I am specifically asking about the cross product method, I already know the comp

Question

I am specifically asking about the cross product method, I already know the component method. I need to know why the 80 lb forces are negative when the standard is positive for counter clockwise rotation. if you cannot answer that do not waste my time and MONEY by answering it the other way. I ONLY NEED TO KNOW THE CROSS PRODUCT METHOD AND WHY THE 80 LB FORCES ARE NEGATIVE, DO NOT GIVE ME ANY OTHER WAY OF SOLVING IT. Thank you, I hope...

4-80 Two couples act on the frame. If d 4 ft, determine the resultant couple moment. Compute the result by resolving each force into x and y components and (a) finding the moment of each couple (Eq. 4-13) and (b) summing the moments of all the force components about point A. 2 ft-3t 3050 lb I ft 30° 50 lb SOLUTION 80 lb 3 ft 80 lb 0 50sin 30° -50 cos 30° 1-4(80) -5(80) 0 Mc (126k) lb.ft Ans 5 4 (b) + Mc-- (80)(3) + (80)(7) + 50 cos 30°(2)-50 cos 30°(5) Mc 126 lb ft Ans.

Explanation / Answer

Here the moment of the 80lb force is calculated at the point exactly at 3ft above point A where one of the 80lb force is acting. So this is the point where the moment is calculated. So the remaining 80 lb force that is below point B is divided into components in negative x and y directions. So those components will have negative sign and forms the force vector.

A position vector is also made between the two forces which has only y component of position vector which is 4ft.

The cross product is calculated between these position and force vector and force vectors.

SimolaS procedure is followed for the 50lb force also.then these two moments are added to calculate the total moment.

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