Find Magnitude of Force F3 for Min Resultant FR

AI Thread Summary
To find the magnitude of force F3 that minimizes the resultant force FR from the given forces F1 and F2, the components of F3 must be expressed in terms of its angle of 30 degrees from the positive y-axis. The resultant force is calculated by combining the x and y components of all forces, leading to the equations x = 5 kN + x' and y = -4 kN + y'. By establishing a relationship between the x' and y' components of F3, one can derive a function dependent on F3. To minimize this resultant function, calculus techniques such as finding the derivative and setting it to zero can be employed. This approach will yield the required magnitude of F3 for the minimum resultant force.
quantum_enhan
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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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