Principle of Conservation of Energy | Physics Grade XI

Conservation of Energy

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Principle of Conservation of Energy | Physics Grade XI

Principle of Conservation of Energy

Principle of Conservation of Energy

According to this principle, energy of an isolated system is constant. In other words, "The energy can neither be created nor be destroyed but can be transformed from one form to another".

Energy conservation for freely falling bodies:

The mechanical energy of a freely falling body is constant. Prove.

Object falling freel

Let a body of mass ‘m’ at point A at a height of H from the ground. Let the body fall from height. Let B be any instant point between A and C at distance x from a. Then its height from the ground is (h-x). Let C be the ground level and its height is 0.

At A,

K.E. = 0, since the body is in rest
P.E. = mg H,
Where H is the distance between the body and the ground
Total mechanical energy = K.E. + P.E.
= 0 + mg H
= mgH  …… (i)

At B,

Let the velocity of the body at point B be vb, then
K.E. = ½ mvb2 ……… (i)
From the equation of motion,
V2 = u2 + 2as
vb2 = 0 + 2gx, where ‘g’ is the acceleration due to gravity and x is the distance traveled by the body from A to B
vb2 = 2gx
In equation (i),
K.E. = ½ mvb2
       = ½ m. 2gx
       = mgx
P.E. = mg (H-x)
        = mgH - mgx
Total mechanical energy = K.E. + P.E.
                                    = mgx + mgH – mgx
                                    = mgH   ..…. (ii)

At point C,

K.E. = ½ mvc2  ……. (ii), where vc is the velocity at point C
From the equation of motion,
V2 = u2 + 2as
vc2= 0 + 2gH
vc2 = 2gH
K.E. = ½ m. 2gH
K.E. = mgH
P.E. = mgH = 0
Total mechanical energy = K.E + P.E.
                                    = mgH   ……. (iii)

From this, we can conclude that the total mechanical energy remains same at all the points during the journey since equations (i), (ii), and (iii) are equal.

Conservative and non-conservative forces

A force is said to be conservative if the work done by or against the force in moving body depends upon only the initial and final positions of the body i.e. the distance between those bodies. If the work done by the body while bringing it into a round circle at same point, then the force applied on it is called conservative force.

A force is said to be non-conservative if work done by or against the force on a moving body from one position to another depends upon the path followed by the body.

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