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\includegraphics[max width=\textwidth, alt={}, center]{3d7f53af-dbf2-499b-9966-ae85514cef02-10_336_803_258_671} Two particles \(A\) and \(B\) of masses \(m \mathrm {~kg}\) and 4 kg respectively are connected by a light inextensible string that passes over a fixed smooth pulley. Particle \(A\) is on a rough fixed slope which is at an angle of \(30 ^ { \circ }\) to the horizontal ground. Particle \(B\) hangs vertically below the pulley and is 0.5 m above the ground (see diagram). The coefficient of friction between the slope and particle \(A\) is 0.2 .

1. In the case where the system is in equilibrium with particle \(A\) on the point of moving directly up the slope, show that \(m = 5.94\), correct to 3 significant figures.
2. In the case where \(m = 3\), the system is released from rest with the string taut. Find the total distance travelled by \(A\) before coming to instantaneous rest. You may assume that \(A\) does not reach the pulley.