Two blocks, $A$ and $B$, of masses 2 kg and 4 kg respectively are attached to the ends of a light inextensible string.

Initially $A$ is held on a fixed rough plane. The plane is inclined to horizontal ground at an angle $\theta$, where $tan \theta =\frac{3}{4}$.

The string passes over a small smooth light pulley $P$ that is fixed at the top of the plane.
The part of the string from $A$ to $P$ is parallel to a line of greatest slope of the plane.

Block $A$ is held on the plane with the distance $AP$ greater than 3 m.
Block $B$ hangs freely below $P$ at a distance of 3 m above the ground, as shown in Figure 4.

The coefficient of friction between $A$ and the plane is $\mu$.

Block $A$ is released from rest with the string taut.

By modelling the blocks as particles, find the potential energy lost by the whole system as a result of $B$ falling 3 m.

1.2. Given that the speed of $B$ at the instant it hits the ground is 4.5 m s⁻¹ and ignoring air resistance, use the work-energy principle to find the value of $\mu$

1.3. After $B$ hits the ground, $A$ continues to move up the plane but does not reach the pulley in the subsequent motion.
Block $A$ comes to instantaneous rest after moving a total distance of $(3+d)$ m from its point of release.

Ignoring air resistance, use the work-energy principle to find the value of $d$.