| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Multi-stage motion: changing surface conditions or external intervention |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem with two phases of motion (smooth then rough surface). Parts (a)-(d) follow routine procedures: forming F=ma equations, solving simultaneous equations, and applying SUVAT. Part (e) tests conceptual understanding. While multi-stage, each step uses well-practiced techniques with no novel insight required, making it slightly easier than average. |
| Spec | 3.03b Newton's first law: equilibrium3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys3.03u Static equilibrium: on rough surfaces |
**Question 5:**
- Block mass $3m$ on horizontal surface
- Particle mass $2m$ hanging
- Smooth A→B, rough B→C ($\mu = 0.8$)
**(a)** Acceleration A→B [4 marks] **(b)** Speed at B, given AB = 1.2 m [3 marks] **(c)** Acceleration B→C [5 marks] **(d)** Speed at C, given BC = 0.9 m [3 marks] **(e)** Why negligible block size matters [1 mark]
To get the actual mark scheme, you would need the official AQA MM1B June 2015 mark scheme document.
I can see these are answer space pages from what appears to be an AQA Mechanics exam (P/Jun15/MM1B). The pages shown (12-16) contain only blank answer spaces for questions 5, 6, and 7 - the actual mark scheme content is not visible in these images.
However, based on the question content visible on page 14 and 16, I can provide worked solutions:
---5 A block, of mass $3 m$, is placed on a horizontal surface at a point $A$. A light inextensible string is attached to the block and passes over a smooth peg. The string is horizontal between the block and the peg. A particle, of mass $2 m$, is attached to the other end of the string. The block is released from rest with the string taut and the string between the peg and the particle vertical, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{01338c87-302c-420f-a473-39b0796ccaed-10_170_726_536_657}
Assume that there is no air resistance acting on either the block or the particle, and that the size of the block is negligible.
The horizontal surface is smooth between the points $A$ and $B$, but rough between the points $B$ and $C$. Between $B$ and $C$, the coefficient of friction between the block and the surface is 0.8 .
\begin{enumerate}[label=(\alph*)]
\item By forming equations of motion for both the block and the particle, find the acceleration of the block between $A$ and $B$.
\item Given that the distance between the points $A$ and $B$ is 1.2 metres, find the speed of the block when it reaches $B$.
\item By forming equations of motion for both the block and the particle, find the acceleration of the block between $B$ and $C$.
\item Given that the distance between the points $B$ and $C$ is 0.9 metres, find the speed of the block when it reaches $C$.
\item Explain why it is important to assume that the size of the block is negligible.\\[0pt]
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2015 Q5 [16]}}