Potential Energy Overview
In the fascinating world of physics, energy plays a pivotal role in explaining the behavior of objects and systems. One essential type of energy is potential energy, which represents the stored energy within an object due to its position or state. Energy is the ability of any object to perform a specific activity. It refers to anything that we cannot create or destroy, but only modify. When a thing does work, it loses energy. When work is done on it, it gains energy. We divide energy into two types: kinetic energy and potential energy. Kinetic energy is the energy contained in an object as a result of its motion. Potential energy, on the other hand, is energy that has been stored due to its state of rest. It's easy to get mixed up between these two, so let's look at what potential energy means.
In this article, we will delve deep into the concept of potential energy, exploring its various forms, mathematical expressions, and real-world applications.
What is Potential Energy?
Potential energy, expressed as U is a fundamental concept in physics that describes the energy an object possesses due to its position or condition, and it is typically associated with the potential to do work. It is a crucial component of the law of conservation of energy, which states that energy cannot be created or destroyed but can only change from one form to another.
Potential energy can exist in various forms, and it is directly related to the forces acting on an object and the object's position or state.
Potential Energy Formula
The formula for potential energy depends on the force acting on the two objects. For the gravitational force, the formula is:
W = m×g×h = mgh |
Where,
- m is the mass in kilograms
- g is the acceleration due to gravity
- h is the height in meters
Types of Potential Energy
There are several types of potential energy, each arising from different physical phenomena. The most common forms of potential energy include:
Gravitational Potential Energy
Gravitational potential energy (GPE) is associated with an object's position in a gravitational field, such as the Earth's gravitational field. It depends on the height (or distance) of the object above a reference point. The formula for calculating gravitational potential energy is:
GPE= m*g*h
Where:
- GPE is the gravitational potential energy.
- m is the mass of the object.
- g is the acceleration due to gravity.
- h is the height or vertical distance above a reference point.
Elastic Potential Energy
Elastic potential energy is associated with objects that can be compressed or stretched, such as a spring or a rubber band. The amount of elastic potential energy stored in the object depends on how much it is deformed from its equilibrium position. The formula for elastic potential energy is:
Elastic PE = 
k 
Where:
- Elastic PE is the elastic potential energy.
- k is the spring constant, a measure of the spring's stiffness.
- x is the displacement from the equilibrium position.
Chemical Potential Energy
Chemical potential energy is stored within chemical bonds and is released during chemical reactions. This type of potential energy is responsible for powering various processes in biological organisms and fueling combustion reactions. Examples include the energy stored in batteries, gasoline, and food.
Electric Potential Energy
Electric potential energy is related to the position of charged particles within an electric field. It plays a fundamental role in understanding the behavior of electric charges and their interactions. The formula for electric potential energy between two point charges is:
Where:
Electric PE = 
Where:
- Electric PE is the electric potential energy.
- k is Coulomb's constant, a fundamental constant of nature.
- q1​ and q2 are the magnitudes of the two point charges.
- r is the separation distance between the charges.
Energy as a Negative Constraint
It's essential to understand that potential energy can be thought of as a negative constraint on an object. In other words, it limits what the object can do until it changes its position or state. When the constraint is released, the potential energy is converted into kinetic energy or other forms of energy.
Potential Energy: Topics under Work, Energy, and Power
Before delving into potential energy types and examples, let's briefly explore some related topics within the field of work, energy, and power:
- Kinetic Energy: Kinetic energy is the energy associated with the motion of an object. It is defined as one-half of the mass of an object times its velocity squared, represented by the equation KE = 1/2 * m * v^2.
- Mechanical Energy: Mechanical energy is the sum of an object's kinetic and potential energies. In other words, it encompasses both the energy of motion (kinetic) and stored energy (potential).
- Conservation of Energy: According to the law of conservation of energy, energy cannot be created or destroyed; it can only change from one form to another. This principle is crucial in understanding how energy behaves in various systems.
Potential Energy: Real-World Applications
Potential energy is a fundamental concept with numerous practical applications across various fields. Some notable examples include:
- Hydropower: Gravitational potential energy is harnessed in hydropower plants by allowing water to flow from a higher elevation to a lower one, thereby converting the potential energy into electrical energy.
- Energy Storage: Elastic potential energy is used in devices like springs and rubber bands to store energy for various applications, including shock absorbers and wind-up toys.
- Chemical Reactions: Chemical potential energy is crucial in the field of chemistry, as it drives reactions and powers batteries and fuel cells.
- Electrostatic Applications: Electric potential energy is used in electronic devices, from capacitors in circuits to the operation of generators and transformers.
Potential Energy: Other Examples around Us
Potential energy is a fundamental concept that can be observed in various everyday situations. Here are a few examples:
- A stretched rubber band contains elastic potential energy.
- A compressed spring stores elastic potential energy.
- Water stored in a dam has gravitational potential energy.
- A book placed on a high shelf possesses gravitational potential energy.
- A charged battery stores chemical potential energy.
Potential Energy: Solved Example
What will be the gravitational potential energy of a ball of mass 1 kg when it is raised to 6 m above the ground? (g = 9.8 m s–2)
Solution:
Here, the mass of the object (m) = 1 kg,
Displacement (height) (h) = 10 m,
Acceleration due to gravity (g) = 9.8 m s–2.
Hence, Potential energy (P) = m×g×h = 1 kg × 9.8 m s–2 × 10 m = 98 J.
A body is falling from a height h. After it has fallen a height h/2, it will possess
- only potential energy
- only kinetic energy
- half potential and half kinetic energy
- more kinetic and less potential energy
Solution: (c) At height h the K.E of the object is 0 while P.E is mgh. At height h/2 the P.E becomes mgh/2 while the other half of P.E is converted into K.E due to the virtue of its motion. So mgh – mgh/2 = mgh/2. Hence, the body has half its energy in the form of potential energy and the other half is in the form of kinetic energy