Equilibrium of Bodies under the Action of Coplanar Forces

Equilibrium of Bodies under the Action of Coplanar Forces

If a body remains at rest or moves with uniform speed, it is said to be in equilibrium. A body at rest is said to be in static equilibrium, while a body in uniform motion along a straight line is said to be in dynamic equilibrium. All the bodies, in static or dynamic equilibrium, do not possess any acceleration.

Let us consider a spherical ball of weight 5N suspended from the ceiling by a string. The ball is in static equilibrium. There are two forces acting on the ball.

(i) The force of gravity W = 5N directed downward,

(ii) The upward pull of the string, known as tension T in the string. These two forces balance each other, so the ball is at rest.

The forces on the ball are represented. Thus if a body is to remain in static equilibrium, the upward force must balance the downward force.

As another example of static equilibrium, consider a block which is placed on a smooth surface and is being pulled at two ends. Suppose the weight of the block is 100N. A boy is pulling one end of the rope to the left. The block is attached to the wall by a spring balance which reads 50N. For simplicity we ignore the force of friction. Four forces are acting on the block and it is at rest. Weight of the block acting vertically downward is balanced by the push of the surface acting vertically upward. The block is being pulled towards left by hand and it is being pulled towards right by the spring balance. As the block remains at rest, so these forces must also balanced each other. If the black is to remain in static equilibrium, the force towards left must be balanced by the force towards right and the upward force must be balanced by the downward force. The forces acting on the block are represented. Thus the resultant of all the four forces acting on the block is zero.

A paratrooper falling with uniform velocity is an example of dynamic equilibrium. When a paratrooper jumps from an aeroplane, it moves down with an acceleration due to gravity.