The Law of conservation of energy states that “Energy cannot be created or destroyed, but only it can be changed from one form to another form.”
This law does not differentiate between useful and wasted energy. Law of conservation of energy neglects ‘losses’ from the closed system into the environment.
In this process, the energy transferred from one form to another forms but can not destroy.
In a closed system containing a certain mass and energy, various energy transformations may take place from one form to another. The total mass and energy in the closed system same as it was before.
Law of Conservation of Energy Derivation:
We can consider the potential energy of the ground surface to be zero. To derive the equation we will take an example of fruit falling from a tree.
We will consider a point A on H height from the ground. This point A is on the tree. As fruit is in the rest state hence the velocity of the fruit will be zero and potential energy will be maximum.
E = mgH ———- (1)
When the fruit starts falling from the tree, its potential energy is decreasing and kinetic energy is increasing.
At point B, which is close to the lower part of the tree, the fruit is falling openly under gravity and is at a height X from the ground, it has speed as it arrives at point B. Thus, now, it will have both kinetic and potential energy.
E = K.E + P.E
P.E = mgX ——— (2)
As per third equation of motion,
v2=2g(H–X)⇒12mv2=12m.2g(H–X)⇒K.E=12m.2g(H–X)⇒K.E=mg(H–X)
K.E=mg(H-X)——– (3)
Using (1), (2) and (3)
E = mg(H – X) + mgX
E = mg(H – X + X)
E = mgH
Point C is at the bottom of the tree. The energy of point C will be mgH. we can observe the fruit is falling to the bottom and here, potential energy is getting converted into kinetic energy. There should be a point where kinetic energy becomes equal to potential energy. Suppose we required to find that height ‘x’ from the ground. We know at that point,
K.E = P.E
=> P.E = K.E = E2 ——– (4)
E2 is the new energy
Where, E = mgH2
H2 is the new height.
As the body is at height X from the ground,
P.E = mgX ——— (5)
Using equations (4) and (5) we get,
mgX=mgH2⇒X=H2
Where H2 is the new height
Frequently Asked Questions
State the law of conservation of energy?
Ans: In a closed system, that is isolated from its surroundings, the total energy of the system remains the same.