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How come when I try using the formula M = rF (sintheta) I get Moment at D = .223 * 300 * sin(25)= 28.4 Nm but it's wrong. The answer uses cross product but I thought I could just use the magnitudes of r and F and sine to get the same thing. How come it's not working? enter image description here

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    $\begingroup$ Nevermind it's the angle betwen r and F $\endgroup$
    – r2d2
    Feb 28, 2022 at 1:28

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The cross product is equivalent to multiplying the component R by the component of the force. There are two components of force that cause a moment:

  • The horizontal component = Fcos(25) acting at a distance of 0.2 m = 54.38 Nm
  • The vertical component = Fsin(25) acting at a distance of 0.1 m = 12.68 Nm

Because those two moments are in opposite directions, the total moment is the difference: 41.7 N*m counterclockwise about D.

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