A sled at rest is suddenly pulled in three horizontal directions at the same tim

Question

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 37 lb. Johnny pulls at an angle of 42° south of due west with a force of 64 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:

       ° North of East

Explanation / Answer

a) Express the boys two forces in terms of the usual unit vectors.
37 lb x cos 45deg = 26.162i
37 lb x sin 45 deg = 26.162i
Paul:26.162 lb i + 26.162 j answer

= 180 + 42 = 222deg
64 lb x cos 222deg = - 47.56i
66 lb x sin 220 deg = -42.82j
Johnny: -47.56 lb i - 42.82lb j answer

b) Fx = 26.162i - 47.56i + xi = 0
xi = 21.398 i

Fy = 26.162i -42.82j + yj = 0
yj = 16.658j

Therefore, F(Connie) = 21.398 lb i + 16.658 lb j answer

Magnitude = sqrt[21.398^2 + 16.658^2] = 27.1175 lb
Direction: = arctan(16.658/21.398) = 37.90 North of East answer

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