1.1. This question involves a particle of mass 5 kg in motion on a rough plane which is inclined at $30^{\circ}$ to the horizontal.  The coefficient of friction between the particle and the plane is 0.3.

Initially the particle is projected up a line of greatest slope of the plane, and moves upwards until the combined forces of friction and gravity cause it to come to rest.

By first decomposing the weight of the particle into components parallel and perpendicular to the plane, determine the frictional force acting on the particle as it moves up the plane.  Be sure to give both the magnitude and the direction of the force.

1.2. Using your results from part (a), along with the Newton’s Second Law of Motion equation $F=ma$,  determine the acceleration of the particle while it is moving up the plane.  Be sure to give both the magnitude and the direction of the acceleration.

1.3. After coming momentarily to rest, the particle begins to slide back down the plane.

Determine the frictional force acting on the particle as it slides down the plane, being sure to give both the magnitude and the direction of the force.

1.4. Determine the acceleration of the particle while it is sliding down the plane, being sure to give both the magnitude and the direction of the acceleration.