Equilibrant Force

Reference data and engineering information about equilibrant force for mechanics applications.

equilibrantforceCalculator

Overview

Engineering reference data for Equilibrant Force in mechanics.

Key Formulas

Work

$W = Fd\cos\theta$

Work = force × displacement × cos(angle).

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Potential Energy

$E_p = mgh$

Gravitational potential energy.

Variables

Symbol	Description	Unit
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/s²
$v$	Velocity	m/s

The equilibrant force $\vec{E}$ is equal in magnitude but opposite in direction to the resultant force of the system. For a system of two forces $\vec{F_1}$ and $\vec{F_2}$ , the resultant $\vec{F_{1,2}}$ and equilibrant $\vec{E}$ are defined as:

$\vec{F_{1,2}} = \vec{F_1} + \vec{F_2}$

$\vec{E} = -\vec{F_{1,2}}$

Therefore, for a system to be in equilibrium, the vector sum of all applied forces ( $\vec{F_1}, \vec{F_2}, ...$ ) and the equilibrant force must be zero:

$\sum \vec{F}_{\text{applied}} + \vec{E} = \vec{0}$

Properties of the Equilibrant

Purpose: It is the single force needed to bring a system into static equilibrium.
Magnitude: It has the same magnitude as the resultant force of the system.
Direction: It acts in the exact opposite direction of the resultant force's line of action.
Application: Essential in engineering for determining loads on supports, anchors, or other constraints required to keep a structure or mechanism stationary under multiple applied forces.