particle is zero. * According to the first law, this means that, the particle is either at rest or in uniform motion. If two forces F and F , act on a particle, equilibrium requires F = − F ( . ) i.e.
the two forces on the particle must be equal and opposite. Equilibrium under three concurrent forces F , F and F requires that the vector sum of the three forces is zero. F + F + F = ( . ) Fig.
. Equilibrium under concurrent forces. In other words, the resultant of any two forces say F and F , obtained by the parallelogram law of forces must be equal and opposite to the third force, F . As seen in Fig.
. , the three forces in equilibrium can be represented by the sides of a triangle with the vector arrows taken in the same sense. The result can be generalised to any number of forces. A particle is in equilibrium under the action of forces F , F ,...
F n if they can be represented by the sides of a closed n-sided polygon with arrows directed in the same sense. Equation ( . ) implies that F 1x + F 2x + F 3x = F 1y + F 2y + F 3y = F 1z + F 2z + F 3z = ( . ) where F 1x , F 1y and F 1z are the components of F along x , y and z directions respectively.
Example . See Fig. . .
A mass of kg is suspended by a rope of length m from the ceiling. A force of N in the horizontal direction is applied at the mid- point P of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ? (Take g = m s - ).
Neglect the mass of the rope. (a) (b) (c) Fig. . * Equilibrium of a body requires not only translational