Mathematics 9709 · AS & A Level · Probability

Probability — practice question

A rough horizontal disc turns about a fixed vertical axis that goes through its centre. A particle $P$ of mass $0.2\,\text{kg}$ stays in contact with the surface and, without slipping, moves with the disc at a distance of $0.5\,\text{m}$ from the axis. The largest speed of $P$ for which this motion can occur is $1.5\,\text{m s}^{-1}$.
(i)[2]

Calculate the coefficient of friction for the disc and $P$.

(ii)[5]

Find the greatest and least values of $\omega$ for which this motion is possible.

(iii)[2]

Calculate the value of $\omega$ at which the disc exerts no frictional force on $P$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies Newton’s second law with centripetal acceleration: $\dfrac{0.2\times1.5^2}{0.5}=F_r$

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