Resolve forces perpendicular to the plane:

\(R = P \sin 35 + 0.6g \cos 35\)

Resolve forces parallel to the plane:

\(F + P \cos 35 = 0.6g \sin 35\)

Using \(F = 0.4R\), substitute into the parallel resolution equation:

\(0.4R + P \cos 35 = 0.6g \sin 35\)

Substitute \(R = \frac{0.6g}{\cos 35 + 0.4 \sin 35}\) into the equation:

\(0.4 \left( \frac{0.6g}{\cos 35 + 0.4 \sin 35} \right) + P \cos 35 = 0.6g \sin 35\)

Solve for \(P\):

\(P = \frac{0.6g \sin 35 - 0.4 \times 0.6g \cos 35}{\cos 35 + 0.4 \sin 35}\)

Calculate \(P\) to get \(P = 1.41 \text{ N}\).