Find Magnitude of Force F3 for Min Resultant FR

In summary, to determine the magnitude of F3 that will result in a minimum resultant force for all three forces, you can use the given angle to find a relationship between the x and y components of F3. This relationship can then be used to create a function that is a function of F3, which can be minimized to find the magnitude of F3.
  • #1
quantum_enhan
23
0

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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  • #2
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?
 

Related to Find Magnitude of Force F3 for Min Resultant FR

What is the definition of "magnitude of force"?

The magnitude of force is the size or strength of a force, represented by a numerical value and a unit of measurement. It is a vector quantity, meaning it has both magnitude and direction.

How do you find the magnitude of a force?

To find the magnitude of a force, you need to know its components in the x, y, and z directions. Then, you can use the Pythagorean theorem to calculate the resultant force, which is the magnitude of the original force.

What is a resultant force?

A resultant force is a single force that has the same effect as all the original forces acting on an object. It is the vector sum of all the individual forces, taking into account their magnitudes and directions.

What is the minimum resultant force?

The minimum resultant force is the smallest possible value for the resultant force. It occurs when the individual forces are aligned in a way that cancels out their effects, resulting in a smaller magnitude of the resultant force.

How do you calculate the minimum resultant force for multiple forces?

To calculate the minimum resultant force, you need to find the vector sum of all the forces acting on an object. This can be done by breaking down the forces into their components and using vector addition to find the resultant force. The magnitude of the minimum resultant force will be smaller than the magnitudes of the individual forces.

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