Suppose that h 4 m Determine the magnitude of the resultant

Suppose that h = 4 m. Determine the magnitude of the resultant force of the two force acting on the Sign at points A Express your answer to three significant figures and include the appropriate units E_R Determine the coordinate direction angle alpha of the resultant force of the two forces acting on the sign at point A Express your answer using three significant figures alpha =___Determine the coordinate direction angle beta of the resultant force of the two forces acting on the sign at point A Express your answer using three significant figures beta =___Determine the coordinate direction angle gamma of the of the two forces acting on the sign at point A. Express your answer using three significant figures gamma =___

Solution

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