Law of Conservation of Energy Derivation
Law of Conservation of Energy can be derived with the help of the following example, take a ball falling from the height H and the initial velocity is zero, also the potential energy at the surface of the earth is zero.
Now at the height H from the ground,
Etotal = Epotential + Ekinetic
⇒ Etotal = 1/2mv2 + mgH
⇒ Etotal = 1/2m(0)2 + mgH
⇒ Etotal = mgH…(A)
As the ball falls to the ground, its potential energy decreases, and kinetic energy increases.
At any point B, which is at a height X from the ground, it has speed ‘v’ as it reaches point B. So, at this point, it has both kinetic and potential energy.
Etotal = Epotential + Ekinetic…(1)
and Epotential = mgX…(2)
According to the third equation of motion,
v2 = 2g(H-X)
⇒ 1/2mv2 = 1/2m×2g(H-X)
⇒ 1/2mv2 = mg(H-X)
⇒ Ekinetic = mg(H-X)…(2)
Using (1), (2), and (3)
E = mg(H – X) + mgX
⇒ E = mg(H – X + X)
⇒ E = mgH…(B)
Also, at point C, at the ground,
Etotal = Epotential + Ekinetic…(a)
⇒ Epotential = 0…(b) (as height is zero)
According to the third equation of motion,
v2 = 2g(H-0)
⇒ 1/2mv2 = 1/2m×2g(H)
⇒ 1/2mv2 = mg(H)
⇒ Ekinetic = mg(H)…(c)
Using (a), (b), and (c)
E = mg(H) + 0
⇒ E = mgH…(C)
Thus, from A, B, and C it is clear that the total energy at any point of the falling of the ball is constant (mgH).
Law of Conservation of Energy
Law of Conservation of Energy is the most fundamental law of physics which states that “Energy can neither be created nor be destroyed it can only change from one form of the energy to another form of the energy.” It is the fundamental law of Physics that governs various processes in our environment.
Before learning deeply about the Law of Conservation of Energy we must know about Energy. Energy is the capacity of the object to do work, It is a physical quantity that allows an object to do different types of work.
Table of Content
- What is Energy?
- What is the Law of Conservation of Energy?
- Law of Conservation of Energy Derivation
- Law of Conservation of Energy Examples
- Application of Conservation of Energy
- Why Can Perpetual Motion Machines Never Work?
- Solved Examples on Conservation of Energy
Let’s learn more about the Law of Conservation of Energy, and others in detail in this article.
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