Q. 444.0( 4 Votes )

Prove that the mechanical energy of a freely falling object in the gravitational field remains constant at every point.

Answer :


In the figure, the height of the building is h and let the object be at a height x above the ground level.


1: The total energy(E) of the object when it was at the top of the building was potential energy(U)


E = U = mgh


2: The total energy of the object when at a height of x above the ground level is partly kinetic energy (K) and potential energy.



The velocity v of the object is gien by,



As the initial energy is 0,



So,




Now the potential energy is


U = mgx


Hence, the total energy of the object is


E = K + U = mg(h-x) + mgx


E = mgh


Hence, it is proved that the mechanical energy of freely falling on object in gravitational the eld remain constant remains point as x is any arbitrary distance.


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