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Difficult Mechanics 2 Problem

1. A uniform Lamina is in the shape of an Equilateral triangle ABC, and rests in equilibrium inside a vertical hoop with B and C in contact with the hoop, and A at the center of the circle. Contact is smooth at C but rough at B, where the coefficient of friction is U (mu). The lamina is in limiting equilibrium with B lower than C, and the axis of symmetry through A makes an angle theta with the vertical. By first taking moments about A show that =U*/(-U)
2. (Original post by Electric-man7)
A uniform Lamina is in the shape of an Equilateral triangle ABC, and rest in equilibrium inside a vertical hoop with B and C in contact with the hoop, and A at the center of the circle. Contact is smooth at C but rough at B, where the coefficient of friction is U (mu). The lamina is in limiting equilibrium with B lower than C, and the axis of symmetry through A makes an angle theta with the vertical. By first taking moments about A show that tan(theta)=U*sqrt(3)/sqrt(3)-U
What have you tried??
3. (Original post by RDKGames)
What have you tried??
I have tried to take the moments about A, and also the moments about C, but when I take the moments about C I have to include not only the the moment of the normal force at B, but also the moment of the force of friction. I have also tried resolving all the forces ( contact forces at B, C, and the weight of the lamina) in the directions perpendicular and parallel to BC, but I can't seem to continue to from here. Any Ideas?
4. (Original post by Electric-man7)
A uniform Lamina is in the shape of an Equilateral triangle ABC, and rests in equilibrium inside a vertical hoop with B and C in contact with the hoop, and A at the center of the circle. Contact is smooth at C but rough at B, where the coefficient of friction is U (mu). The lamina is in limiting equilibrium with B lower than C, and the axis of symmetry through A makes an angle theta with the vertical. By first taking moments about A show that =U*/(-U)
Having spent several hours trying to do it via the suggested method and getting it wrong, I resorted to triangle of forces (combined the forces at B into one to reduce the count to three).

And get

Which although different to the desired result in your first post, does agree with a thread on stackexchange. And the working was a hell of a lot simpler.
5. (Original post by ghostwalker)
Having spent several hours trying to do it via the suggested method and getting it wrong, I resorted to triangle of forces (combined the forces at B into one to reduce the count to three).

And get

Which although different to the desired result in your first post, does agree with a thread on stackexchange. And the working was a hell of a lot simpler.
Thanks a lot, I have eventually managed to use the suggestion, to solve the problem but I can't imagine how this problem was ever on an OCR exam.

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