6
\includegraphics[max width=\textwidth, alt={}, center]{edf90396-5e17-44ef-bf25-e09cbc5785ba-4_451_729_255_708}
Particles \(A\) and \(B\), of masses 0.2 kg and 0.45 kg respectively, are connected by a light inextensible string of length 2.8 m . The string passes over a small smooth pulley at the edge of a rough horizontal surface, which is 2 m above the floor. Particle \(A\) is held in contact with the surface at a distance of 2.1 m from the pulley and particle \(B\) hangs freely (see diagram). The coefficient of friction between \(A\) and the surface is 0.3. Particle \(A\) is released and the system begins to move.
- Find the acceleration of the particles and show that the speed of \(B\) immediately before it hits the floor is \(3.95 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), correct to 3 significant figures.
- Given that \(B\) remains on the floor, find the speed with which \(A\) reaches the pulley.