| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Two particles over pulley, vertical strings |
| Difficulty | Standard +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. |
| Spec | 3.02d 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.
\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]}}