FOUR CO-PLANERFORCES OF MAGNITUDE 10N ,17N,6N AND 20N ACT AT POINT O AS SHOWN IN D DIAGRAM ABOVE DETERMINE THE MAGNITUDE OF D RESULTANT FORCE
To determine the magnitude of the resultant force, we need to find the vector sum of the four given forces.
Step 1: Break down each force into its components.
Since the forces are acting in a plane (coplanar), we can use the x-y coordinate system.
Let's assume the positive x-axis is horizontal and the positive y-axis is vertical.
Force A: 10N
Resolve it into x and y components:
Ax = 10N * cos(theta_A)
Ay = 10N * sin(theta_A)
Force B: 17N
Resolve it into x and y components:
Bx = 17N * cos(theta_B)
By = 17N * sin(theta_B)
Force C: 6N
Resolve it into x and y components:
Cx = 6N * cos(theta_C)
Cy = 6N * sin(theta_C)
Force D: 20N
Resolve it into x and y components:
Dx = 20N * cos(theta_D)
Dy = 20N * sin(theta_D)
Step 2: Find the sum of the x-components and the sum of the y-components:
Sum of x-components = Ax + Bx + Cx + Dx
Sum of y-components = Ay + By + Cy + Dy
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant force:
Resultant magnitude (R) = sqrt((Sum of x-components)^2 + (Sum of y-components)^2)
By following these steps and substituting the appropriate values for the forces and angles, you will be able to calculate the magnitude of the resultant force.