| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Multiple angled forces in vertical plane |
| Difficulty | Standard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions, calculation of normal reaction, and comparison of applied force with limiting friction. While multi-step, it follows a completely routine procedure with no novel insight required, making it slightly easier than average. |
| Spec | 3.03e Resolve forces: two dimensions3.03i Normal reaction force3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Diagram showing: Weight \(50g\) down, Normal reaction \(N\) up, Friction \(F\) horizontally, \(80\text{ N}\) at \(30°\), \(40\text{ N}\) at \(20°\) | B1 B1 | |
| (b) \(N = 50g - 80\sin30° + 40\sin20°\) | M1 A1 | |
| \(N = 490 - 40 + 13.68 \approx 463.7\text{ N}\) | A1 | |
| (c) Net horizontal force \(= 80\cos30° - 40\cos20° \approx 69.28 - 37.59 = 31.69\text{ N}\) | M1 A1 | |
| Max friction \(= 0.6 \times 463.7 \approx 278\text{ N}\) | M1 A1 | |
| Since \(31.69 < 278\), crate does not move | A1 | Must state conclusion |
| (d) Rotation/turning effect ignored | B1 |
## Question 7:
**(a)** Diagram showing: Weight $50g$ down, Normal reaction $N$ up, Friction $F$ horizontally, $80\text{ N}$ at $30°$, $40\text{ N}$ at $20°$ | B1 B1 | |
**(b)** $N = 50g - 80\sin30° + 40\sin20°$ | M1 A1 |
$N = 490 - 40 + 13.68 \approx 463.7\text{ N}$ | A1 | |
**(c)** Net horizontal force $= 80\cos30° - 40\cos20° \approx 69.28 - 37.59 = 31.69\text{ N}$ | M1 A1 |
Max friction $= 0.6 \times 463.7 \approx 278\text{ N}$ | M1 A1 |
Since $31.69 < 278$, crate does not move | A1 | Must state conclusion |
**(d)** Rotation/turning effect ignored | B1 | |
I can see these are answer space pages from what appears to be an AQA mechanics exam (P/Jun15/MM1B), but these pages (17-20) only contain blank answer spaces for questions 7 and 8. They do not contain any mark scheme content.
To extract mark scheme content, you would need to provide the actual **mark scheme document** for this paper, which is a separate document published by AQA. The pages shown here are from the **question paper** only, and the answer spaces are blank.
If you can provide the mark scheme pages, I would be happy to extract and format the content as requested.
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However, based on the **question content visible on page 18**, I can outline what a solution to **Question 8** would involve:7 Two forces, which act in a vertical plane, are applied to a crate. The crate has mass 50 kg , and is initially at rest on a rough horizontal surface. One force has magnitude 80 N and acts at an angle of $30 ^ { \circ }$ to the horizontal and the other has magnitude 40 N and acts at an angle of $20 ^ { \circ }$ to the horizontal. The forces are shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{01338c87-302c-420f-a473-39b0796ccaed-16_241_999_493_523}
The coefficient of friction between the crate and the surface is 0.6 .
Model the crate as a particle.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the crate.
\item Find the magnitude of the normal reaction force acting on the crate.
\item Does the crate start to move when the two forces are applied to the crate? Show all your working.
\item State one aspect of the possible motion of the crate that is ignored by modelling it as a particle.\\[0pt]
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2015 Q7 [11]}}