+185
find the resultant of the following sets of forces, where f1 is the force and 0 the angle each force makes with the positive x-axis.
a. f1 = 15, 01 = 65 degrees, f2 = 37, 02 = 142 degrees
b. f1 = 6280, 01 = 37 degrees 10', f2 = 2840, 02 = 16 degrees 40'
c. f1 = 6800, 01 = 210 degrees, f2 = 7200, 02 = 315 degrees, f3 = 5600, 03 = 90 degrees
+33616 Try them this way:
x-component of resultant, fx = f1*cos(theta1) + f2*cos(theta2)
y-component of rsultant, fy = f1*sin(theta1) + f2*sin(theta2)
magnitude of resultant f = sqrt(f1^2 + f2^2)
angle of resultant to positive x-axis theta = tan-1(fy/fx)
+33616 For example a.
fx = 15*cos(65°) + 37*cos(142°) so fx = --22.817
fy = 15*sin(65°) + 37*sin(142°) so fy = 36.374
f = sqrt((-22.817)^2 + 36.374^2) so f = 42.938
Angle theta = tan-1(fy/fx) = tan-1(36.374/-22.817) = -57.9° However, because fy is positive and fx is negative this is in the second quadrant, so the angle from the positive x-direction going anti-clockwise around to the resulatnt is 180°-57.9° = 122.1°
