6 A particle \(P\) of weight 8 N rests on a horizontal surface. A horizontal force of magnitude 3 N acts on \(P\), and \(P\) is in limiting equilibrium.
- Calculate the coefficient of friction between \(P\) and the surface.
- Find the magnitude and direction of the contact force exerted by the surface on \(P\).
\includegraphics[max width=\textwidth, alt={}, center]{66eb8290-3a80-40bf-be40-a936ed7d5a1b-4_190_579_580_598}
The initial 3 N force continues to act on \(P\) in its original direction. An additional force of magnitude \(T \mathrm {~N}\), acting in the same vertical plane as the 3 N force, is now applied to \(P\) at an angle of \(\theta ^ { \circ }\) above the horizontal (see diagram). \(P\) is again in limiting equilibrium.
(a) Given that \(\theta = 0\), find \(T\).
(b) Given instead that \(\theta = 30\), calculate \(T\).