Equilibrium of Concurrent Force
Category : JEE Main & Advanced
(1) If all the forces working on a body are acting on the same point, then they are said to be concurrent.
(2) A body, under the action of concurrent forces, is said to be in equilibrium, when there is no change in the state of rest or of uniform motion along a straight line.
(3) The necessary condition for the equilibrium of a body under the action of concurrent forces is that the vector sum of all the forces acting on the body must be zero.
(4) Mathematically for equilibrium \[\sum{{{{\overset{\scriptscriptstyle\rightharpoonup}{F}}}_{\text{net}}}=0}\] or \[\sum{{{F}_{x}}=0}\]; \[\sum{{{F}_{y}}=0}\]; , \[\sum{{{F}_{z}}=0}\]
(5) Three concurrent forces will be in equilibrium, if they can be represented completely by three sides of a triangle taken in order.
(6) Lami's Theorem : For three concurrent forces in equilibrium \[\frac{{{F}_{1}}}{\sin \alpha }=\frac{{{F}_{2}}}{\sin \beta }=\frac{{{F}_{3}}}{\sin \gamma }\]
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