AQA M1 2014 June — Question 3 15 marks

Exam BoardAQA
ModuleM1 (Mechanics 1)
Year2014
SessionJune
Marks15
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNewton's laws and connected particles
TypeTwo connected particles, horizontal surface
DifficultyModerate -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.
Spec3.02d 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

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.
  1. Find the speed of the van and the skip when they have moved 6 metres.
  2. Draw a diagram to show the forces acting on the skip while it is accelerating.
  3. 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.
  4. Find the magnitude of the friction force acting on the skip.
  5. Find the tension in the rope.
  6. \(\quad\) Find \(P\).
    \includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-06_771_1703_1932_155}

Question 3:
Part (a)
AnswerMarks Guidance
\(v^2 = 0 + 2 \times 0.05 \times 6\)M1 Use of \(v^2 = u^2 + 2as\)
A1Correct substitution
\(v = 0.775 \text{ m s}^{-1}\)A1 cao
Part (b)
AnswerMarks Guidance
Diagram showing: Weight down, Normal reaction up, Friction force backwards, Tension forwardsB1 All four forces correctly labelled and directed
Part (c)
AnswerMarks Guidance
Diagram showing: Weight down, Normal reaction up, Tension backwards, Driving force \(P\) forwardsB1 Forces correctly shown
Can treat all mass as acting at a single point (no turning effects/moments)B1 Advantage stated
Part (d)
AnswerMarks Guidance
\(F = \mu R = 0.4 \times 800 \times 9.8\)M1 Use of \(F = \mu mg\)
A1Correct values
\(F = 3136 \text{ N}\)A1 cao (allow \(g = 9.81\): \(3139.2\) N)
Part (e)
AnswerMarks 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
Part (f)
AnswerMarks 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
I can see these are answer space pages (blank lined pages for student responses) for Questions 3 and 4 of paper P71586/Jun14/MM1B, along with the question text for Question 4. These pages do not contain any mark scheme content — they are the student answer booklet pages.
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?
# 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 |

I can see these are answer space pages (blank lined pages for student responses) for Questions 3 and 4 of paper P71586/Jun14/MM1B, along with the question text for Question 4. These pages do not contain any mark scheme content — they are the student answer booklet pages.

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]}}