Standard +0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two perpendicular directions and basic trigonometry. While it involves multiple steps (resolving forces, setting up equations, solving for angle and resultant), the techniques are routine and commonly practiced. It's slightly easier than average A-level because it's a straightforward application of standard methods without requiring geometric insight or proof.
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\includegraphics[max width=\textwidth, alt={}, center]{dafc271d-a77b-4401-9170-e13e484d6e5f-2_582_751_255_696}
Three coplanar forces act at a point. The magnitudes of the forces are \(5.5 \mathrm {~N} , 6.8 \mathrm {~N}\) and 7.3 N , and the directions in which the forces act are as shown in the diagram. Given that the resultant of the three forces is in the same direction as the force of magnitude 6.8 N , find the value of \(\alpha\) and the magnitude of the resultant.
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\includegraphics[max width=\textwidth, alt={}, center]{dafc271d-a77b-4401-9170-e13e484d6e5f-2_582_751_255_696}
Three coplanar forces act at a point. The magnitudes of the forces are $5.5 \mathrm {~N} , 6.8 \mathrm {~N}$ and 7.3 N , and the directions in which the forces act are as shown in the diagram. Given that the resultant of the three forces is in the same direction as the force of magnitude 6.8 N , find the value of $\alpha$ and the magnitude of the resultant.
\hfill \mbox{\textit{CAIE M1 2010 Q1 [4]}}