- #1
sergiokapone
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Homework Statement
Uniform sphere of mass ##m## and radius ##r##, rolling without slipping on a horizontal surface at a velocity ##v_0##, hits the end of a rod of length ##l## and mass ##10m##, hanging on a hinge (Figure). Determine how the ball will move and the rod after the impact. What time after, the motion of the ball goes into pure rolling? What is the speed of the roller? An impact is perfectly elastic and instantaneous. The coefficient of friction of the ball on the plane is ##k##. Rolling friction neglected.
Homework Equations
Eqs of conservations:
Angular momentun: ##mv_0l=\dfrac{10ml^2}{3}\omega-mvl##
Energy: ##\underbrace{\dfrac{mv_0^2}{2}+\dfrac{2}{5}mr^2\dfrac{v_0^2}{2r^2}}_{\dfrac{7mv_0^2}{10}}=\dfrac{10ml^2}{3}\dfrac{\omega^2}{2}+\dfrac{mv^2}{2}##
The Attempt at a Solution
I feel that I made a conceptual error in the conservation laws, but I do not know where.