Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A slender groove is made along a diameter on the top face of a horizontal disc with centre $O$. Particles $P$ and $Q$, with masses $0.2\,\text{kg}$ and $0.3\,\text{kg}$ respectively, are placed in the groove, and the coefficient of friction between each particle and the groove is $\mu$. The particles are joined to opposite ends of a light inextensible string of length $1\,\text{m}$. The disc turns with angular velocity $\omega\,\text{rad s}^{-1}$ about a vertical axis through $O$, and the particles travel in horizontal circles (see diagram).
(i)[6]
Calculate the greatest possible value of $\omega$ and the matching tension in the string, given that $\mu = 0.36$ and that both $P$ and $Q$ travel in the same horizontal circle of radius $0.5\,\text{m}$.
(ii(a))[3]
Calculate the radius of the circle in which $P$ moves and the radius of the circle in which $Q$ moves, given instead that $\mu = 0$ and that the tension in the string is $0.48\,\text{N}$.
(ii(b))[3]
Calculate the speeds of the particles in each case.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme.