Question

6.) Consider three force vectors F1 with magnitude 98 N and direction 9◦ , F2 with magnitude 83 N and direction 133◦ , and F3 with magnitude 76 N and direction 285◦ . All direction angles θ are measured from the positive x axis: counter-clockwise for θ > 0 and clockwise for θ < 0.

What is the direction of F as an angle between the limits of −180◦ and +180◦ from the positive x axis with counterclockwise as the positive angular direction? Answer in units of ◦

Answer 1

given

F1 = 98 N at an angle of 9 deg

F2 = 83 N at an angle of 133 deg

F3 = 76 N at an angle of 285 deg

F1x = 98 cos 9 = 96.79 N

F1y = 98 sin 9 = 15.33 N

F2x = 133 cos 83 = 16.20 N

F2y = 133 sin 83 = 132 N

F3x = 76 cos 285 = 19.67 N

F3y = 76 sin 285 = -73.41 N

Net x component (x) = 19.67 + 16.20 + 96.79 = 132.66 N

Net y component (y) = -73.41 +132 +15.33 = 73.92 N

R = ( x^{2 + y 2 ) 1/2 =}  

(132.66^2 + 73.92^2)^0.5  = 151.86 N angle = tan^-1 y/x = tan ^-1 73.92 / 132.66 = 29.12 deg