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STATICS - CASE STUDY SOLUTION

    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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