Question #281372

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?


1
Expert's answer
2021-12-20T10:30:19-0500

1.

0<mv22<2mgl,0<\frac{mv^2}2<2mgl,

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

2.

mv22>2mgl,\frac{mv^2}2>2mgl,

v>2gl.v>2\sqrt{gl}.


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