Moderate -0.8 This is a straightforward equilibrium problem requiring resolution of forces in two perpendicular directions with a given angle. The solution involves basic trigonometry (finding sin α and cos α from tan α), then applying T cos α = mg and T sin α = F. It's simpler than average A-level mechanics as it's a standard two-force equilibrium with no complications, though it does require careful handling of the 8-15-17 triangle.
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\includegraphics[max width=\textwidth, alt={}, center]{3e58aa5a-3789-4aaf-8656-b5b98cd7f693-2_291_591_255_776}
A particle \(P\) of mass 0.3 kg is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point \(X\). A horizontal force of magnitude \(F \mathrm {~N}\) is applied to the particle, which is in equilibrium when the string is at an angle \(\alpha\) to the vertical, where \(\tan \alpha = \frac { 8 } { 15 }\) (see diagram). Find the tension in the string and the value of \(F\).
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\includegraphics[max width=\textwidth, alt={}, center]{3e58aa5a-3789-4aaf-8656-b5b98cd7f693-2_291_591_255_776}
A particle $P$ of mass 0.3 kg is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point $X$. A horizontal force of magnitude $F \mathrm {~N}$ is applied to the particle, which is in equilibrium when the string is at an angle $\alpha$ to the vertical, where $\tan \alpha = \frac { 8 } { 15 }$ (see diagram). Find the tension in the string and the value of $F$.
\hfill \mbox{\textit{CAIE M1 2013 Q1 [4]}}