A particle of mass m moves along the internal smooth surface of a vertical cylinder of the radius R . Find the force with which the particle acts on the cylinder wall if at the initial moment of time its velocity equals v 0 . and forms an angle α with the horizontal.

Step-by-step solution

The direction of the velocity of the particle may be shown as in the diagram. This velocity V 0 is resolved in two components. Here V 0 cos α component is tangential horizontal and V 0 sin α is along the surface but vertically downwards. Here, if the particle exerts a force N on the surface of the cylinder, the cylinder will also apply equal and opposite force on the particle and this will provide a centripetal force to the particle. So, N = m V 0 cos α 2 / R = mV 0 2 cos 2 α / R or, N = mV 0 2