physics
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.
Paul:
2)
3) Johnny:
4)
5) Determine the third force (from Connie), expressing it first in component form and then as a magnitude and direction (angle). Neglect friction.
Connie:
6)
7) Magnitude:
8) Direction
Thank you!

Paul: F1 = 39Lb[45o] = 27.6 + 27.6i.
Johnny: F2 = 68Lb[224o] = 48.9  47.2i.
F1+F2 = (27.6+27.6i) + (48.947.2i),
F1+F2 = 21.3  19.6i = 28.9Lb[42.6o]S. of W. = 28.9Lb[222.6] CCW.
Connie:
Connie's force is the equilibrant force, because it reduces the resultant force to zero:
F3 = (F1+F2) = (21.319.6i) = 21.3 + 19.6i = 28.9Lb[42.6o] N. of E. = 28.9Lb[42.6o] CCW.
posted by Henry
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