| Masoud
Masoud |
A uniform solid consists of a hemisphere of radius r and a right circular cone of base radius r and height h, fixed together so that their plane faces coincide. The solid can rest in equilibrium with any point ot the curved surface area in contact with a horizontal plane. Find h in terms of r. I know that in this question the centre of mass must be assumed to be on the part of the solid where both circular faces meet however I don not know how to get h in terms of r, what's the strategy? Thank you |
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| Mark
Durkee |
Say that the sum of the moments of the two components of the solid about the line of intersection is zero. Therefore: pr2 h/3×h/4=2pr3/3×3r/8 |
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| Mark
Durkee |
I've just realised that i didn't explain where the parts of the equation come from. pr2 h/3 is the volume of the cone (proportional to its mass and therefore its weight) h/4 is the distance of the COM of a solid cone from its base 2pr3/3 is the volume of the hemisphere 3r/8 is the distance of the COM of the hemisphere from the flat surface So for the sum of the moments to be zero about the line of intersection: Volume of cone x Distance of COM of cone from the line of intersection = Volume of hemishpere x Distance of COM of hemisphere from line of intersection |
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| Masoud
Masoud |
Thank you for taking the time to answer my question. |