AQA M1 2011 June — Question 5 14 marks

Exam BoardAQA
ModuleM1 (Mechanics 1)
Year2011
SessionJune
Marks14
PaperDownload PDF ↗
TopicPulley systems
TypeTwo particles over pulley, vertical strings
DifficultyStandard +0.3 This is a standard M1 pulley problem with straightforward application of Newton's second law to connected particles. Parts (a)-(c) are routine bookwork requiring F=ma for each particle and solving simultaneous equations. Part (d) uses basic SUVAT equations with given values. The only slight elevation above average is the multi-part structure and careful handling of directions, but no novel problem-solving is required.
Spec3.02d Constant acceleration: SUVAT formulae3.03l Newton's third law: extend to situations requiring force resolution3.03o Advanced connected particles: and pulleys

5 Two particles, \(P\) and \(Q\), are connected by a string that passes over a fixed smooth peg, as shown in the diagram. The mass of \(P\) is 5 kg and the mass of \(Q\) is 3 kg . \includegraphics[max width=\textwidth, alt={}, center]{7ac7dfd0-4c3e-4eb7-920f-ce5b24ad1281-3_209_433_1009_808} The particles are released from rest in the position shown.
  1. By forming an equation of motion for each particle, show that the magnitude of the acceleration of each particle is \(2.45 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  2. Find the tension in the string.
  3. State two modelling assumptions that you have made about the string.
  4. Particle \(P\) hits the floor when it has moved 0.196 metres and \(Q\) has not reached the peg.
    1. Find the time that it takes \(P\) to reach the floor.
    2. Find the speed of \(P\) when it hits the floor.

5 Two particles, $P$ and $Q$, are connected by a string that passes over a fixed smooth peg, as shown in the diagram. The mass of $P$ is 5 kg and the mass of $Q$ is 3 kg .\\
\includegraphics[max width=\textwidth, alt={}, center]{7ac7dfd0-4c3e-4eb7-920f-ce5b24ad1281-3_209_433_1009_808}

The particles are released from rest in the position shown.
\begin{enumerate}[label=(\alph*)]
\item By forming an equation of motion for each particle, show that the magnitude of the acceleration of each particle is $2.45 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\item Find the tension in the string.
\item State two modelling assumptions that you have made about the string.
\item Particle $P$ hits the floor when it has moved 0.196 metres and $Q$ has not reached the peg.
\begin{enumerate}[label=(\roman*)]
\item Find the time that it takes $P$ to reach the floor.
\item Find the speed of $P$ when it hits the floor.
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA M1 2011 Q5 [14]}}