PROBLEM 2.135 Find the magnitude and direction of the resultant of the two forces shown knowing that P = 600 N and Q = 450 N.
SOLUTION P = (600 N)[sin 40° sin 25°i + cos 40°j + sin 40° cos 25°k ] = (162.992 N)i + (459.63 N) j + (349.54 N)k Q = (450 N)[cos 55° cos 30°i + sin 55°j − cos 55° sin 30°k ] = (223.53 N)i + (368.62 N) j − (129.055 N)k R =P+Q = (386.52 N)i + (828.25 N) j + (220.49 N)k R = (386.52 N) 2 + (828.25 N) 2 + (220.49 N) 2 = 940.22 N cos θ x =
Rx 386.52 N = R 940.22 N Ry
cos
θy = cos θ z =
R
R = 940 N W
θ x = 65.7° W
828.25 N =
940.22 N
Rz 220.49 N = R 940.22 N
θ y = 28.2° W θ z = 76.4° W