Find Magnitude of Force F3 for Min Resultant FR

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SUMMARY

The discussion focuses on determining the magnitude of the unknown force F3, which acts at a 30-degree angle from the positive y-axis, to minimize the resultant force FR of three forces: F1 = [5i] kN and F2 = [-4j] kN. The relationship between the components of F3 (x' and y') is established using trigonometric functions based on the given angle. By applying algebraic techniques to express the resultant force as a function of F3, participants are guided towards methods for minimizing this function, ultimately leading to the solution for F3's magnitude.

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  • Familiarity with algebraic manipulation and minimization techniques
  • Basic principles of force equilibrium
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Homework Statement


Suppose we have the following forces:
F1=[5i]kN
F2=[-4j]kN
F3= unknown force 30 degrees from + y-axis.

How do you determine the magnitude of F3 such that the resultant FR for all three forces is a minimum?

Thanks in advance.
 
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You know that the resultant 'r' of any given force broken down into x & y components is r=(x^2+y^2)^(1/2), but what is your total x & y component...
well its x=5kN+x' and y=-4kN+y' (where x' & y' represent the unknown components of F3)

From this you can get a relationship between x' & y' of F3 using the given angle..

With some algebra you will end up with something that is a function of F3, and how do you minimize a function?
 

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