Cartesian Notation

Cartesian Notation Diagram  

Choose an axis system as shown and write the two vectors in Cartesian notation. It is important that the correct sign is used.

     F1 = 0i - 500j  lb

     F2 = 500 sin30i - 500 cos30j  lb

         = 250i - 433j  lb

    Addition of Forces

Addition of Forces Diagram  


Now that the two vectors are described using the unit vectors, i and j, they can been easily added. Adding the two forces will give the total force in Cartesian notation,

     FR = F1 + F2 = 250i - (500 + 433)j

         = 250i - 933j  lb

The magnitude of the total force can be determined by squaring the i and j magnitudes, and then taking the square root,

     FR = (2502 + 9332)0.5 = 965.9 lb

The angle at which the total force acts is,

     θ = tan-1 (250/933) = 15o

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