Three forces act on an object. Two of the forces are at an angle of 100◦to each other and have magnitude 25N and 12N. The third is perpendicular to the plane of these two forces and has magnitude 4N. Calculate the magnitude of the force that would exactly counterbalance these three forces.

F₄ = 29.819 N

Explanation:

Given

F₁ = ( - 25*Cos 50° i + 25*Sin 50° j + 0 k) N

F₂ = (12*Cos 50° i + 12*Sin 50° j + 0 k) N

F₃ = (0 i + 0 j + 4 k) N

Then we have

F₁ + F₂ + F₃ + F₄ = 0

⇒ F₄ = - (F₁ + F₂ + F₃)

⇒ F₄ = - (( - 25*Cos 50° i + 25*Sin 50° j) N + (12*Cos 50° i + 12*Sin 50° j) N + (4 k) N) = (13*Cos 50° i - 37*Sin 50° j - 4 k) N

The magnitude of the force will be

F₄ = √ ((13*Cos 50°) ² + ( - 37*Sin 50°) ² + ( - 4) ²) N = 29.819 N