Question

To find the resultant of multiple forces using Cartesian components and to determine the direction of this resultant from its components.As shown, three forces act on the tip of a pole. F2 =110 lb and forms the following angles with the x, y, and z axes, respectively: , and 7 = 135.3n. Fi = 120 lb, forms the angle = 24* with the z axis, and forms the angle 9 = 15n between the x axis and the projection of F3 in the xy plane.

Answer 1

The magnitude of the three vectors is 182.85lb which is between the x axis and the projection of F3 in the xy plane

How to calculate the force vectors?

To calculate the force vectors

for Force F1

F1 = -60i+ 125j+45k

For the force F2

F2 = F2(cosai+cosbj+cosck)

=110(cos55.7+cos65.1j+cos135.3k)

= 61.98i + 46.31j-78.18k

For the force F3

F3 = F3(cososinoi - sinosinoj+cosok)

= 120(cos15sin24i-sin15sin24j+cos24k)

=47.145i-12.63j+109.62k

To calculate the resultant force for forces F1 and F3

F1 + F3

= -60i+125j+45k+47.145i-12.63j+109.62k

F13 = -28.85i + 112.37j+154.62k

To calculate the resultant force by considering all the forces

F123 = F1+F2+F3

= 49.125i + 158.68j+76.44k

Calculate the magnitude of the resultant force

Squareroot(49.125  ^ 2 + 158.68 ^ 2 + 76.44 ^2

= 182.85lb

Thus the magnitude of the force is 182.85 lb

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