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Show that the semi-vertical angle of the cone is $45^\circ$ and calculate the size of the force exerted on $P$ by the cone’s surface.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A particle $P$ with mass $0.5\,\text{kg}$ travels in a horizontal circle on the smooth inner face of a hollow cone, fixed with its axis vertical and vertex downwards. $P$ moves with angular speed $5\,\text{rad s}^{-1}$ in a circle of radius $0.4\,\text{m}$ (see diagram).