Rod in Hemispherical Bowl

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Homework Statement



A uniform rod AB of length 3R weight W rests inside a hemispherical bowl with radius of R. Determine the angle corresponding to equilibrium.

Homework Equations




The Attempt at a Solution


[/B]
Moment about A: -1.5R*mg cos(theta)+B*AB=0
Sum Fx: Acos(theta)-mg sin(theta)=0
Sum Fy: Asin(theta)-mg cos(theta)+B=0
sin(theta)/R=Sin(180-2theta)/AB

I have 4 equations and 4 unknowns: A, B, AB, theta

Does that seem right?
 

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  • #2
haruspex
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Does that seem right?
Yes, that all looks correct.
You could make it a bit simpler by taking moments about B instead of A, and leaving out sum Fy. That eliminates force B.
Also, the last equation can be simplified a lot. Just consider how to find AB/2 from R and theta.
 
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If I take the moment about B, how would I get the perpendicular distance between the y component of the weight and B?
AB/2=Rcos(theta)
 
  • #4
haruspex
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If I take the moment about B, how would I get the perpendicular distance between the y component of the weight and B?
AB/2=Rcos(theta)
Yes, that gives you AB. Subtract half the rod length from that to get the distance from B to the midpoint of the rod, then multiply by cos(theta) to get the horizontal distance.
 

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