Determine the Magnitude of Force F

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SUMMARY

The discussion focuses on determining the magnitude of force F to minimize the resultant force FR from three vectors. Participants emphasize the importance of resolving vectors into their x- and y-components to facilitate calculations. The solution requires the application of calculus to find the optimal value of F that minimizes the vector sum. The discussion highlights the necessity of understanding vector components and calculus principles for effective problem-solving.

PREREQUISITES
  • Vector resolution into components
  • Basic calculus principles
  • Understanding of resultant forces
  • Familiarity with vector notation
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  • Study vector resolution techniques in physics
  • Learn how to apply calculus to optimize functions
  • Explore the concept of resultant forces in multiple dimensions
  • Practice problems involving vector addition and minimization
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Students in physics courses, particularly those focusing on mechanics, as well as educators and tutors assisting with vector analysis and optimization problems.

Nacha
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Homework Statement



Determine the magnitude of force F so that the resultant FR of the three forces is as small as possible


Homework Equations



Question 2-33.gif


The Attempt at a Solution



Need some help??

Thanks,

Nacha
 
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Do you know how to resolve vectors into components? The most direct way to deal with this is to find separately the x-components and y-components for each of the three vectors (calling the magnitude of the unknown vector F for now), then find the sums of the x- and y-components.

You are asked to find the value of F that will make the magnitude of the vector sum smallest. The most direct way to do this requires calculus. Is your course calculus-based?
 

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