Three professional wrestlers are fighting over a champion's belt, and each exerts a force on the belt. wrestler 1 exerts a force f1 = 40.0 n in the +x-direction, wrestler 2 exerts a force f2 = 80.0 n in the -y-direction, and wrestler 3 exerts a force f3 = 60.0 n at an angle of 36.9∘ counterclockwise from the +x-direction. find the x- and y-components of the net external force f⃗ on the belt.

The x-component of the net external force Fx = 88.0 N î

The y-component of the net external force Fy = - 44 N ĵ

Explanation:

Net force acting on an object is the sum of all forces acting upon it.

F = F1 + F2 + F3

Forces in terms of x,y-components:  

F₁ = 40 N î             (where î is the unit vector in x-direction)

F₂ = -80 N ĵ             (where ĵ is the unit vector in y-direction)

F₃ = 60 N

= F₃cosθ î + F₃sinθ ĵ

= 60*cos(36.9°) î + 60*sin(36.9°) ĵ

=  48î   + 36ĵ

Net External Force = F1 + F2 + F3

= 40 î - 80 ĵ  + 48 î  + 36 ĵ

= 40 î  + 48 î  - 80 ĵ  + 36 ĵ

= 88 î  - 44 ĵ

Here, only like components(same direction) can be added into each other.

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