 0.1 kg is now attached to $Q$ and the system starts to move.\\
(iii) Find the tension in the string while the particles are in motion.
\hfill \mbox{\textit{CAIE M1 2006 Q5 [8]}}