EXAMPLE 5.0.1: MOMENT OF COPLANAR FORCES

Determine the moment of force F about point A

With force F lying on plane xy, we can solve this problem using either the vector method (r x F) or with the scalar method (Fd). With either case, it is longer if we use the force directly, that is, it is more difficult to determine the perpendicular distance from point A to the line of action of force F. Thus, the force needs to be converted to its components.

USING THE VECTOR METHOD

Force F in vector form is computed as follows:

                                   

Next is to identify the distance of these components from point A. Remember the transmissibility of the force which makes it travel to its line of action. Force is considered a sliding vector and from the illustration, we can identify the exact distance using three points - B, C, and D. Let us use point B for this method.

Distances from point A to point B shows -4inches horizontally and +6inches vertically. In vector form

                                     

By taking the cross product of these two, we obtain the moment of the force 
about point A.

                                   

        ANSWER

USING SCALAR METHOD

The easier method for coplanar moments is the scalar method though trickier. Check the rotation to have the proper sign when solving the resultant.

1. Point B as force origin:

By using the sign convention (clockwise-positive, counterclockwise-negative), the moment shows

                ANSWER

2. Point C as force origin:

Using point C as the origin, notice that F2 runs through point A. This will not yield any perpendicular distance d2, thus d2 = 0. So,











3. Point D as force origin:

Similar with point C, F1 will run through point A if the components are slid down to point D. d1 for this case will also be zero, thus

                                                             ANSWER


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