What is Root Force?
Root force is the magnitude of a resultant force calculated from its perpendicular components. When a force acts in two dimensions, it can be broken into x (horizontal) and y (vertical) components. The root force combines these components back into a single value representing the total force magnitude, using the Pythagorean theorem.
How to Calculate Root Force
Here is the formula:
[F = \sqrt{F_{x}^{2} + F_{y}^{2}}]
Where:
- F is the root force (magnitude of the resultant).
- F_x is the x-component of the force.
- F_y is the y-component of the force.
For three dimensions, add the z-component:
[F = \sqrt{F_{x}^{2} + F_{y}^{2} + F_{z}^{2}}]
Calculation Example
A force has an x-component of 40 N and a y-component of 30 N.
Square each component:
- 40² = 1,600
- 30² = 900
Add the squares:
[F = \sqrt{1{,}600 + 900} = \sqrt{2{,}500} = 50]
The root force is 50 N.