A particle of weight W newtons is held in equilibrium on a rough inclined plane by a horizontal force of magnitude 4 N - Edexcel - A-Level Maths Mechanics - Question 3 - 2011 - Paper 1

To find the normal reaction (R), we start by analyzing the forces acting on the particle on the inclined plane. The forces in the vertical and horizontal directions can be expressed as:

1. Radial component:

   $R imes ext{cos} heta + 4 imes ext{cos} heta = W imes ext{sin} heta$

2. Tangential component:

   $R imes ext{sin} heta = 4 imes ext{sin} heta + W$

From these equations, we can isolate R. Setting $\text{tan} \alpha = \frac{3}{4}$ gives us:

$\text{cos} \alpha = \frac{4}{5} \quad \text{and} \quad \text{sin} \alpha = \frac{3}{5}$

Then we substitute:

$R \cdot \frac{4}{5} + 4 \cdot \frac{4}{5} = W \cdot \frac{3}{5}$

This leads to:

$R = 20 N$.