Rod rotating on hinge collides with hanging particle, find L2/L1 ratio

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mistasong
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Homework Statement


A uniform rod of length L1 and mass M = 0.75 kg is supported by a hinge at one end and is free to rotate in the vertical plane (Figure). The rod is released from rest in the position shown. A particle of mass m = 0.5 kg is supported by a thin string of length L2 from the hinge. The particle sticks to the rod on contact. What should be the ratio L2/L1 so that θmax = 60o after the collision?

Homework Equations


Kf − Ki +Uf −Ui = 0

The Attempt at a Solution


I used energy concept to get Kf +Uf −Ui = 1/2(1/3ML)ω^2 +MgL1/2 − MgL1 = 0
I do not know where to go from here though and the teacher said there would be a cubic equation.
 

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mistasong said:

Homework Statement


A uniform rod of length L1 and mass M = 0.75 kg is supported by a hinge at one end and is free to rotate in the vertical plane (Figure). The rod is released from rest in the position shown. A particle of mass m = 0.5 kg is supported by a thin string of length L2 from the hinge. The particle sticks to the rod on contact. What should be the ratio L2/L1 so that θmax = 60° after the collision?

Homework Equations


Kf − Ki +Uf −Ui = 0

The Attempt at a Solution


I used energy concept to get Kf +Uf −Ui = 1/2(1/3ML)ω^2 +MgL1/2 − MgL1 = 0
I do not know where to go from here though and the teacher said there would be a cubic equation.
There is no figure.

From what angle is the rod released?

Also, we've provided icons to facilitate the use of subscripts, X2, and superscripts X2 .
 
You have to take into account inelastic collision. You can use conservation of work to find the speed of the rod just before collision, but you have to do something else to find the speeds after collision... Any ideas?