# Simple moments q. with diagramWatch

#1
Heinemann Edexcel- Review exercise 2 q. 35.

The diagram shows a uniform solid hemisphere of mass m, base radius a and with centre of mass G. The hemishere is freely pivoted at a point A on the circumference of it's plane face and a light string connects B to a point C on the horizontal plane through A. The system is in equilibrium with A, B, C and G in the same vertical plane, BC is perpendicular to AB and AB is inclined to AC at an angle &#32;θ where tan &#32;θ = 4/3. Show that the thrust in the spring has magnitude 3mg/20.

Here's what I've done so far: I took moments from A, perpendicular to the plane =>
mga cos &#32;θ = 2aT
cos &#32;θ = 3/5 &#32;∴ 3mga/5 = 2aT
T = 3mg/10

Where have I gone wrong? Thanks in advance.
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#2
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9 years ago
#3
Please draw the diagram, with the points labelled, and the spring shown. As it stands, I can't make any sense of it.
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#4
ok, here's the revised diagram.
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9 years ago
#5
I think you are making the mistake of assuming that the centre of mass of the solid hemisphere is in the middle of the flat face.
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#6
Right, now I see. I was trying to 'turn' the action of the mass by using the cosine function, which I now know is wrong. Thanks
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