7 A particle of mass 30 kg is on a plane inclined at an angle of \(20 ^ { \circ }\) to the horizontal. Starting from rest, the particle is pulled up the plane by a force of magnitude 200 N acting parallel to a line of greatest slope.

1. Given that the plane is smooth, find
   (a) the acceleration of the particle,
   (b) the change in kinetic energy after the particle has moved 12 m up the plane.
2. It is given instead that the plane is rough and the coefficient of friction between the particle and the plane is 0.12 .
   (a) Find the acceleration of the particle.
   (b) The direction of the force of magnitude 200 N is changed, and the force now acts at an angle of \(10 ^ { \circ }\) above the line of greatest slope. Find the acceleration of the particle.