- #1

kisengue

- 12

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## Homework Statement

In a 3-dimensional coordinate system, a hook is placed in A=(0,0,3). Two lines connect the hook down to a hatch that resides completely within the XY-plane. These lines keep the hatch horizontal. The lines attach to the corners of the hatch in B=(4,0,0) and C=(4,5,0). The magnitudes of the forces in the lines are S[AB]=P and S[AC]=sqrt(2)*P. (Did not know how to index S properly). What is the magnitude of the total force acting on the hook?

## The Attempt at a Solution

First, i figure out the complete description of the line forces one by one by multiplying the magnitude of the force with the force vector divided by the length of the force vector, F=P*(AB)/|AB|;

F[AB]= P*(B-A)/|B-A| = P*(4,0,-3)/sqrt(4²+3²) = P*(4,0,-3)/5

F[AC]= sqrt(2)*P*(C-A)/|C-A| = sqrt(2)*P*(4,5,-3)/|4²+5²+3²| = sqrt(2)*P*(4,5,-3)/(5*sqrt(2)) = P*(4,5,-3)/5

Then, i sum the line forces= P*(4,0,-3)/5 + P*(4,5,-3)/5 = P*(8,5,-3)/5.

The magnitude of the total force acting upon the hook would then be 1/5*P. But it isn't. The answer says sqrt(5)*P. What did i miss?

Sorry if it's not optimally legible, i tried to tidy it up as best i could... thankful for any help!