Equilibrium of Forces

The force is the external agent capable of changing the body’s state from rest or motion. In equilibrium, all the experienced forces are adjusted such that the total or net force acting on the system is zero. It plays a crucial role in understanding the body's dynamic and static status. The article covers the concept of equilibrium of forces in detail.

Image: Equilibrium of Forces

Table of Contents

Types of Equilibrium
The Equation for Equilibrium of Forces

Types of Equilibrium

The equilibrium is of two types, static and dynamic.

1. Static Equilibrium

The static equilibrium is such that the resultant of the forces on the body is zero. It further conveys that net acceleration and the body's velocity will also be zero. The overall interpretation is the status of the body is rest. Such a body will be assumed to be in static equilibrium.

A common example of static equilibrium is a pen resting on the table, an apple hanging from a tree, a book on top of the table, and multiple others.

2. Dynamic Equilibrium

The dynamic equilibrium is such that the resultant of all forces acting on the body is zero, similar to the condition of net acceleration. However, the velocity of the body is non-zero. The body will remain in motion with constant velocity.

Common examples include simple harmonic motion, the car moving with constant velocity on a straight road, running on a treadmill and others.

The Equation for Equilibrium of Forces

The equation for the equilibrium of forces follows Newton's second law of motion, which mathematically states that the net force acting on the body is zero if the force is defined as the product of mass and acceleration.

The equation representing the net force to be zero is:

, where is the vector sum of all the forces acting on the body. The equation hence is a vector equation as it includes the forces acting in all directions. The equation is applicable for both translational and rotational equilibrium.

On further expansion and specificity, the equilibrium of forces can be divided into horizontal and vertical components. It will be further represented as

The implication of the above equations indicates the necessity for the net sum of 0 in forces acting in each horizontal and vertical direction.

Rule of Equilibrium of Forces

The rule of equilibrium of forces is derived from Newton’s second law of motion and the concept of vector addition. Let us assume a body in equilibrium under the action of three forces (F₁,F₂ and F₃). Further, assuming the forces F₁ and F₂ act in the same direction while force F₃ acts in the opposite direction. Hence, according to the rule of equilibrium of forces, the equation will depict the sum of forces as zero.

Practice Problems

Q1. What are the conditions required for the equilibrium of forces?

a. The vector sum of all the forces must be zero.
b. The vector sum of all the torques must be zero
c. The object must be at rest or have a constant velocity
d. All of the above

Ans. d. All of the above.

Explanation: All the conditions must be met collectively for the object to be in a state of equilibrium.

Q2. What is the normal force exerted by the ladder on 200N inclined at 60 degrees on the wall?

a. 100 N
b. 50 N
c. 0 N
d. -50 N

Ans. a. 100 N

Explanation:

Normal forces = 100 N

Q3. What is static equilibrium?

a. Condition when net forces acting on the body are zero.
b. Condition when the body is in constant motion.
c. Condition when the body is at rest.
d. Both a and c

Ans. d. Both a and c

Explanation: The static equilibrium in the body's condition at rest.