Angle of a semicircle on a ramp

AI Thread Summary
The discussion focuses on determining whether a semicylinder on a rough inclined plane will slide down or tip over. The semicylinder, with a mass m and radius r, is on a plane inclined at 10 degrees, with a static friction coefficient of 0.3. It is established that the semicylinder does not slide down the plane. The main challenge is calculating the tipping angle θ of its base AB, which involves understanding equilibrium positions and accurately drawing the forces acting on the semicylinder. The solution ultimately involves applying the law of sines to find the angle θ.
stewood
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Homework Statement


The semicylinder of mass m and radius r lies on the rough inclined plane for which ϕ = 10∘ and the coefficient of static friction is μs = 0.3. Determine if the semicylinder slides down the plane, and if not, find the angle of tip θ of its base AB

Homework Equations


f=uN

The Attempt at a Solution


I think this requires some weird trigonemetry... I already calculated that the cylinder does not slide down but I cannot calculate the angle of theta
upload_2015-11-20_8-51-14.png
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stewood said:
but I cannot calculate the angle of theta
What did you try so far?
What do you know about equilibrium positions?
 
Your drawing of the forces could be a little more accurate. Where will the line of action of the normal force intersect AB?
 
mfb said:
What did you try so far?
What do you know about equilibrium positions?
I've tried a few different triangles, but I can't figure it out. I know nothing about equilibrium positions.
 
haruspex said:
Your drawing of the forces could be a little more accurate. Where will the line of action of the normal force intersect AB?
How can I calculate that?
 
Never mind, I figured it out. In case your curious you use the law of sines...
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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