6 A particle of mass 0.5 kg is held at rest at a point \(P\), which is at the bottom of an inclined plane. The particle is given an impulse of 1.8 Ns directed up a line of greatest slope of the plane.
- Find the speed at which the particle starts to move.
The particle subsequently moves up the plane to a point \(Q\), which is 0.3 m above the level of \(P\).
- Given that the plane is smooth, find the speed of the particle at \(Q\).
It is given instead that the plane is rough. The particle is now projected up the plane from \(P\) with initial speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and comes to rest at a point \(R\) which is 0.2 m above the level of \(P\).
- Given that the plane is inclined at \(30 ^ { \circ }\) to the horizontal, find the magnitude of the frictional force on the particle.