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Calculate Magnitude of Moment in 3D

  • #1
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Homework Statement



The turnbuckle is tightened until the tension in cable AB is 1.5 kN. Calculate the magnitude of the moment about point O of the force acting on point A.


Homework Equations


ƩMO = sqrt(Mx2 + My2 + M2)


The Attempt at a Solution



First I identified the coordinates of points A and B:

A = (1.6, 0, 2.4)
B = (2.3, 1.4, 0)

OA = r = <1.6, 1.4, 0>
AB = <0.7, 1.4, -2.4>

|AB| = 2.865

λAB = AB/|AB|
λAB = 0,2443i + 0.4877j - 0.8377k

Then I took the dot product with the tension in the cable AB and the unit vector of AB

TABAB = 0.36645i + 0.73305J - 1.25655K

ƩMO = rXTAB

(0-1.75932)i -(-2.81796)J + (1.17288)k

ƩMO = 3.523

But it says my answer is wrong and I don't know where I'm going wrong.

Suggestions would be appreciated
 

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Answers and Replies

  • #2
249
0
I've just checked my working and found that I miscalculated the dot product.

<1.6, 0, 2.4> X <0.36645, 0.73305, -1.25655>

= -1.75932i + 2.88996J + 1.17288K

When I take the magnitude of this I get 3.58 which is the correct answer.
 

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