Question

Two forces, F⃗ 1 and F⃗ 2, act at a point. F⃗ 1 has a magnitude of 8.80 N and is directed at an angle of 58.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 6.60 N and is directed at an angle of 53.9 ∘ below the negative x axis in the third quadrant. Part A What is the x component of the resultant force?

Answer 1

Rx = -8.55 N : x component of the resultant force

Step-by-step explanation:

Look at the attached graphic

The given forces are shown in the graph:

F₁= 8.8N : F₁ magnitude , α=58° : F₁ direction

F₂= 6.6N : F₂ magnitude , β= 53.9° : F₂ direction

F₁ component x

F₁x = -F₁cos α = -8.8N*cos58°

F₁x : -4.66N

F₂ component x

F₂x= -F₂*cos β = - 6.6N*cos53.9°

F₂x= - 3.89 N

x component of the resultant force (Rx)

Rx = F₁x+ F₂x

Rx = -4.66N - 3.89 N

Rx = -8.55 N