Calculate the magnitude of the total resultant force F⃗ r=F⃗ 1+F⃗ 2+F⃗ 3 acting on the mass. Express your answer in Newtons to three significant figures.

Resultant = (0.54î - 1.75j) N

Magnitude = 1.83 N, Direction = - 72.9°

Explanation:

From the free body diagram, the resultant is a vector sum of all the three individual forces.

F₁ = 4(cos 25°î + sin 25°j) = (3.625î + 1.691j) N

F₂ = 6(cos 325î + sin 325j) = (4.915î - 3.441j) N

F₃ = (- 8î) N

Resultant force = F₁ + F₂ + F₃ = (3.625î + 1.691j) + (4.915î - 3.441j) + (- 8î) = (0.54î - 1.75j) N

Magnitude = √[(0.54²) + (-1.75²)] = 1.83 N

Direction = tan⁻¹ (-1.75/0.54) = - 72.9°

its a 5.5 n

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