Finding Minimum Magnitude of Force Fr

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SUMMARY

The discussion focuses on determining the minimum magnitude of force F required to achieve the smallest resultant force Fr from three forces: a 5N horizontal force, a 4N vertical force, and force F directed at a 30-degree angle from the vertical. The solution involves resolving the known forces into their components and expressing the resultant force in terms of F. By applying differentiation to minimize the resultant force, participants confirm that the relationship between the components can be established using trigonometric functions.

PREREQUISITES
  • Understanding of vector resolution and force components
  • Knowledge of trigonometric functions and their applications in physics
  • Familiarity with differentiation techniques for optimization
  • Basic principles of static equilibrium in mechanics
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  • Study vector resolution techniques in physics
  • Learn about optimization methods using calculus
  • Explore the application of trigonometric identities in force analysis
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Students and educators in physics, particularly those focusing on mechanics and force analysis, as well as anyone involved in solving vector-related problems in engineering contexts.

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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. What is the minimum magnitude of Fr?


Homework Equations


Their is a 5N force heading horizontally to the right,
a 4 N force heading vertically downwards,
Force F is directed upwards and to the left, at an angle of 30 degrees south east of vertical (30 degrees from the 4N force)


The Attempt at a Solution



My prof said to leave it as a variable and solve it as normal, but i don't see how i can solve it. Do i find the resultant of the two known forces and use F as a variable from then on, seperating both into their separate components to find the final resultant force?
 
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Yes. Once you have the expression for the resultant force, minimize in the usual way by differentiation.
 
Well I think you'll have an expression for the magnitude of Fr in terms of, say, Fx and Fy, but Fx and Fy are related through trig since you were given an angle, so you can find them both and then the magnitude of F for the minimum Fr
 

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