physics

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.

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!

  1. Henry

    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:
    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.

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