# Potential energy of a free fall body decreases . does this violate law of conservation of energy .

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by sandipLodi

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by sandipLodi

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No, because according to this law energy can neither be created nor be destroyed.

As the potential energy decreases it changes into kinetic energy, the energy due to the motion of an object.

As the potential energy decreases it changes into kinetic energy, the energy due to the motion of an object.

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No,the Ep of a body in free fall is converted into Ek( kinetic energy)and thus the amount of total energy is same at every point.

__proof __

let there be a mass 'm' at a maximum height 'h'

let the peak be point A and let B be the closest point to the ground

__C is a point anywhere b/t ____A and B __

*total energy=Ep+Ek*

at point A ,tot.e=mgh+o=mgh

at C,i.e. after travelling a distance x,tot.E= mg(h-x)+1/2mv^2

but, v^2-u^2=2gx (as x is the distance traveled and g is the acceleration in this case),

u=0, v^2=2gx

hence tot.E @ C= mg(h-x)+mgx =mgh

now, at point B,tot.E=0+mgh( as h is the distance covered at point B)

=mgh

**Hence it is proved that eventhough Ep decreases during a freefall,the law of conservation of energy is not violated as mgh is constant at any point during this motion**

let the peak be point A and let B be the closest point to the ground

at point A ,tot.e=mgh+o=mgh

at C,i.e. after travelling a distance x,tot.E= mg(h-x)+1/2mv^2

but, v^2-u^2=2gx (as x is the distance traveled and g is the acceleration in this case),

u=0, v^2=2gx

hence tot.E @ C= mg(h-x)+mgx =mgh

now, at point B,tot.E=0+mgh( as h is the distance covered at point B)

=mgh