Masses of $1.5\ \text{kg}$ and $3\ \text{kg}$ are placed on a plane inclined at angle $\alpha$ to the horizontal, with $\tan \alpha = \frac{3}{4}$. The part of the plane from $A$ to $B$ is smooth, whereas the part from $B$ to $C$ is rough. The $1.5\ \text{kg}$ particle is kept at rest at $A$, and the $3\ \text{kg}$ particle is in limiting equilibrium at $B$. Let $AB = x\ \text{m}$ and $BC = 4\ \text{m}$.
(a)[3]
Show that the coefficient of friction acting between the particle at $B$ and the plane equals $0.75$.
(b)[6]
The $1.5\ \text{kg}$ particle is let go from rest. In the following motion the two particles collide and stick together. The time for the merged particle to move from $B$ to $C$ is $2\ \text{s}$. The coefficient of friction between the merged particle and the plane remains $0.75$. Find $x$.
(c)[3]
Find the total energy lost by the particles from the moment the $1.5\ \text{kg}$ particle is released until the combined particle arrives at $C$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Determines $R=3g\cos\alpha$” …