# Find Equilibrant Force Using Trig Method

• nikmar
In summary, to find the equilibrant force for a system, you need to consider the resultant force, which is the sum of the two forces in the system. The equilibrant force will have the same magnitude as the resultant force, but will be pointing in the opposite direction. This can be calculated using trigonometric methods by finding the x and y components of the forces and using the inverse trigonometric functions to determine the angles.
nikmar
force system a:
force no. 1: 5.0N at 0 deg
force no. 2: 5.0N at 90 deg
force system b:
force no. 1: 5.0N at 0 deg
force no. 2: 5.0N at 60 deg
force system c:
force no. 1: 5.0N at 30 deg
force no. 2: 5.0N at 150 deg

how do you find the equilibrant force using the trigonometric method? Do you multiply the force 1 (5.0) times cos 0 deg; force 2 (5.0) times cos 90 deg; etc?

Well, you have a few systems consisting of two forces here. Now, for every system, i.e. for every couple of forces, you must consider the resultant force, which is the sum of the two forces of a system. For example, for the system a, you have $$\vec{R}=\vec{F}_{1}+\vec{F}_{2}=5\vec{i}+5\vec{j}$$. So, the force which will set the system of equilibrium is a force with the same magnitude as the resultant force R, but pointing in the opposite direction. Now you have a clue.

Thank you for your input...I think I have it.

## 1. What is the trigonometric method for finding equilibrant force?

The trigonometric method for finding the equilibrant force involves using the principles of trigonometry to determine the magnitude and direction of the equilibrant force needed to balance out the given set of forces acting on an object.

## 2. How does the trigonometric method differ from other methods of finding equilibrant force?

The trigonometric method differs from other methods, such as the graphical or analytical methods, in that it uses specific trigonometric functions, such as sine, cosine, and tangent, to determine the components of the equilibrant force.

## 3. What are the steps involved in using the trigonometric method to find equilibrant force?

The steps involved in using the trigonometric method to find equilibrant force are:

1. Identify all the forces acting on the object and their respective magnitudes and directions.
2. Draw a vector diagram to represent the forces.
3. Choose a reference angle and determine the components of the given forces along that angle.
4. Use trigonometric functions to find the components of the equilibrant force along the same reference angle.
5. Combine the components to find the magnitude and direction of the equilibrant force.

## 4. Can the trigonometric method be used for any type of force system?

Yes, the trigonometric method can be used for any type of force system, including concurrent, coplanar, and non-coplanar force systems. It is a versatile method that can be applied to various types of problems involving equilibrant force.

## 5. How important is it to find the equilibrant force in a force system?

Finding the equilibrant force is crucial in understanding the overall balance of forces in a system. It helps determine whether an object is in equilibrium or not. Additionally, the equilibrant force can be used to calculate other important quantities, such as the net force and resultant force, in a given system.

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