Moderate -0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions. Students must resolve horizontally and vertically to form two simultaneous equations, then solve for F and G. While it requires careful angle work and simultaneous equations, it's a routine textbook exercise with no novel insight needed—slightly easier than average due to its straightforward method.
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A particle \(P\) is in equilibrium on a smooth horizontal table under the action of horizontal forces of magnitudes \(F\) N, \(F\) N, \(G\) N and 12 N acting in the directions shown. Find the values of \(F\) and \(G\). [6]
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\includegraphics[max width=\textwidth, alt={}, center]{b5873699-d207-4cad-9518-1321dc429c15-2_508_1011_1096_568}
A particle $P$ is in equilibrium on a smooth horizontal table under the action of horizontal forces of magnitudes $F$ N, $F$ N, $G$ N and 12 N acting in the directions shown. Find the values of $F$ and $G$. [6]
\hfill \mbox{\textit{CAIE M1 2006 Q3 [6]}}