posted by olivia .
A sled at rest is suddenly pulled in three horizontal directions at the same time, but it does not move. Paul pulls to the northeast with a force of 39 lb. Johnny pulls at an angle of 44° south of due west with a force of 68 lb. Connie pulls with a force to be determined.
1) Express the boys' two forces in terms of the usual unit vectors.
5) Determine the third force (from Connie), expressing it first in component form and then as a magnitude and direction (angle). Neglect friction.
Paul: F1 = 39Lb[45o] = 27.6 + 27.6i.
Johnny: F2 = 68Lb[224o] = -48.9 - 47.2i.
F1+F2 = (27.6+27.6i) + (-48.9-47.2i),
F1+F2 = -21.3 - 19.6i = 28.9Lb[42.6o]S. of W. = 28.9Lb[222.6] CCW.
Connie's force is the equilibrant force, because it reduces the resultant force to zero:
F3 = -(F1+F2) = -(-21.3-19.6i) = 21.3 + 19.6i = 28.9Lb[42.6o] N. of E. = 28.9Lb[42.6o] CCW.