Sum of magnitude of the two forces acting at a point is 16 N. If their resultant is normal to the smaller force…

Q: Sum of magnitude of the two forces acting at a point is 16 N. If their resultant is normal to the smaller force, and has a magnitude 8N, then the forces are

Sol: F₁ + F₂ = 16  …(i)

Resultant force is perpendicular of F₁ , then

F₂² – F₁² = 8²

⇒ (F₂-F₁)(F₂ + F₁) = 64

(F₂ – F₁) × 16 = 64    ….(ii)

Solving (i) & (ii), we get

F₁ = 6 N , F₂ = 10 N.