4\\
\includegraphics[max width=\textwidth, alt={}, center]{c9e725ad-561b-4e98-9b8f-7c9d3c8e67e6-3_494_255_258_945}

Particles $P$ and $Q$, of masses 0.4 kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley and the sections of the string not in contact with the pulley are vertical. $P$ rests in limiting equilibrium on a plane inclined at $60 ^ { \circ }$ to the horizontal (see diagram).
\begin{enumerate}[label=(\roman*)]
\item (a) Calculate the components, parallel and perpendicular to the plane, of the contact force exerted by the plane on $P$.\\
(b) Find the coefficient of friction between $P$ and the plane.\\
$P$ is held stationary and a particle of mass 0.2 kg is attached to $Q$. With the string taut, $P$ is released from rest.
\item Calculate the tension in the string and the acceleration of the particles.\\
\includegraphics[max width=\textwidth, alt={}, center]{c9e725ad-561b-4e98-9b8f-7c9d3c8e67e6-3_579_1195_1553_475}

The $( t , v )$ diagram represents the motion of two cyclists $A$ and $B$ who are travelling along a horizontal straight road. At time $t = 0 , A$, who cycles with constant speed $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, overtakes $B$ who has initial speed $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. From time $t = 0 B$ cycles with constant acceleration for 20 s . When $t = 20$ her speed is $11 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, which she subsequently maintains.
\end{enumerate}

\hfill \mbox{\textit{OCR M1 2010 Q4 [10]}}