# OCR A Level: Mechanics 2 - Sliding And Toppling [June 2011 Q7]

Classical Mechanics Level pending

A uniform solid cone of height $$0.8m$$ and semi-vertical angle $$60°$$ lies with its curved surface on a horizontal plane. The point $$P$$ on the circumference of the base is in contact with the plane. $$V$$ is the vertex of the cone and $$PQ$$ is a diameter of its base. The weight of the cone is $$550 \text{N}$$. A force of magnitude $$F \text{N}$$ and line of action $$PQ$$ is applied to the base of the cone (see Fig. 1). The cone topples about $$V$$ without sliding.

$$(\text{i})$$ Calculate the least possible value of $$F$$.

The force of magnitude $$F \text{N}$$ is removed and an increasing force of magnitude $$T \text{N}$$ acting upwards in the vertical plane of symmetry of the cone and perpendicular to $$PQ$$ is applied to the cone at $$Q$$ (see Fig. 2). The coefficient of friction between the cone and the horizontal plane is $$\mu$$.

$$(\text{ii})$$ Given that the cone slides before it topples about $$P$$, calculate the greatest possible value for $$\mu$$.

Input the nearest integer to $$1000 \mu$$ as your answer.

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