Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

Particle $P$, with mass $0.2\,\text{kg}$, is tied to one end of a light inextensible string of length $0.6\,\text{m}$. Its other end is connected to particle $Q$, which has mass $0.3\,\text{kg}$. The string goes through a tiny hole $H$ in a smooth horizontal plane. Particle $Q$ is linked to fixed point $A$ by a light elastic string with natural length $0.3\,\text{m}$ and modulus of elasticity $15\,\text{N}$, where $A$ lies $0.4\,\text{m}$ vertically beneath $H$. Particle $P$ travels across the surface in a horizontal circle centred at $H$ (see diagram).
(i)[4]

Calculate the maximum possible speed of $P$ so that the elastic string remains unstretched.

(ii)[5]

Find the distance $HP$ when the angular speed of $P$ is $8\,\text{rad s}^{-1}$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct radius $r = 0.6 - (0.4 - 0.3) = 0.5$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI