Question

At what angle should the two forces vectors of 2F and root 2F
act so that the resultant force is root 10F​

Answer 1

Given :

Two force vectors of magnitudes 2F and √2 F whose resultant force is √10 F

• |F₁| = 2 F
• |F₂| = √2  F
• |R|  = √10  F

To find :

• Angle between force vector F₁ and F₂, θ = ?

Knowledge required :

• Formula to find the magnitude of Resultant of two vectors

       |R|² = |A|² + |B|² + 2 |A| |B| cos θ

[ where |R| is the magnitude of resultant of two vectors A and B with magnitudes |A| and |B| respectively, and θ is the angle between vectors A and B ]

Solution :

Using formula

→ |R|² = |F₁|² + |F₂|² + 2 |F₁| |F₂| cos θ

→ (√10 F)² = (2F)² + (√2 F)² + 2 (2F) (√2 F) cos θ

→ 10 F² = 4 F² + 2 F² + 4√2 F² cos θ

→ 10 F² = 6 F² + 4√2 F² cos θ

→ 10 F² = F² ( 6 + 4√2 cos θ )

→ 10 = 6 + 4 √2 cos θ

→ 4 = 4√2 cos θ

→ cos θ = 1 / √2

→ θ = cos⁻¹ ( 1 / √2 )

→ θ = π/4  

Therefore,

• The angle between Forces must be π/4.