AQA M1 2012 June — Question 6 10 marks

Exam BoardAQA
ModuleM1 (Mechanics 1)
Year2012
SessionJune
Marks10
PaperDownload PDF ↗
TopicNewton's laws and connected particles
TypeBlock on rough horizontal surface – accelerating (finding acceleration or applied force)
DifficultyModerate -0.3 This is a standard M1 connected particles question requiring a force diagram, resolving vertically to find normal reaction (R = 8g - 0.5T), then horizontally with friction (F = 0.3R) to find T. The calculation is straightforward with familiar techniques, making it slightly easier than average for M1, though the multi-part structure and angle resolution keep it close to typical difficulty.
Spec1.10h Vectors in kinematics: uniform acceleration in vector form3.02g Two-dimensional variable acceleration3.02h Motion under gravity: vector form

6 A child pulls a sledge, of mass 8 kg , along a rough horizontal surface, using a light rope. The coefficient of friction between the sledge and the surface is 0.3 . The tension in the rope is \(T\) newtons. The rope is kept at an angle of \(30 ^ { \circ }\) to the horizontal, as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{828e8db1-efcf-4878-8292-ba5bbd80115c-4_273_775_516_644} Model the sledge as a particle.
  1. Draw a diagram to show all the forces acting on the sledge.
  2. Find the magnitude of the normal reaction force acting on the sledge, in terms of \(T\).
  3. Given that the sledge accelerates at \(0.05 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), find \(T\).

6 A child pulls a sledge, of mass 8 kg , along a rough horizontal surface, using a light rope. The coefficient of friction between the sledge and the surface is 0.3 . The tension in the rope is $T$ newtons. The rope is kept at an angle of $30 ^ { \circ }$ to the horizontal, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{828e8db1-efcf-4878-8292-ba5bbd80115c-4_273_775_516_644}

Model the sledge as a particle.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show all the forces acting on the sledge.
\item Find the magnitude of the normal reaction force acting on the sledge, in terms of $T$.
\item Given that the sledge accelerates at $0.05 \mathrm {~m} \mathrm {~s} ^ { - 2 }$, find $T$.
\end{enumerate}

\hfill \mbox{\textit{AQA M1 2012 Q6 [10]}}