Moderate -0.3 This is a standard two-dimensional equilibrium problem requiring resolution of forces in perpendicular directions and solving simultaneous equations. While it involves multiple forces at various angles and requires careful trigonometry (using given sine values to find cosines), it follows a routine procedure taught in M1 with no novel insight needed. The calculation is somewhat involved but methodical, making it slightly easier than average.
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\includegraphics[max width=\textwidth, alt={}, center]{ba29ddb2-3558-4be1-a8a8-134e27a70149-04_456_767_260_689}
Four coplanar forces act at a point. The magnitudes of the forces are \(20 \mathrm {~N} , 30 \mathrm {~N} , 40 \mathrm {~N}\) and \(F \mathrm {~N}\). The directions of the forces are as shown in the diagram, where \(\sin \alpha ^ { \circ } = 0.28\) and \(\sin \beta ^ { \circ } = 0.6\).
Given that the forces are in equilibrium, find \(F\) and \(\theta\).
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\includegraphics[max width=\textwidth, alt={}, center]{ba29ddb2-3558-4be1-a8a8-134e27a70149-04_456_767_260_689}
Four coplanar forces act at a point. The magnitudes of the forces are $20 \mathrm {~N} , 30 \mathrm {~N} , 40 \mathrm {~N}$ and $F \mathrm {~N}$. The directions of the forces are as shown in the diagram, where $\sin \alpha ^ { \circ } = 0.28$ and $\sin \beta ^ { \circ } = 0.6$.
Given that the forces are in equilibrium, find $F$ and $\theta$.\\
\hfill \mbox{\textit{CAIE M1 2021 Q3 [6]}}