State the law of conservation of energy. Explain briefly with a suitable example.
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State the law of conservation of energy. Explain briefly with a suitable example.
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Explanation:
Whenever energy gets transformed,the total energy remains unchanged. According to this law,energy can only be converted from one form to another,it can neither be created or destroyed. The total energy before and after transformation remains same. ... The energy of a freely falling ball is conserved.
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The law of conservation of energy can be seen in these everyday examples of energy transference: Water can produce electricity. Water falls from the sky, converting potential energy to kinetic energy. The cue ball loses energy because the energy it had has been transferred to the 8 ball, so the cue ball slows down.
Law of Conservation of Energy Derivation
Considering the potential energy at the surface of the earth to be zero. Let us see an example of a fruit falling from a tree.
Consider a point A, which is at height ‘H’ from the ground on the tree, the velocity of the fruit is zero hence potential energy is maximum there.
E = mgH ———- (1)
When the fruit is falling, its potential energy is decreasing and kinetic energy is increasing.
At point B, which is near the bottom of the tree, the fruit is falling freely under gravity and is at a height X from the ground, and it has speed as it reaches point B. So, at this point, it will have both kinetic and potential energy.
E = K.E + P.E
P.E = mgX ——— (2)
According to 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
Similarly, if we see the energy at point C, which is at the bottom of the tree, it will come out to be mgH. We can see as the fruit is falling to the bottom and here, potential energy is getting converted into kinetic energy. So there must be a point where kinetic energy becomes equal to potential energy. Suppose we need 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 (4) and (5) we get,
mgX=mgH2⇒X=H2
H2 is referred to the new height
Law of Conservation of Energy Examples: