| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Elastic string two-particle system |
| Difficulty | Challenging +1.2 This is a multi-stage mechanics problem requiring energy methods, elastic strings, and friction. While it involves several concepts (EPE, work against friction, connected particles), the question provides significant scaffolding through parts (a)(i) and (a)(ii), and the calculations follow standard M2 techniques without requiring novel insight. The complexity is above average due to the two-particle system and energy accounting, but well within expected M2 scope. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings |
9 Two particles, $A$ and $B$, are connected by a light elastic string that passes through a hole at a point $O$ in a rough horizontal table. The edges of the hole are smooth. Particle $A$ has a mass of 8 kg and particle $B$ has a mass of 3 kg .
The elastic string has natural length 3 metres and modulus of elasticity 60 newtons.\\
Initially, particle $A$ is held 3.5 metres from the point $O$ on the surface of the table and particle $B$ is held at a point 2 metres vertically below $O$.
The coefficient of friction between the table and particle $A$ is 0.4 .\\
The two particles are released from rest.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Show that initially particle $A$ moves towards the hole in the table.
\item Show that initially particle $B$ also moves towards the hole in the table.
\end{enumerate}\item Calculate the initial elastic potential energy in the string.
\item Particle $A$ comes permanently to rest when it has moved 0.46 metres, at which time particle $B$ is still moving upwards.
Calculate the distance that particle $B$ has moved when it is at rest for the first time.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2013 Q9 [14]}}