| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Two connected particles, horizontal surface |
| Difficulty | Moderate -0.8 This is a straightforward M1 connected particles question with standard bookwork throughout. Parts (a)-(c) are routine recall (SUVAT, force diagrams), while (d)-(f) apply F=ma systematically to each particle. The friction is limiting (μR), and all forces are horizontal with given values, requiring no problem-solving insight—just methodical application of standard techniques. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| \(v^2 = 0 + 2 \times 0.05 \times 6\) | M1 | Use of \(v^2 = u^2 + 2as\) |
| A1 | Correct substitution | |
| \(v = 0.775 \text{ m s}^{-1}\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Diagram showing: Weight down, Normal reaction up, Friction force backwards, Tension forwards | B1 | All four forces correctly labelled and directed |
| Answer | Marks | Guidance |
|---|---|---|
| Diagram showing: Weight down, Normal reaction up, Tension backwards, Driving force \(P\) forwards | B1 | Forces correctly shown |
| Can treat all mass as acting at a single point (no turning effects/moments) | B1 | Advantage stated |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = \mu R = 0.4 \times 800 \times 9.8\) | M1 | Use of \(F = \mu mg\) |
| A1 | Correct values | |
| \(F = 3136 \text{ N}\) | A1 | cao (allow \(g = 9.81\): \(3139.2\) N) |
| Answer | Marks | Guidance |
|---|---|---|
| For skip: \(T - F_{friction} = 800 \times 0.05\) | M1 | Newton's 2nd law for skip |
| \(T = 3136 + 40\) | A1 | Correct equation |
| \(T = 3176 \text{ N}\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| For van: \(P - T - F_{van friction} = 1700 \times 0.05\) | M1 | Newton's 2nd law for van |
| No friction on van / or for whole system: \(P - 3136 = 2500 \times 0.05\) | M1 | Correct method |
| \(P = 3136 + 85 + 3176 = \) ... | A1 | |
| \(P = 6397 \text{ N}\) | A1 | cao |
# Question 3:
## Part (a)
| $v^2 = 0 + 2 \times 0.05 \times 6$ | M1 | Use of $v^2 = u^2 + 2as$ |
|---|---|---|
| | A1 | Correct substitution |
| $v = 0.775 \text{ m s}^{-1}$ | A1 | cao |
## Part (b)
| Diagram showing: Weight down, Normal reaction up, Friction force backwards, Tension forwards | B1 | All four forces correctly labelled and directed |
## Part (c)
| Diagram showing: Weight down, Normal reaction up, Tension backwards, Driving force $P$ forwards | B1 | Forces correctly shown |
|---|---|---|
| Can treat all mass as acting at a single point (no turning effects/moments) | B1 | Advantage stated |
## Part (d)
| $F = \mu R = 0.4 \times 800 \times 9.8$ | M1 | Use of $F = \mu mg$ |
|---|---|---|
| | A1 | Correct values |
| $F = 3136 \text{ N}$ | A1 | cao (allow $g = 9.81$: $3139.2$ N) |
## Part (e)
| For skip: $T - F_{friction} = 800 \times 0.05$ | M1 | Newton's 2nd law for skip |
|---|---|---|
| $T = 3136 + 40$ | A1 | Correct equation |
| $T = 3176 \text{ N}$ | A1 | cao |
## Part (f)
| For van: $P - T - F_{van friction} = 1700 \times 0.05$ | M1 | Newton's 2nd law for van |
|---|---|---|
| No friction on van / or for whole system: $P - 3136 = 2500 \times 0.05$ | M1 | Correct method |
| $P = 3136 + 85 + 3176 = $ ... | A1 | |
| $P = 6397 \text{ N}$ | A1 | cao |
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The question text for Question 4 is visible, but no mark scheme or model answers are shown in these images.
To extract mark scheme content, I would need images of the actual mark scheme document for this paper. Could you provide those pages instead?
3 A skip, of mass 800 kg , is at rest on a rough horizontal surface. The coefficient of friction between the skip and the ground is 0.4 . A rope is attached to the skip and then the rope is pulled by a van so that the rope is horizontal while it is taut, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-06_237_1118_497_463}
The mass of the van is 1700 kg . A constant horizontal forward driving force of magnitude $P$ newtons acts on the van. The skip and the van accelerate at $0.05 \mathrm {~ms} ^ { - 2 }$.
Model both the van and the skip as particles connected by a light inextensible rope. Assume that there is no air resistance acting on the skip or on the van.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of the van and the skip when they have moved 6 metres.
\item Draw a diagram to show the forces acting on the skip while it is accelerating.
\item Draw a diagram to show the forces acting on the van while it is accelerating. State one advantage of modelling the van as a particle when considering the vertical forces.
\item Find the magnitude of the friction force acting on the skip.
\item Find the tension in the rope.
\item $\quad$ Find $P$.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-06_771_1703_1932_155}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2014 Q3 [15]}}