What is concurrent force? What is the necessary condition for the… - Vidyadip

Question

What is concurrent force? What is the necessary condition for the balance of concurrent forces?

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Answer

Concurrent forces : If the lines of action of forces acting on an object pass through a common point then it is called concurrent forces.
In the figure, the lines of action of $\vec{F}_1, \vec{F}_2$ and $\vec{F}_3$ are passing forces $F _1, F_2$ and $F _3$ are passing
through a common point $O$. Hence $\vec{F}_1$, $\rightarrow \quad \rightarrow$ $F_2$ and $F_3$ are concurrent forces. When concurrent forces are applied on a body only linear acceleration can occur in that body.

Equilibrium of concurrent forces : When many forces are acting on an object yet there is no change in state of object then the object is said to be in equilibrium. In this situation, the vector sum of forces should be zero. Hence if vector sum of accompanying forces is zero then it is called the equilibrium state of forces.That is, concurrent forces $\overrightarrow{ F }_1, \overrightarrow{F_2} \ldots \ldots . \overrightarrow{ F }_n$ will be in equilibrium if,
$
\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}+\overrightarrow{F_4}+\overrightarrow{F_5}+\ldots \ldots . \overrightarrow{F_n}=0$
On writing as components,
$\begin{array}{l}
\overrightarrow{F}_{1 x}+\overrightarrow{F}_{2 x}+\overrightarrow{F}_{3 x}+\ldots \ldots \cdot \overrightarrow{F}_{n x}=0 \\
\overrightarrow{F}_1 y+\overrightarrow{F}_{2 y}+\overrightarrow{F}_{3 y}+\ldots \ldots \cdot \overrightarrow{F}_{n y}=0 \\
\overrightarrow{F}_{1 z}+\overrightarrow{F}_{2 z}+\overrightarrow{F}_{3 z}+\ldots \ldots \cdot \overrightarrow{F}_{n z}=0
\end{array}$
Therefore, for concurrent forces to balance, the sum of component of forces along any axis (direction) must be zero.

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