A sphere of mass m slides over the outer surface of a cone with angle ϕ and height h. The...

A sphere of mass m slides over the outer surface of a cone with angle ϕ and height h. The sphere was released at a height h0 with a velocity of magnitude υ0 and a direction that was completely horizontal. Assume that the opening angle of the cone and the value of υ0 are such that the sphere does not separate from the surface of the cone once put in motion. In addition, assume that the friction between the sphere and the cone is negligible. Determine the vertical component of the sphere’s velocity as a function of the vertical position z (measured from the base of the cone), υ0, h, h0, and ϕ.

Figure P5.91