| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | January |
| Marks | 11 |
| 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 system question requiring Newton's second law applied to connected particles. While it involves multiple steps (resolving forces on the incline, applying F=ma to both particles, finding tension and acceleration), these are routine techniques practiced extensively in M1. Part (b) requires vector addition of tensions at the pulley, which is slightly less routine but still a standard extension. Part (c) tests understanding of modeling assumptions, which is straightforward recall. The question is slightly easier than average because the setup is very standard and the methods are well-practiced, though it requires careful systematic working. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
## Part (a)
**Answer/Working:**
- $A$: $T - 4g \sin 30 = 4a$
- $B$: $3g - T = 3a$
- $\Rightarrow T = \frac{18g}{7} = 25.2 \text{ N}$
**Marks:** M1, A1, M1, A1, M1, A1 (6 marks)
---
## Part (b)
**Answer/Working:**
- $R = 2T \cos 30$
- $\approx 44$ or $43.6 \text{ N}$
**Marks:** M1, A1, A1 (3 marks)
---
## Part (c)
**Answer/Working:**
- (i) String has no weight/mass
- (ii) Tension in string constant, i.e. same at $A$ and $B$
**Marks:** B1, B1 (2 marks)
---\includegraphics{figure_3}
A particle $A$ of mass 4 kg moves on the inclined face of a smooth wedge. This face is inclined at 30° to the horizontal. The wedge is fixed on horizontal ground. Particle $A$ is connected to a particle $B$, of mass 3 kg, by a light inextensible string. The string passes over a small light smooth pulley which is fixed at the top of the plane. The section of the string from $A$ to the pulley lies in a line of greatest slope of the wedge. The particle $B$ hangs freely below the pulley, as shown in Fig. 3. The system is released from rest with the string taut. For the motion before $A$ reaches the pulley and before $B$ hits the ground, find
\begin{enumerate}[label=(\alph*)]
\item the tension in the string, [6]
\item the magnitude of the resultant force exerted by the string on the pulley. [3]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item The string in this question is described as being 'light'.
\begin{enumerate}[label=(\roman*)]
\item Write down what you understand by this description.
\item State how you have used the fact that the string is light in your answer to part (a). [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q5 [11]}}