STATICS problem: Minimum Resultant Force

In summary, the problem involves determining the minimum magnitude of F1 and the resultant force, with ∅=30 deg. The components of each force have been calculated and set up into a resultant vector, with F1 expressed symbolically. To find the minimum, the derivative of the resultant must be taken, using the given angles to write the components in terms of one variable and applying the standard derivative. The significance of the 'u' axis is unclear.
  • #1
SnaggleSquatch
1
0
Problem Statement: If the resultant force acting on the bracket is required to be a minimum, determine the magnitude of F1 and the resultant force. Set ∅=30 deg.

Probs.2-51_52_53.jpg


I have found the components of each force and set them up into a resultant vector, with F1 solved symbolically into its components. I'm not sure how to find the magnitude of F1 so that the resultant is a minimum.

Also, what is the significance of the 'u' axis?

I understand I have to take the derivative of the resultant but I'm not sure how its done. Any help is appreciated, Thanks!
 
Physics news on Phys.org
  • #2
You should have something that looks like ##R=(A+x)\hat x + (B + y)\hat y## where x and y are the components of F1. Minimize the magnitude of R.
Using the angles, you should be able to write x and y in terms of magnitude times either sine or cosine to get them to one variable.
Then you can use the standard derivative with respect to magnitude variable to find the minimum.
 

1. What is a "statics problem" in relation to minimum resultant force?

A statics problem is a type of engineering problem that deals with analyzing the forces acting on a stationary object. In the context of minimum resultant force, the problem involves determining the minimum amount of force required to keep an object in equilibrium.

2. How is minimum resultant force calculated in a statics problem?

To calculate the minimum resultant force, you need to first identify all the external forces acting on the object, including their magnitudes and directions. Then, using the equations of statics, you can determine the net force and moment on the object. The minimum resultant force is the force needed to counteract these external forces and maintain equilibrium.

3. What are the key principles involved in solving a minimum resultant force statics problem?

The key principles involved in solving a minimum resultant force statics problem are Newton's laws of motion, specifically the first and second laws. The first law states that an object at rest will remain at rest unless acted upon by an external force. The second law states that the net force on an object is equal to its mass multiplied by its acceleration.

4. Can minimum resultant force be negative in a statics problem?

No, minimum resultant force cannot be negative in a statics problem. This is because the minimum resultant force is the minimum amount of force required to maintain equilibrium, and a negative force would cause the object to accelerate in the opposite direction, breaking equilibrium.

5. How can understanding minimum resultant force in statics problems be applied to real-world situations?

Understanding minimum resultant force in statics problems is crucial in many real-world engineering applications, such as designing structures or analyzing the stability of objects. It allows engineers to determine the minimum amount of force needed to keep an object or structure in equilibrium, which is essential for ensuring safety and stability in various constructions and designs.

Similar threads

Engineering Resultant Force and Direction using Parallelogram Law
    • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
Engineering Hydrodynamic force on hinged flap gate
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Engineering Solving a Moment Vector Direction Problem: An Example from Statics Textbook
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Force Required to be a minimum
    • Engineering and Comp Sci Homework Help
Replies
13
Views
4K
Engineering Two approaches in statics not adding up
    • Engineering and Comp Sci Homework Help
Replies
5
Views
831
Statics problem on the resolution of forces
    • Introductory Physics Homework Help
Replies
18
Views
800
Projection of Resultant Force: Why Do We Need to Add B-Component?
    • Engineering and Comp Sci Homework Help
Replies
9
Views
4K
Simple Equivalence Problem- help please (First Year Statics)
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
To find the resultant of forces on a lamina
    • Introductory Physics Homework Help
Replies
5
Views
2K
Engineering Need help verifying symbolic calculations for an FBD statics problem
    • Engineering and Comp Sci Homework Help
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top