Conservation of Energy

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The Law of Conservation of energy states that energy can neither created nor destroyed, but it can undergo phase transition which means that it can change from one form of energy to another form of energy. The conservation of energy principle also means that in a closed isolated system, the total amount of energy remains constant and thus it is conserved.

Example 1: Andy drops a stone from the roof of a building 60m high. What is the velocity with which the stone hits the ground? (Assume negligible air resistance).

Solution: According to the Law of Conservation of Energy, we can say that:

PE intital + KE initial = PE final + KE final

Since the stone is dropped from rest, its initial velocity= 0 ==>KE initial= 0.

When the stone hits the ground, PE final= 0 since the height= 0.

Hence, mgh= 1/2 * mv2 mass cancels.

v2= 2gh ==> v = √(2 * 9.8m/sec2 * 60m)= 34.3m/sec.
 
Example 2: A ball is thrown up into the air with a velocity of 25m/sec. What is the maximum height reached by the ball? (Assume negligible air resistance).

Solution: According to the Law of Conservation of Energy, we can say that:

PE intital + KE initial = PE final + KE final

Let the initial height be = 0==> PE initiall= 0

If the ball is thrown up into the air, its final velocity=0 ==>KE final= 0.

Hence, 1/2 * mv2 = mgh (mass gets cancelled)

h= v2/(2g) ==> h = 252/ (2*9.8)= 31.9m

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