Question

how to verify the law of conservation of energy

Answer 1

Hlo friend.. Cutiepie Here..

Here is ur answer :

LAW OF CONSERVATION OF ENERGY :

According to law of conservation of energy, energy can only be transferred from one form to another, it can neither be created nor be destroyed. the total energy before and after transformation, always remain constant.

CONSERVATION OF ENERGY DURING THE FREE FALL OF A BODY :

Consider a body of mass m, lying at position B. It is made to fall freely from a height (h) above the ground as shown in the figure.

At point B

At the start, the potential energy is mgh and kinetic energy is zero (as its velocity is zero).

i. e. PE = mgh

KE = 0

Therefore,

Total energy, TE = PE + KE = mgh


At point A

As it falls, its potential energy will change into kinetic energy. if v is the velocity of the object at a given instant, its kinetic energy would be
1/2 mv²

PE = mg ( h - x )

From Newton's Third equation of motion,

v² = u² + 2gx

v² = 2gx ( because u = 0 )

KE = 1/2 mv²

= 1/2 * m * 2gx ( because v² = 2gx)

= mgx

Therefore,

Total energy = mg( h - x) + mgx

= mgh - mgx + mgx

= mgh


At point C

As The Fall of the object continuous, the potential energy would decrease while the kinetic energy would increase. When the object is about to reach the ground, h = 0 and v will be the highest point.

PE = 0

KE = 1/2 mv²

= 1/2m ( 2gh) {because v² = 2gh}

= mgh

Therefore,

Total energy, TE = mgh

Thus, the sum of the potential energy and kinetic energy of the object would be same at all points, that is

PE + KE = Constant

Or mgh + 1/2 mv² = constant



This verifies the law of conservation of energy.

HOPE IT HELPS YOU..

:-)