( Figure 1 ) What is the moment about the origin due to the applied force F ? M
ID: 1861591 • Letter: #
Question
(Figure 1)
What is the moment about the origin due to the applied force F?
MO=[ i,j,k]N?m 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 = 135 N and is directed as shown. The dimensions are x1 = 1.9 m, x2 = 10.3 m, y1 = 11.9 m, andz1 = 1.7 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
Cordinates of B=(1.9,11.9,1.7)
Let the point where rope is attached be C
Cordinates of C=(10.3,0,0)
OB=10.3i +11.9j +1.7k
CB=(10.3-1.9)i +(0-11.9)j +(0-1.7)=8.4i -11.9j -1.7k
|CB|=(8.4^2+11.9^2+1.7^2)^0.5=14.6649
F=|F|*CB/|CB|=135*(8.4i -11.9j -1.7k)/14.6649=77.3275i -109.5473j -15.6496k
Moment about origin=OBxF=(10.3i +11.9j +1.7k) x (77.3275i -109.5473j -15.6496k)
a
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