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The term potential energy was introduced by William Rankine in the 19th century and is an essential concept in chemistry and physics. Potential energy and equilibrium are concepts that are related to each other. When conservative forces act on the system, it helps connect and define equilibrium in terms of potential energy. Any system’s potential energy helps explain the stability of any system concerning its mean position.
How are potential energy and equilibrium related to each other?
Any object, based on its position, can store energy. The potential energy is the overall energy stored by an object based on its position concerning other objects, its electric charge or stress within it. The potential energy and equilibrium are connected. As soon as an object is displaced from its equilibrium, it gains potential energy due to the change in position or state. Here are some examples of potential energy, which are:
- Gravitational potential energy is the energy processed or acquired by an object when there is a change in its position in the presence of the gravitational field. When the body of mass (m) moves from infinity to a point within the gravitational field of mass without accelerating, the amount of work done for displacing the body is known as its gravitational potential energy.
- Electric potential energy is the energy that is defined as the total potential energy when an object is moved against an electric field and the total electric field it gains during the process.
- Elastic potential energy is the total energy stored in the elastic material as a result of compressing or stretching the object. Such energy is stored in objects like rubber bands, springs etc.
The formulae of potential energy are presented by
W = m x g x h
Where
m = mass in kilograms
g = acceleration due to gravity
h = height (in m)
Understanding the concept of equilibrium
When an object or system is at equilibrium, its state of motion or internal state does not change with time. According to the state of motion or rest for a body, the equilibrium can be divided into two categories which include:
Dynamic Equilibrium
- A body is said to be in dynamic equilibrium when the body is in a state of uniform motion with zero as the resultant force.
- Examples of dynamic Equilibrium include rotation of the earth around its axis or movement of the ball on a frictionless floor.
Static Equilibrium
- It is defined as the body’s physical state or system where the total force and torque are zero when the body is at rest. It occurs when the body or system is at rest.
- Examples of static Equilibrium include when an apple is placed on the table, or a truck is parked in the garage.
According to the potential energy and equilibrium of the system, the dynamic equilibrium can be further categorised into the following types:
Stable equilibrium | When a small distance displaces a body, it is maintained in stable equilibrium and hence produces a force opposing the displacement. This tends to return the body to a state of equilibrium, making the body stable. It is restoring the system or body to its original stable state. The connection between potential energy and equilibrium is in such equilibrium, the body’s potential energy is less. |
Unstable equilibrium | In this, when a small distance displaces the body, the state produces a force that does not oppose the displacement. In such a case, when the body moves from its original position. |
Neutral equilibrium | In this type of equilibrium, when an object is pushed from its position, it will not move forward or return to its original position. |
Equation connecting the Potential energy and equilibrium
The equation shows the connection between the potential energy and equilibrium. The two terms are related when conservative forces act on the system. Hence, the system’s stability depends on the system’s potential energy when it is associated with its mean position.
Here are the few equations which help in solving potential energy and equilibrium questions:
When a system or object is at equilibrium, the sum of all the forces is equal to zero. The following equation represents it:
Fx = – dU/dx = 0
In the case of the stable equilibrium, it is found that potential energy and equilibrium is associated. This is as potential energy is minimum in such a situation.
Hence, it is represented by
d2U / dx2 > 0
In the case of neutral equilibrium, when there is slight displacement, there is no force. Hence, it is represented as
d2U / dx2 = 0
Summary
The potential energy and equilibrium are important in physics. As both the concepts are connected, it helps understand the energy stored by a system or object concerning its position or movement. The comprehensive notes on the topic will help solve the potential energy and equilibrium questions and break down the concepts.
