Would the change sign or the moment from positive to negative (or vice versa) Mo

Question

Would the change sign or the moment from positive to negative (or vice versa) Moment due to a force specified by magnitude and endpoints As shown, a member is fixed at the origin, point o. and has an applied force F. the tension in the rope. applied at the free end, point B. The force has magnitude F - 150 N and is directed as shown. The dimensions are x_1 = 0.450 in, x_2 = 180 m. y_1 = 2.60 in. and Z_1 =1.10 m. What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas.

Explanation / Answer

vector along the force vector,

BC = C - B = (0.450+1.80, 0, 0) - (0.450, 2.60, 1.10)

= 1.80i - 2.60j - 1.10k

unit vector = BCcap = (1.80i - 2.60j - 1.10k ) / sqrt(1.80^2 + 2.60^2 + 1.10^2)

= 0.538i - 0.777j - 0.328k

F vector = |F| BCcap = 80.7i - 116.55j -49.28k N

r = OB = B - 0 = 0.450i + 2.60j + 1.10k

moment = r x F

= ( 0.450i + 2.60j + 1.10k ) x ( 80.7i - 116.55j -49.28k N )

= - 52.45(k) - 22.18 (-j) + 209.82 (-k) - 128.13 (i) + 88.77j - 128.2(-i)

= 0i + 110.95j - 262.27k N m

Ans( 0 , 111 , - 262) N m

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