Determine the magnitude of the resultant force Figure 1 Expr

Determine the magnitude of the resultant force. (Figure 1) Express your answer to three significant figures and include the appropriate units. Determine the coordinate direction angle alpha of the resultant force. Express your answer using three significant figures. Determine the coordinate direction angle of the resultant force. Express your answer using three significant figures. Determine the coordinate direction angle gamma of the resultant force. Express your answer using three significant figures.

Solution

F1 = 90 (4/5 i + 0j + 3/5 k) = 72i + 54k N

F2 = 150 [ (cos60)(sin45)i + (cos60)(cos45)j + sin60 k]

F2 = 53.03 i + 53.03 j + 129.90 k N

F3 = 200 k N

F = F1 + F2 + F3

F = 125.03 i + 53.03 j + 383.90k

(A) magnitude = sqrt[ 125.03^2 + 53.03^2 + 383.90^2] = 407.21 N

(B) alpha = cos^-1(Fx/ F) = cos^-1(125.03 / 407.21) = 72.12 deg

(C) beta = cos^-1(Fy / F) = cos^-1(53.03 / 407.21) = 82.52 deg

(D) gamma = cos^-1(Fz / F) = 19.48 deg