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The diagram shows the cross-section \(O A B C D E\) through the centre of mass of a uniform prism on a rough inclined plane. The portion \(A D E O\) is a rectangle in which \(A D = O E = 0.6 \mathrm {~m}\) and \(D E = A O = 0.8 \mathrm {~m}\); the portion \(B C D\) is an isosceles triangle in which angle \(B C D\) is a right angle, and \(A\) is the mid-point of \(B D\). The plane is inclined at \(45 ^ { \circ }\) to the horizontal, \(B C\) lies along a line of greatest slope of the plane and \(D E\) is horizontal.
- Calculate the distance of the centre of mass of the prism from \(B D\).
The weight of the prism is 21 N , and it is held in equilibrium by a horizontal force of magnitude \(P \mathrm {~N}\) acting along \(E D\).
- (a) Find the smallest value of \(P\) for which the prism does not topple.
(b) It is given that the prism is about to slip for this smallest value of \(P\). Calculate the coefficient of friction between the prism and the plane.
The value of \(P\) is gradually increased until the prism ceases to be in equilibrium. - Show that the prism topples before it begins to slide, stating the value of \(P\) at which equilibrium is broken.
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