4.
\begin{figure}[h]
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\caption{Figure 2}
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\end{figure}
A box of mass 6 kg lies on a rough plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal. The box is held in equilibrium by means of a horizontal force of magnitude \(P\) newtons, as shown in Fig. 2. The line of action of the force is in the same vertical plane as a line of greatest slope of the plane. The coefficient of friction between the box and the plane is 0.4 . The box is modelled as a particle.
Given that the box is in limiting equilibrium and on the point of moving up the plane, find,
- the normal reaction exerted on the box by the plane,
- the value of \(P\).
The horizontal force is removed.
- Show that the box will now start to move down the plane.