The three supporting cables exert the force shown in Represents force F_N as a C

Question

The three supporting cables exert the force shown in Represents force F_N as a Cartesian vector. Express your answer in terms of the unit vector i, j, and k. Use the 'vet' button to denote vectors in your answers. Express your answer using three significant figures. F_N =___N Represents force C_N as a Cartesian vector Express your answer in terms of the unit vector i, j, and k. Use the 'vet' button to denote vectors in your answers. Express your answer using three significant figures. F_C =___N Represents force F_E as a Cartesian vector. Express your answer in terms of the unit vector i, j, and k. Use the 'vet' button to denote vectors in your answers. Express your answer using three significant figures. F_E =___N

Explanation / Answer

A = (5, 0, 0) m

B = (0, 2, 4) m

C = (0, -2, 4) m

AB is along Fb vector.

AB vector = -5i + 2j + 4k

|AB| = sqrt(5^2 + 2^2 + 4^2) = 6.708

ABcap = AB/|AB|

Fb = 400 N ( ABcap) = - 298.14 i + 119.26 j + 238.51 k N

AC is along Fc vector.

AC vector = -5i - 2j + 4k

|AC| = sqrt(5^2 + 2^2 + 4^2) = 6.708

ACcap = AC/|AC|

Fc = 400 N ( ACcap) = - 298.14 i - 119.26 j + 238.51 k N   

F = Fb + Fc = - 596.28 i + 477.03 k

(A) magnitude = |F| = sqrt(596.28^2 + 477.03^2) = 763.61 N

(B) alpha = cos^-1(Fx/ F) = cos^-1(-596.28/763.61) = 141.34 deg

(C) beta = cos^-1(Fy / F) = cos^-1(0) = 90 deg

(D) gamma = cos^-1(477.03 / 763.61) = 51.34 deg

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