TWO-DIMENSIONAL MOTION OF A PARTICLE ON AN INCLINED PLANE

A particle on an inclined plane is under the action of a constant sliding force due to the gravity and a frictional force, with the direction of the frictional force varying with the velocity. When the ratio of the friction factor to the slope gradient of the inclined plane, i.e. the equivalent frictional factor, λ> 1, the particle will eventually stop on the slope; when 0:5 <λ≤1, the particle will not stop but with a limit in the horizontal direction; and when λ≤0:5, the particle can move to an infinite distance in the horizontal direction. The curves of the particle trajectories have an outer envelope for the same equivalent friction factor.