Definition:Equilibrant

Definition

Let $\mathbf F_1, \mathbf F_2, \ldots, \mathbf F_n$ be a set of $n$ forces acting on a particle $B$ at a point $P$ in space.

The equilibrant of $\mathbf F_1, \mathbf F_2, \ldots, \mathbf F_n$ is defined as the force which is needed to prevent $B$ from moving.

Examples

Forces at $\polar {100 \, \mathrm {kg}, 150 \degrees}, \polar {75 \, \mathrm {kg}, 60 \degrees}, \polar {50 \, \mathrm {kg}, -45 \degrees}$

Three forces $\mathbf F_1, \mathbf F_2, \mathbf F_3$ act on a particle $B$ at a point $P$ embedded in the complex plane:

\(\ds \mathbf F_1\)

\(=\)

\(\ds \polar {100 \, \mathrm {kg}, 150 \degrees}\)

\(\ds \mathbf F_2\)

\(=\)

\(\ds \polar {75 \, \mathrm {kg}, 60 \degrees}\)

\(\ds \mathbf F_3\)

\(=\)

\(\ds \polar {50 \, \mathrm {kg}, -45 \degrees}\)

The equilibrant $\mathbf E$ of $\mathbf F_1, \mathbf F_2, \mathbf F_3$ is:

$\mathbf E = \polar {80.8 \, \mathrm {kg}, -80.2 \degrees}$

Also see

• Magnitude and Direction of Equilibrant

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Polar Form of Complex Numbers: $86$