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# Applied Mathematics Question watch

1. --------------------------------------------------------------------------------

Uniform sphere of radius a and weight W is resting on a horizontal ground in contact with a step of height a/5.

coefficient of friction between sphere and the ground is 3/4
coefficient of friction between sphere and the step is µ

PICTURE ATTACHED

A gradually increasing force P is applied to the highest point of the sphere in a direction perpendicular to the edge of the step.

If equilibrium is broken by the sphere rotating about the step (rather than by slipping against the step and the ground) show that this happens when P=W/3.

If, on the other hand, equilibrium is broken by slipping, show that this happens when P=1/6W(3+µ)/(2-µ)

For what range of values of µ is the equilibrium broken by slipping?
Attached Files
2. mechanics diagram.doc (23.5 KB, 77 views)

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Updated: November 15, 2005
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