Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A particle $P$ weighs $10\,\text{N}$ and is in limiting equilibrium on a rough horizontal table. The forces drawn in the diagram are the weight of $P$, an applied force of magnitude $4\,\text{N}$ acting on $P$ at $30^{\circ}$ above the horizontal, and the contact force from the table on $P$ (the resultant of the frictional and normal components) with magnitude $C\,\text{N}$.
(i)[3]

Determine the value of $C$.

(ii)[2]

Determine the coefficient of friction between $P$ and the table.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate triangle of forces with $60^\circ$ indicated, or accurate components $C\cos\phi=4\cos30$, $C\sin\phi=10-4\sin30$

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