Root Force Calculator, Formula, RF Calculation

Root Force Calculator

Enter the values of force component along the x-axis, F_x(N) and force component along the y-axis, F_y(N) to determine the value of root force, RF_(N).

Root Force Formula

The root force is calculated to find the resultant force magnitude when multiple forces are acting along different axes (for example, along the x and y axes). It is derived using the Pythagorean theorem in the context of vector addition.

Root force, RF_(N) in Newtons is calculated by the squareroot of the sum of square of force component along the x-axis, F_x(N) in Newtons and square of force component along the y-axis, F_y(N) in Newtons.

Root force, RF_(N) = √( F_x²_(N) + F_y²_(N) )

RF_(N) = root force in Newtons, N.

F_x(N) = force component along the x-axis in Newtons, N.

F_y(N) = force component along the y-axis in Newtons, N.

Root Force Calculation:

1. Given a situation where two perpendicular forces are acting on an object with magnitudes of 3 N and 4 N along the x and y axes, respectively. Calculate the root force.

Given: F_x(N) = 3N, F_y(N) = 4N.

Root force, RF_(N) = √( F_x²_(N) + F_y²_(N) )

RF_(N) =  √( 3² + 4² )

RF_(N) = √( 9 + 16 )

RF_(N) = √( 25)

RF_(N) = 5N.

2. A root force (RF) of 10 N and a force along the x-axis of 6 N, calculate the force along the y-axis.

Given: F_x(N) = 6N, RF_(N) = 10N.

Root force, RF_(N) = √( F_x²_(N) + F_y²_(N) )

F_y(N) = √( F_x²_(N) + F_y²_(N) )

F_y(N) = √( RF²_(N) – F_x²_(N) )

F_y(N) = √( 10² – 6²)

F_y(N) = √( 100 – 36 )

F_y(N) = 8N.

How does a Calculator find the Square Root?