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# What are the conditions for a system to be in a static equilibrium?

Last updated date: 21st Jul 2024
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Hint:An object is in static equilibrium if and only if the sum of the all forces acting on it in each direction is zero. Use this condition to solve the problem.The word equilibrium means balance. In particular, if a system is static equilibrium then it means that the system is at a stable condition and it is at rest.

Static equilibrium is defined as the state in which a system is stable and at rest. If a system is in complete static equilibrium, this system must have both rotational equilibrium (net torque on the system is zero) and translational equilibrium (net force on the system is zero).

For an object to be in equilibrium, the net acceleration of the object must be zero. Meaning that both the net force acting on the body and the net torque on the object must be equal to zero. Here we will discuss the first condition that is when the net force is zero.The mathematical expression of the first condition is given by ${F_{net}} = 0$.

For this condition of the system, the forces acting along each of the axes of motion of the object must be equal to zero. In a 2D system that can be written as, the net external forces acting along the x– and y-axes are zero. This can be written as,
$net\,{F_x} = 0\,\,and\,\,net\,{F_y} = 0$
The condition ${F_{net}} = 0$ have to be true for both types of static equilibrium, where the velocity of the object is zero, and for dynamic equilibrium of the system, the object will be moving at a constant velocity only.

The second condition of static equilibrium states that the net torque acting on an object must be equal to zero. This second condition is necessary. To achieve absolute equilibrium by an object involves avoiding any type of accelerated motion that includes accelerated rotation (a constant angular velocity). A rotating body or system can be said to be in equilibrium if its rate of rotational motion is constant and remains unchanged with respect to time by the torques acting on it.

The mathematical expression of the magnitude of torque is given by, $\tau = rFsin\theta$ where $\tau$ the symbol for torque is, $r$ is the distance from the pivot point to the point where the force is applied, $F$ is the magnitude of the parallel force, and $\theta$ is the angle between the force and the vector directed from the point of application to the pivot point.

Note: Static equilibrium is a valuable tool for analyzing motions: for example, if two forces are applied on an object which is in static equilibrium, then they will add up to zero. If we know the direction and magnitude of one of the forces, we can write an equation to determine the magnitude and direction of the unknown force.