If F 1 = 109 N , F 2 = 128 N and F 3 = 87 N , determine the magnitude and coordi

Question

If F1 = 109N , F2 = 128N and F3 = 87N , determine the magnitude and coordinate direction angles of the resultant couple moment.

If F1 = 109N , F2 = 128N and F3 = 87N , determine the magnitude and coordinate direction angles of the resultant couple moment. Determine the magnitude of the resultant couple moment. (The magnitude is not 70.33! Mastering engineering said that 78.17 was close) Determine the coordinate direction angle ? of the resultant couple moment. Determine the coordinate direction angle ? of the resultant couple moment. Determine the coordinate direction angle ? of the resultant couple moment. I'll paste the link to the diagram for the problem below and an explaination of how you got the problem would be nice.

Explanation / Answer

M1 = -F1*0.2 j = -21.8 j

M2 = F2*0.2 i = 25.6 i

M3 = -F3*0.2 k = -17.4 k

M4 = 150*0.3*Cos30 along that pipe.

Origin of M4 = (-0.2, 0.2, 0.3)

Position vector = of M4 = (0, 0, 0.2)

Therefore, Vector M4 = (0.2, -0.2, -0.1)

Magnitude = sqrt (0.2^2 + 0.2^2 + 0.1^2) = 0.3

Thus, M4 in Cartesian form = (150*0.3*Cos30)*0.2/0.3 i - (150*0.3*Cos30)*0.2/0.3 j - (150*0.3*Cos30)*0.1/0.3 k

M4 = 25.98 i - 25.98 j - 12.99 k

Resultant M = M1 + M2 + M3 + M4

M = 51.58 i - 47.78 j - 30.39 k

Magnitude of M = sqrt (51.58^2 + 47.78^2 + 30.39^2) = 76.596 Nm

Coord. direction angle, alpha = acos (25.98/76.596) = 70.17 deg

Angle beta = acos (-47.78 / 76.596) = 128.59 deg

Angl gama = acos (-30.39 / 76.596) = 113.37 deg

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