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M3 statics watch

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    Heinemann M3, p. 195 ex. 5C q 5:

    A uniform thin hemispherical bowl rests in equilibrium with its axis of symmetry horizontal and its curved surface on a rough inclined plane. Find the angle between the plane and the horizontal.

    The centre of mass of the bowl, using the standard result, is 0.5r (where r is the radius) from either end, and the vertical dropped through the centre of mass must pass through the point of contact between the bowl and the plane.

    Diagram:


    Now, how do I find the angle from here, or have I totally missed something? (The answer given in the book's 30 degrees, by the way.)

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    Join the point of contact to the centre of the sphere and notice you get a triangle inside the hemisphere. Use trig in that triangle, and then notice that the small angle in that triangleis equal to the angle you want.

    Also, I don't think what you've labelled as r is r.
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    Acknowledge that the line which is perpendicular to the tangent at the contact point is rather interesting...
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    (Original post by generalebriety)
    Join the point of contact to the centre of the sphere and notice you get a triangle inside the hemisphere. Use trig in that triangle, and then notice that the small angle in that triangleis equal to the angle you want.

    Also, I don't think what you've labelled as r is r.
    Ah, thanks, and you're right, it's not, and I've just realised why that's a right angle. Thanks a lot, I'll rep you at midnight.
 
 
 
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Updated: July 14, 2008

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