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law of conservation of energy in case of freely falling body
Asked by mdowaisraza581 | 16 May, 2023, 10:06: PM
Let the body is dropped from height h . Just before dropping it has only potential energy (mgh) ,
where m is mass of body, g is acceleratio due to gravity and h is height.

Hence intial total energy Ei  is

................................... (1)

Let us consider it has fallen a distance y from initial point .

Potential energy U at this point is

...............................(2)

Speed of body at this point is determined from the following equation

Hence kineti energy K at this point is

Total energy Ey at this point is sum of potential energy and kinetic energy

...........................(3)

Finally, when the body reaches ground , its potential energy is zero and has only kinetic energy.

Final kinetic energy Kf is

where vf is the final speed when body reaches the ground.

Final speed vf is determined from the following equation

Hence final kinetic energy , or total energy at ground is

......................................(4)

Hence from eqn.(1) , eqn.(3) and eqn.(4) , we see that total energy always remain same as ( m g h ) .

This is due to conservation of energy.  At a height h, all total energy is in the form of potential energy.

After falling a distance y from starting point , potential energy decreases but kinetic energy increases .

We found that sum of potential energy and kinetic energy is ( m g h ) .

When the body is reaching ground, just before hitting the ground , it has only kinetic energy that equals ( m g h ) .

Hence loss in potential energy equals gain in kinetic energy so that sum of kinetic enrgy and potential energy at all the points is same.
Answered by Thiyagarajan K | 17 May, 2023, 11:27: AM
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