All Problems

The Fundamental Equation of Dynamics

Problem 1.87

A small body \(A\) starts sliding off the top of a smooth sphere of radius \(R\). Find the angle \(\theta\) (Fig. 1.25 ) corresponding to the point at which the body breaks off the sphere, as well as the break-off velocity of the body.

Reveal Answer
θ=arccos(2/3)48,v=V2gR/3\theta=\arccos (2 / 3) \approx 48^{\circ}, \quad v=V \overline{2 g R / 3}