- #1
Helena54321
- 5
- 0
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
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
