Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
A small ring $R$ is fastened to one end of a light inextensible string of length $70\,\text{cm}$. The string passes through a fixed rough vertical wire. Its other end is tied to a point $A$ on the wire, vertically above $R$. A horizontal force of magnitude $5.6\,\text{N}$ acts at the point $J$ of the string, which is $30\,\text{cm}$ from $A$ and $40\,\text{cm}$ from $R$. The system is in equilibrium, with both parts $AJ$ and $JR$ taut and angle $AJR$ equal to $90^\circ$ (see diagram).
(i)[5]
Determine the tension in the segment $AJ$ of the string, and determine the tension in the segment $JR$ of the string.
(ii)[4]
Hence show that the coefficient of friction between $R$ and the wire is $0.341$, correct to $3$ significant figures.
(iii)[3]
With the coefficient of friction unchanged, determine the value of $m$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolve the forces horizontally or vertically” …