(695, #31) Two forces F1 and F2 with magnitudes 10 lb and 12 lb act on an object at a point P as shown in the figure. Find the resultant force F acting at P as well as its magnitude and its direction. (Indicate the direction by finding the angle theta shown in the figure.)

Solution:

F1 = F1( -cos45)i + F1( sin45)i = 10(-)i + 10()j = -5i + 5j

F2 = F2( cos30)i + F2( sin30)i = 12()i + 12(1 / 2)j = 6i + 6 j

F = F1 + F2 = -5i + 5j+ 6i + 6 j = (-5+ 6)i + ( 6 + 5)j

F is the vector (-5+ 6)i + ( 6 + 5)j, has a magnitude of 13.5, and is at an angle of 75.7 degrees.

by: nl