An open bucket of water is placed on a smooth flat surface inclined to the horizon at an angle a0. Denoting the velocity of the bucket by v and its acceleration by a, determine the angle of inclination a to the horizon of the free surface of the water under the following conditions: a) the bucket is at rest on the surface; b) the bucket is allowed to slide down at a constant speed; c) the bucket slides down without friction; d) what happens if the surface along which the bucket moves has variable curvature?

Detailed solution. Format gif