Answer to Question #281372 in Classical Mechanics for EdwardD

Question

A light rod of length L and a little weight of mass m make up the pendulum. In a vertical plane, the rod can complete a full rotation. The weight is initially in the bottom equilibrium position. A horizontally directed velocity v is applied to the weight. What values of v will cause the pendulum to oscillate, and what values will cause it to rotate in the vertical plane? At what starting velocity v will the rod be crushed at the top point, and at what initial velocity v will it be stretched?

Answer 1

1.

$0<\frac{mv^2}2<2mgl,$

$0<v<2\sqrt{gl},$

2.

$\frac{mv^2}2>2mgl,$

$v>2\sqrt{gl}.$