Understanding the Center of Mass in a Hemispherical Bowl in Equilibrium

AI Thread Summary
The discussion revolves around understanding the center of mass (c.o.m) of a uniform hemispherical bowl in equilibrium when a mass is placed on its rim. The key point is the justification for the center of the circular rim being vertically aligned with the point of contact on the table. It is established that the table is tangent to the hemisphere's surface, making the line from the center of the hemisphere to the contact point perpendicular to the table. The participant expresses confusion over this concept, despite successfully calculating the c.o.m of the combined system. The conversation emphasizes the importance of grasping fundamental principles in physics to solve equilibrium problems effectively.
Helena54321
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I know and understand why the c of m of a uniform hemispherical shell (i.e a hollow hemisphere) is r/2 on the axis of symmetry (where r=radius of shell). I looked at the solution of the following question and still don't understand.

Question:

A hemispherical bowl, which may be modeled as a uniform hemispherical shell, has mass 3kg. A mass of of 2kg is placed on the rim and the bowl rests in equilibrium on a smooth horizontal plane. The plane surface of the bowl makes an angle theta with the horizontal. Show that tan theta= 4/3.

Answer: Taking moments about S (the point of contact with the table) :

3g x (r/2)sintheta= 2g x rcostheta.

My problem is I don't understand/know the justification for 0 (the centre of the circular rim of the shell) being on the same vertical line that passes through the point of contact with the horizontal table S.

I first considered the two masses into a composite body and worked out the centre of mass (0.4r, 0.3r) where x-axis is the plane of the circular rim and the y-axis the axis of symmetry of the bowl. This obviously yields the correct answer. But in order to even get this you need to know/understand that 0 is directly above S. Why does this have to be the case?

Can anybody help me? :/ x pweese x

It's in the edexcel M3 book. Exercise 5C Qstn 12. baa humbug
 
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Helena54321 said:
My problem is I don't understand/know the justification for 0 (the centre of the circular rim of the shell) being on the same vertical line that passes through the point of contact with the horizontal table S.
Would you agree that the table is tangent to the surface of the hemisphere, regardless of where contact is made? And thus a line drawn between the center of the sphere and the point of contact must be perpendicular to table?
 
Man am I stupid. I never get difficult things misunderstood, it's always the easy obvious most important things that I don't see.

THANK YOU! merci! arrigato! xie xie! dou zie! mgoisi!
 
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