A particle of mass 0.5 kg is moving down a rough slope (with coefficient of friction = 0.2) inclined at 30 degrees to the horizontal. Find the acceleration of the particle. Use g = 9.8 ms^-2.

Resolving perpendicular to the plane: R - mg cos30 = 0. Therefore, R = m g cos30, where R is the reaction force perpendicular to the plane. Resolving down the plane: ma = m g sin30 - 0.2 R = m g sin30 - 0.2 m g cos30. Dividing by m, we find that a = g sin30 - 0.2 g cos30 and so a = 3.2 ms^-2 (2 s.f.).