Determine the magnitude of the resultant force. Express your answer to three sig

Question

Determine the magnitude of the resultant force. 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 beta 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.

Explanation / Answer

Here, for the given forces

F1 = 400 * (cos(45) i + cos(60) j - cos(60) k)

F2 = 125 * (0.8 * (cos(20) i - j * sin(20)) + 0.6 k)

Now , for the net force

FR = F1 + F2

FR = 400 * (cos(45) i + cos(60) j - cos(60) k) + 125 * (0.8 * (cos(20) i - j * sin(20)) + 0.6 k)

FR = 377 i + 165.8 j -125 k N

magnitude of FR = sqrt(377^2 + 165.8^2 + 125^2)

magnitude of FR = 430.4 N

part B)

for the angle alpha

alpha = acos(377/430.4)

alpha = 28.8 degree

part C)

angle beta = arcos(165.8/430.4)

alpha = 67.34 degree

part D)

angle gamma = acos(-125/430.8)

gamma = 106.9 degree

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