Question

Two forces of magnitude F and √3 F act at right angles to each other. Their resultant makes an angle β with F. The value of β is

Answer 1

Explanation:

let the resultant be equal to R.

R=√F^2 +3F^2

R=√4F^2

R=2F.

Answer 2

Given:

The magnitude of 1st force, F1 = F

The magnitude of 2nd force, F2 = √3 F

The angle between the two forces, θ = 90°

To Find:

The angle β made by the resultant with force F1.

Calculation:

- To calculate the angle, we have:

tan β = (F2 sin θ) / (F1 + F2 cos θ)

⇒ β = tan⁻¹ (√3 F sin 90°) / (F + √3 F cos 90°)

⇒ β = tan⁻¹  (√3 F / F)

⇒ β = tan⁻¹  (√3)

⇒ β = tan⁻¹ ( tan 60°)

⇒ β = 60°

- So the angle made by resultant with F is 60°.