What is the magnitude and direction of the resultant force? A force of F1 of 36 N pulls at an angle of 20° above due east. Pulling in the opposite direction is a force F2 of 48 N acting at an angle of 42° below due west. I have no idea on how to set up this problem. Any help is greatly appreciated.

Expert Answers

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The force F1 component to East = 36cos20 = 33.83N

The force F1 component to North = 36sin20 = 12.31

The force F2 component to West = 48cos42 = 35.67N

The force F2 component to South = 48sin42 = 32.12N


Let take forces to East and north as positive.

Then forces to West and South are negative forces to East and North forces.


Total force to East    = 33.83-35.67 = -1.84N

Total force to North  = 12.31-32.12 = -19.81N


Resultant force = sqrt[(-1.84)^2+(-19.81)^2] = 19.89N


Direction of resultant force = tan^(-1) (-19.81/-1.84)

                                       = 84.69 deg.


The resultant force is a force of 19.89N to the direction of 84.69 deg. below due west.


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