| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | November |
| Marks | 13 |
| Topic | Motion on a slope |
| Type | Particle on slope with pulley |
| Difficulty | Standard +0.3 This is a standard A-level mechanics problem involving connected particles on a pulley system. Part (i) requires routine force diagrams and applying F=ma to find acceleration and tension—straightforward application of Newton's laws. Part (ii) adds friction and limiting equilibrium, requiring consideration of two cases (friction up/down slope), but this is a well-practiced technique. The problem is slightly easier than average because it's methodical with clear structure, standard setup, and no novel insight required beyond textbook methods. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03u Static equilibrium: on rough surfaces |
Two particles, $A$ and $B$, each of mass 1 kg are connected by a light inextensible string. Particle $A$ is at rest on a slope inclined at 30° to the horizontal. The string passes over a small smooth pulley at the top of the slope and particle $B$ hangs freely, as shown in the diagram.
\includegraphics{figure_11}
\begin{enumerate}[label=(\roman*)]
\item \begin{enumerate}[label=(\alph*)]
\item In the case when the slope is smooth, draw a fully labelled diagram to show the forces acting on the particles. Hence find the acceleration of the particles and the tension in the string. [7]
\item Write down the direction of the resultant force exerted by the string on the pulley. [1]
\end{enumerate}
\item In fact the contact between particle $A$ and the slope is rough. The coefficient of friction between $A$ and the slope is $\mu$. The system is in equilibrium. Find the set of possible values of $\mu$. [5]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q11 [13]}}