All Problems

The Fundamental Equation of Dynamics

Problem 1.108

A small body is placed on the top of a smooth sphere of radius R.R . Then the sphere is imparted a constant acceleration w0w_{0} in the horizontal direction and the body begins sliding down. Find: (a) the velocity of the body relative to the sphere at the moment of break-off; (b) the angle θ0\theta_{0} between the vertical and the radius vector drawn from the centre of the sphere to the break-off point; calculate θ0\theta_{0} for w0=gw_{0}=g.

Reveal Answer
1.108. (a) v=2gR/3v=\sqrt{2 g R / 3}; (b) cos⁡θ0=2+η5+9η23(1+η2),\cos \theta_{0}=\frac{2+\eta \sqrt{5+9 \eta^{2}}}{3\left(1+\eta^{2}\right)}, where η=\eta= =w0/g,θ0≈17∘=w_{0} / g, \theta_{0} \approx 17^{\circ}
Prev
Next