Example-2 : Resultant of coplanar concurrent forces | Engineering Mechanics

The resultant of coplanar concurrent forces is the single force that can replace multiple forces acting at different points on an object, such that it has the same effect as the original forces. These forces all act in the same plane, which means they lie on the same flat surface.

To find the resultant of coplanar concurrent forces, you can use the vector addition method. Here are the steps to calculate it:

Break Forces into Components: If the forces are not already given in component form, you'll need to break them down into their horizontal and vertical components. This is typically done using trigonometric functions such as sine and cosine.

Sum the Horizontal Components: Add up all the horizontal components of the forces. This gives you the total horizontal force.

Sum the Vertical Components: Add up all the vertical components of the forces. This gives you the total vertical force.

Combine the Horizontal and Vertical Components: Use the total horizontal and vertical forces to calculate the magnitude and direction of the resultant force. You can use the Pythagorean theorem to find the magnitude, and trigonometry to find the direction.

Here's the formula to calculate the magnitude and direction of the resultant force:

Magnitude (R): R = √(Rx^2 + Ry^2)

Direction (θ): θ = arctan(Ry / Rx)

Where:

Rx is the sum of the horizontal components of the forces.
Ry is the sum of the vertical components of the forces.
θ is the angle the resultant force makes with the horizontal axis.
The direction angle θ is usually measured counterclockwise from the positive horizontal axis.

Once you have calculated R and θ, you will have the resultant force, which can replace the original concurrent forces. This method works for any number of concurrent forces acting in the same plane.