Moderate -0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions and solving simultaneous equations. The setup is straightforward with clearly defined angles, and the method (resolve horizontally and vertically) is a routine textbook technique for M1. Slightly easier than average due to the direct application of standard methods with no geometric complications or proof elements.
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\includegraphics[max width=\textwidth, alt={}, center]{4941e074-2f93-4a0c-80ba-0ca96a48389e-04_442_584_255_778}
Two light inextensible strings are attached to a particle of weight 25 N . The strings pass over two smooth fixed pulleys and have particles of weights \(A \mathrm {~N}\) and \(B \mathrm {~N}\) hanging vertically at their ends. The sloping parts of the strings make angles of \(30 ^ { \circ }\) and \(40 ^ { \circ }\) respectively with the vertical (see diagram). The system is in equilibrium. Find the values of \(A\) and \(B\).
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\includegraphics[max width=\textwidth, alt={}, center]{4941e074-2f93-4a0c-80ba-0ca96a48389e-04_442_584_255_778}
Two light inextensible strings are attached to a particle of weight 25 N . The strings pass over two smooth fixed pulleys and have particles of weights $A \mathrm {~N}$ and $B \mathrm {~N}$ hanging vertically at their ends. The sloping parts of the strings make angles of $30 ^ { \circ }$ and $40 ^ { \circ }$ respectively with the vertical (see diagram). The system is in equilibrium. Find the values of $A$ and $B$.\\
\hfill \mbox{\textit{CAIE M1 2017 Q3 [6]}}