The diagram shows three identical discs in equilibrium in
a vertical plane. Two discs rest, not in contact with each other,
on a horizontal surface
and the third disc rests on the other two. The angle at the upper
vertex of the triangle joining the centres of the discs is \(2\theta\).
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\noindent
The weight of each disc is \(W\).
The coefficient of friction between a disc and the horizontal surface
is \(\mu\) and the coefficient of friction between the discs is also \(\mu\).
- Show that the normal reaction between the horizontal surface and
a disc in contact with the surface is \(\frac32 W\,\).
- Find the normal reaction between
two discs in contact and show that the magnitude of the frictional force between two discs in contact is
\(\dfrac{W\sin\theta}{2(1+\cos\theta)}\,\).
- Show that if
\(\mu <2- \surd3\,\) there is no value of \(\theta\) for which
equilibrium is possible.