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 analyze the forces acting on the particle on the inclined plane. The vertical component of the weight and the vertical component of the applied force must balance due to equilibrium conditions.

The components of the forces can be expressed as:

• Weight (W): The component acting perpendicular to the plane is given by:

  W imes rac{4}{5}

• Horizontal Force (F): The vertical component acting down the plane is given by:

  4 imes rac{3}{5}

Using equilibrium in the vertical direction:

R + 4 imes rac{3}{5} = W imes rac{4}{5}

Replacing W with 2R, since ( \mu = 1/2 ) implies that ( R = 0.5W ):

$R + 4 imes 0.6 = 2R$

This simplifies to:

$R = 20 N$