Introduction of Energy
Energy is what the universe exists in. We are dealing with every kind of energy each and every second and from rest to motion. Energy came from the existence of the universe (not sure before that) and till now the energy has remained conserved. It has just been interchanging its forms. Among different forms of energy, the forms of mechanical energy i.e. kinetic and potential energy are the most important topics to describe characteristics of classical and even the quantum particles.
The position and momentum of a particle are best described by the mechanical energy. The potential energy looks after the rest energy while the kinetic energy looks after the momentum of the particle. The sum of both energies characterizes the total energy of a system. According to the energy conservation theorem, the total energy is always conserved.
As a whole we can say physics is the work of these two forms of energy. The whole concept of physics ends in energy, either it is for classical or quantum particles. Thus, the basic idea on kinetic and potential energies are much required.
Meaning of Kinetic Energy
Kinetic energy is the energy of motion. It is equal to the product of work (F) in the direction of motion and the displacement (s) required to accelerate the object from rest to that motion. Conversely, the same amount of work is done to decelerate the object from its initial speed to rest. The SI unit of energy is the joule. In the USA and some European countries, it is also expressed as Foot-Pound.
For example, a moving car, flowing water in a river, a flying bird etc.
For an object at rest, the kinetic energy becomes zero. As soon as it starts moving, kinetic energy comes into action.
The term kinetic is derived from the Greek word kίnesis, which means “motion”. Gottfried Leibniz and Johann Bernoulli developed the classical mechanics principal E ∝ mv^2. They called kinetic energy as the living force. In 1722, Willem Gravesande confirmed this relationship by his experiment. He performed a dropping weight experiment from various heights into a block of clay. It resulted that their depth of penetration was proportional to the square of their speed of motion. In 1829, Gaspard-Gustave Coriolis wrote the paper Du Calcul de l’Effet des Machines, which explained the mathematical equations of kinetic energy.
Meaning of Potential Energy
In physics, potential energy is the energy due to the position or certain scenario of a particle in reference to another particle. This energy is the same as the work done against any forces like gravity, tension etc. The phrase potential energy was first used by a Scottish physicist William Rankine. It is related to the concept of potentiality given by Aristotle and means ‘stored’. It also has the unit of Joule in the SI system.
The different types of potential energy are gravitational potential energy, electrical potential energy and elastic potential energy. Some examples of this form are, the energy stored in a stretched spring, water stored in a dam, energy of a drawn bow etc.
Potential energy is stored in a body when a number of forces act on that body and the total work done by these forces is determined by the initial and final position of that body. For some forces, their work-done is independent of their path and are known as conservative forces. However, for non-conservative forces, the work is different from then just depending upon the initial and final positions. Hence, potential energy can be more clearly defined by calling it as the energy difference between the energy of initial position and that when viewed from the point of reference.
These kinetic and potential energies can be transferred into each other.
Daily Life Examples
- When a football is kicked, it moves in a certain direction and hits a target. This can be observed as kinetic energy.
- A fast-moving vehicle having greater kinetic energy causes more harm than a slow-moving vehicle as it has greater energy.
- A boiling water has kinetic energy due to the vibration of molecules of water.
- A falling object has kinetic energy but turns to potential energy after hitting the floor.
- A pendulum at its maximum amplitude from the mean position stores potential energy.
- A sitting or resting person has potential energy.
These examples show how we are dealing with these mechanical energies in our practical life.
Formula of Kinetic Energy and Its Explanation
Kinetic energy is calculated as:
Kinetic Energy (KE) = 1/2mv^2 [Equation 1]
where:
- m = mass of the object
- v = velocity of the object
From equation (1) we can say that:
- Kinetic energy depends on the mass of the objects. As a result, a heavier object has more kinetic energy than a lighter one, given that both are moving with the same speed. For example, a truck moving at the same speed as a bicycle has much more kinetic energy.
- Kinetic energy also depends on the square of velocity (v^2). This means that
the speed doubles, kinetic energy becomes four times and so on.
This is the reason that high-speed vehicles with greater masses are more dangerous.
Gravitational Potential Energy Explained with Examples
Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. When a body is at infinity, then the gravitational potential energy is the amount of work to be done to bring that body from the infinity to the point of the gravitational field.
Gravitational Potential Energy (PE) = mgh [Equation 2]
where:
- m = mass of the object
- g = acceleration due to gravity
- h = height above the ground
So if the object is lifted higher, it gains more potential energy. Similarly, a heavier object has more potential energy than the lighter one at the same height.
For example, a pen kept on the table has potential energy. As it falls, the energy form changes to kinetic.
Elastic Potential Energy and Its Simple Explanation
Elastic potential energy is the energy stored in elastic objects when they are stretched or compressed. For example, mass-spring systems, rubber bands, elastic strings etc.
When an elastic object is stretched or compressed, work is done on it which is stored as elastic potential energy. When it comes to its initial shape and position, the stored energy is released. This force to bring back the object in initial condition is the restoring force.
Elastic potential energy is calculated as:
U = ½kΔx² [Equation 3]
where:
- U is the elastic potential energy,
- k is the spring constant,
- Δx is the displacement from the mean position
Inter-relationship Between Kinetic and Potential Energy
This inter-connection between the two mechanical energies can be best described by the examples. Some common examples are given below:
Falling object
- At the top: Potential energy = maximum, kinetic energy = zero
- While falling: Potential energy decreases, kinetic energy increases
- Just before hitting the ground: Maximum kinetic energy
- At extreme positions: Maximum potential energy
- At mean position: Maximum kinetic energy
Roller-Coaster
- At the top of the track: High potential energy
- At the bottom: High kinetic energy
In all these cases, energy is not destroyed. It only changes from one form to another.
Conservation of Mechanical Energy
Kinetic energy and potential energy combinedly result in mechanical energy. The principle of conservation states that for a closed system total mechanical energy remains constant during the motion. The condition is that the forces are conservative. This means that any change in kinetic energy is cancelled out by the change in potential energy. This confirms that the total energy remains constant.
Mathematically, mechanical energy = K.E. + P.E. [Equation 4]
But this condition is violated when external non-conservative forces like friction, air resistance etc. are acting on the system.
The example explaining this theorem is a ball thrown upward. Three conditions arise here,
- At launch: High kinetic energy, low potential energy
- At highest point: Zero kinetic energy, maximum potential energy
- On falling back: Potential energy converts into kinetic energy
The total mechanical energy remains constant if air resistance is ignored.
Quantum Mechanical Energy
As quantum mechanics deals with the probability of the finding of a particle within a system, the role of kinetic and potential energy is vital here. A wavefunction contains every information about the system. Similarly a Hamiltonian is the operator embedded on the wavefunction which is the total energy of that system. It includes both kinetic and potential energy and is given as:
H^ = T^ + V [Equation 5]
Here,
- H^ is the hamiltonian operator
- T^ is the kinetic energy and
- V is the potential energy
The result from the Hamiltonian operator gives the possible outcomes of the energy calculations, which are in the form of eigenvalues. The Hamiltonian can take various forms and sometimes we can also simplify it. This can be done by analyzing the characteristics of the system and includes the number of particles in the system, particle interaction, potential energy type (time varying or time independent), and so on.
Applications of Kinetic and Potential Energy
Some major applications of these two energies are given below:
- Power Generation: The electricity at our homes and offices are first the work of potential energy which is later converted into kinetic and electrical energy. The water reserved in dams gives the account of potential energy while the rotation of the turbine is the kinetic energy.
- Energy of the Vehicles: The fuel stored vehicles represent potential energy, while start of engine and the acceleration provided give rise to the motion of the vehicle.
- Harmonic Oscillators: The periodic motion of the harmonic oscillators results from the continuous exchange between the kinetic and potential energies.
- In Sports: Sports are the continuous action of change in position and momentum of a player. Thus, kinetic and potential energies are vital in sports.
- In Thermal Physics: Heat also increases the motion between two molecules and starts vibrating. Thus, thermal physics is also based on the kinetic and rest energies of the molecules.
Importance of Kinetic and Potential Energy
Understanding kinetic and potential energy is important because:
- It explains motion and forces clearly.
- It helps in designing machines and engines.
- It is used in power generation.
- It explains natural phenomena like waterfalls and planetary motion.
- It forms the foundation for advanced physics topics.
Conclusion
As energy is the major subject for the universe, the concept of kinetic and potential energy has an everlasting imprint in physics. Every object is seen to be moving in some way if we consider deep learning. From atomic to celestial level and from seen to unseen particles, all deal everyday with these two forms of energies. The inter-exchangeable property of these forms has added more interesting ideas in physics like the simple harmonic motion and also the quantum harmonic oscillators. On a closer study we find that these two forms are inseparable from each other.
The physical world is not as simple as we see in our daily life. The non-relativistic cases are more complex. However, they have also been cracked by the basic knowledge of kinetic and potential energy. They also keep within the boundary of nature and always keep the total energy conserved. Thus, from both logical and mathematical analysis, these energies are the basic of nature. Their root study can give much more interesting innovations and applications in all sectors of physics and engineering.
References
Coulson, C. A., & Bell, R. P. (1945). Kinetic energy, potential energy and force in molecule formation. Transactions of the Faraday Society, 41, 141-149.
https://en.wikipedia.org/wiki/Kinetic_energy
https://en.wikipedia.org/wiki/Potential_energy
https://www.geeksforgeeks.org/physics/difference-between-kinetic-energy-and-potential-energ
https://www.sciencing.com/kinetic-and-potential-energy-what-is-the-difference-w-examples-13720801
