Q. 105.0( 3 Votes )

State and prove t

Answer :

Consider a body m lying at a position A at a height h, above the ground. As the body falls, its kinetic energy increases at the expense of its potential energy.



At point A


The body is at rest


The kinetic energy of a body at A = KA



The potential energy of body at A = UA



The total techanical energy of body at A = EA




At point B


Suppose the body falls through a distance x and reaches B with velocity v. Then



u = 0


s = x


a = g



The kinetic energy of body at B = KB





The potential energy of a body at B = UB



The total energy of the body at B = EB




At point C


Suppose the body reaches C (on the ground) with velocity v’. Then considering motion from A to C



u = 0


s = h


a = g


v = v’



Kinetic energy of body at C = KC





Potential energy of body at C = UC



Total mechanical energy of body at C = EC





As a body falls freely under gravity P.E. decreases and K.E increases by equal amounts, however the, total mechanical energy remains constant.


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