Question

The resultant of two forces is 180 N it makes an angle of 40 with each force find magnitude of two forces.

Answer 1

Answer:

Let the force along the x-axis be “Rx” and force along y-axis be “Ry”.(as shown in the figure below)

The resultant of two forces, R = 180 N

R makes an angle of θ= 40° with each of the force  

The magnitude of the resultant force is given by

R = $\sqrt{Rx^2 + Ry^2}$

Or, [180]² = [Rx² + Ry²]

Or, [Rx² + Ry²] = 32400 ….. (i)

The angle θ that R makes with the each of the forces can be calculated by using trigonometry,

tan θ = Ry / Rx

or, tan 40° = Ry / Rx

or, Ry = 0.839 Rx …. (ii)

substituting the eq.(ii) in (i), we get

[Rx² + (0.839 Rx)²] = 32400

Or, [Rx² + 0.7039 Rx²] = 32400

Or, 1.7039 Rx² = 32400

Or, Rx = $\sqrt{\frac{32400}{1.7039}}$ = 137.89 N

And,  

Ry = 0.839 * 137.89 = 115.68 N

Hence, the magnitude of two forces is 137.89 N and 115.68 N.