Law of Conservation of Energy
When energy is converted from potential energy to kinetic energy, the energy lost in one form reappears in the other. When a body falls, the loss of its potential energy is transformed into kinetic energy till it reaches the ground.
â€˜Energy can neither be created nor be destroyed. It can be transformed from one form of energy into another in an equivalent amountâ€™. This is known as the law of conservation of energy.
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To Verify the Law of Conservation of Energy:
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Conservation of Energy |
Consider an object of mass â€˜mâ€™ at a height h (from the ground). Let â€˜gâ€™ be the acceleration due to gravity.
Let us consider the energy possessed by the object at three stages A, B and C.
A is at a height h
B is at a height (h - X)
C is on the ground (ground level)
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Energy at A
Object is at rest at a height h.
Potential energy (P.E.) = mgh joule
Kinetic energy (K.E) = 0 (because object is at rest)
Total energy at A = Potential Energy + Kinetic Energy = mgh + 0
Energy at AÂ Â Â Â Â Â Â Â Â Â = mgh joule
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Energy at B
Object is at a height â€˜Xâ€™ from A and (h - x) from the ground. So it possesses both potential and kinetic energies.
Potential energy = mg (h - x) joule
Kinetic energy = Â½ mv^{2 }------------ (1)
Where â€˜vâ€™ is the velocity of the object at B.
According to the third equation of motion, we have V^{2 }= u^{2 }+ 2as
Here,Â u = 0,Â a = g,Â s = x
V^{2} = 2gx -------- (2)
Substituting (2 in (1), we get
Kinetic energy = mg Â´ joule
Total energy at B = P.E. + K. E.
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = mg (h - x) + mgx
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = mgh - mgx + mgx
Energy at BÂ Â Â Â Â Â Â Â = mgh joule
Energy at C
Since it has struck the ground, the energy is completely kinetic.
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P.E. = mgh joule
Â Â Â Â Â = m Â´ g Â´ 0 = 0; (since h=0)
Potential energy = 0.
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According to the third Equation of motion
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V^{2 }= u^{2 }+ 2as
UÂ = 0
AÂ = g
SÂ = h
V^{2} = 2gh
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Kinetic energyÂ = Â½ mv^{2 }joule
= Â½ Â´ m Â´ 2gh = mgh joule
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Total energy at C = P.E. + K. E.
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0 + mgh
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = mgh joule
Â Â Â Â Â Â Energy at C = mgh joule
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At all three stages A, B and C, the total energy is mgh joule. So energy disappears in one form and reappears in another form. If it is lost as potential energy it is transformed into kinetic energy, thus verifying the law of conservation of energy which states that â€˜Energy can neither be created nor be destroyed, but can be transformed from one form into another form in an equivalent amountâ€™.
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