Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A small smooth ring $R$, with mass $0.6\,\text{kg}$, is placed on a light inextensible string of length $100\,\text{cm}$. One end of the string is fixed at point $A$. A small bead $B$ of mass $0.4\,\text{kg}$ is attached to the other end of the string, and it is threaded on a fixed rough horizontal rod that passes through $A$. The system is in equilibrium, with $B$ located $80\,\text{cm}$ from $A$.
(i)[3]

Find the string tension.

(ii)[4]

Find the contact force components, frictional and normal, acting on $B$.

(iii)[2]

Since the equilibrium is limiting, find the coefficient of friction between the bead and the rod.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: By resolving forces vertically on $R$, obtaining $2T\cos\alpha=0.6g$

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