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 38 lb. Johnny pulls at an angle of 43° south of due west with a force of 66 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:

lb

8)

Direction:

° North of East

Explanation / Answer

Here ,

1) for Paul

Force of Paul = 38 * (cos(45) i + j * sin(45))

Force of Paul = 26.9 i + 26.9 j lb

the force of paul is 26.9 i + 26.9 j lb

1) x component = 26.9 i lb

2)

y copmonent = 26.9 j lb

3) for Johnny

Force = 66 *(- cos(43) i + j * sin(43))

Force = -48.3 i + 45 j lb

x component = -48.3 lb i

4)

y component = 45 j lb

5) as the net force is zero

Force of connie + force of paul + force of jonny = 0

Fc + 26.9 i + 26.9 j -48.3 i + 45 j lb = 0

Fc = 21.4 i - 71.9 j lb

x component of Connie = 21.4 lb i

6)

y component of Connie = - 71.9 j lb

7) magnitude of connie force = sqrt(21.4^2 + 71.9^2)

magnitude of connie force = 75.02 lbs

8)

angle = 360 - arctan(71.9/21.4)

angle = 286.6 degree

the direction of Connie force is 286.6 degree north of east

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