Question

List the way to determine a resultant of forces where each force is expressed as its x and y-components, then the components in each direction are added to determine the resultant

Answer 1

To find the resultant of forces, isolate and sum the x and y components of each force, then use the Pythagorean theorem and arctangent function to determine the magnitude and direction of the resultant vector.

Step-by-step explanation:

How to Determine the Resultant of Forces Using Components

To determine the resultant of forces where each force is given by its x and y components, you need to add the components of individual vectors along the corresponding axis. Here is a step-by-step strategy:

• Isolate the x and y components of each force.
• Sum the x-components of all forces to find the resultant component in the x-direction (Rx).
• Sum the y-components of all forces to find the resultant component in the y-direction (Ry).
• Use the Pythagorean theorem to calculate the magnitude of the resultant vector (R) using the formula R = √(Rx² + Ry²).
• To find the direction of the resultant vector, use the formula θ = tan⁻¹(Ry/Rx).

This method is an analytical technique that simplifies vector addition by using algebra instead of graphical representations.