A particle of mass 0.4 kg is held at rest on a fixed rough plane by a horizontal force of magnitude P newtons - Edexcel - A-Level Maths Mechanics - Question 7 - 2010 - Paper 1

To find the normal reaction force (R), we can use the equilibrium condition in the vertical direction. The forces acting in the vertical direction are:

1. The component of the weight acting perpendicular to the inclined plane: ( mg \cos(\alpha) )
2. The normal reaction force (R)
3. The vertical component of the applied force (P) which is acting parallel to the incline.

Using these relationships, we can set up the equation:

$R = \frac{1}{3} mg = \frac{1}{3}(0.4)(9.81) \approx 1.31 \text{ N}$

Now to find using the horizontal net force:

$R \cos(\alpha) - F \sin(\alpha) = 0.4g$

Substituting ( \tan(\alpha) = \frac{3}{4} ) gives us an angle of ( \alpha ) to calculate the value of R, which results in R being approximately 6.53 or 6.5 N.