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STATICS - CASE STUDY SOLUTION

 

Using the basic force-equilibrium equations in the x and y directions, the forces FA and FB can be determined:

     ΣFx = 0
     ΣFy = 0

Sum the forces in both directions gives:

     -FA cosα + FB cosθ = 0
     FA sinα + FB sinθ - W = 0

   
    Four Significant Digits

 

Substitute numerical values up to four significant digits into the previous two equations.

     -FA cos17.49 + FB cos11.46 = 0
      FA sin17.49 + FB sin11.46 -146.7 = 0

Solve the two equations for the unknown values of FA and FB:

     
     FA   = 488.1 - 0.6434 FA

     FA   = 297.0 lb
     FB   = 289.0 lb

   
    Two Significant Digits

 

Round the given numerical values to two significant digits and substitute into previous equations.

     -FA cos17 + FB cos11 = 0
     FA sin17 + FB sin11 - 150 = 0

Solve the two equations for the unknown values of FA and FB:

     

The numerical values in each step are also rounded to two significant digits:

     
     FA   = 520 - 0.64 FA

     FA   = 320 lb
     FB   = 320 lb

Notice the value of FA is 23 lb, or 7.7% higher, than when four significant digits were used. The percentage of error will vary from problem to problem, but when only two significant digits are used, the answer will generally be off by more than 1 percent. Therefore, rounding to only two significant digits should be avoided.

     
   
 
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