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\includegraphics[max width=\textwidth, alt={}, center]{4a2bad7c-6720-414c-b336-060afb2255e9-12_560_716_258_712} Particles of masses 1.5 kg and 3 kg lie on a plane which is inclined at an angle of \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). The section of the plane from \(A\) to \(B\) is smooth and the section of the plane from \(B\) to \(C\) is rough. The 1.5 kg particle is held at rest at \(A\) and the 3 kg particle is in limiting equilibrium at \(B\). The distance \(A B\) is \(x \mathrm {~m}\) and the distance \(B C\) is 4 m (see diagram).

1. Show that the coefficient of friction between the particle at \(B\) and the plane is 0.75 .
   The 1.5 kg particle is released from rest. In the subsequent motion the two particles collide and coalesce. The time taken for the combined particle to travel from \(B\) to \(C\) is 2 s . The coefficient of friction between the combined particle and the plane is still 0.75 .
2. Find \(x\).
3. Find the total loss of energy of the particles from the time the 1.5 kg particle is released until the combined particle reaches \(C\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.