| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Three or more connected particles |
| Difficulty | Standard +0.8 This is a multi-part pulley problem requiring careful consideration of three connected particles with one (C) resting inside another (B). Students must recognize that C and B move together, apply Newton's second law to multiple bodies, resolve forces in different directions, and handle the non-trivial reaction force calculation. The conceptual leap that C experiences the same acceleration as B while having a reduced normal reaction is above-average difficulty for M1. |
| Spec | 3.03d Newton's second law: 2D vectors3.03f Weight: W=mg3.03o Advanced connected particles: and pulleys |
| Answer | Marks |
|---|---|
| Eqn. of motion for A: \(T - 6g = 6a\) (1) | M1 |
| Eqn. of motion for B & C: \(8g - T = 8a\) (2) | M1 |
| \((1) + (2)\) gives \(2g = 14a\) i.e. \(a = \frac{g}{7}\) m\(s^{-2}\) | M1 A1 |
| Answer | Marks |
|---|---|
| Sub. \(a\) into (1) to get \(T = 6a + 6g = \frac{6g}{7} + 6g\) | M1 |
| Force on pulley = \(2T = \frac{96g}{7}\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve \(\downarrow\) for C: \(3g - R = 3 \times \frac{g}{7}\) | M1 | |
| \(R = 3g - \frac{3g}{7} = \frac{18g}{7}\) | M1 A1 | (10) |
**Part (a)**
Eqn. of motion for A: $T - 6g = 6a$ (1) | M1 |
Eqn. of motion for B & C: $8g - T = 8a$ (2) | M1 |
$(1) + (2)$ gives $2g = 14a$ i.e. $a = \frac{g}{7}$ m$s^{-2}$ | M1 A1 |
**Part (b)**
Sub. $a$ into (1) to get $T = 6a + 6g = \frac{6g}{7} + 6g$ | M1 |
Force on pulley = $2T = \frac{96g}{7}$ | M1 A1 |
**Part (c)**
Resolve $\downarrow$ for C: $3g - R = 3 \times \frac{g}{7}$ | M1 |
$R = 3g - \frac{3g}{7} = \frac{18g}{7}$ | M1 A1 | (10)4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4fe54579-ac77-46f9-85e1-2e95963d6b3e-3_467_348_201_708}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Figure 1 shows a weight $A$ of mass 6 kg connected by a light, inextensible string which passes over a smooth, fixed pulley to a box $B$ of mass 5 kg . There is an object $C$ of mass 3 kg resting on the horizontal floor of box $B$.
The system is released from rest. Find, giving your answers in terms of $g$,
\begin{enumerate}[label=(\alph*)]
\item the acceleration of the system,
\item the force on the pulley.
\item Show that the reaction between $C$ and the floor of $B$ is $\frac { 18 } { 7 } \mathrm {~g}$ newtons.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [10]}}