Question

Show that the total mechanical energy of a freely falling body under gravity is conserved.

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Answer 1

Answer:

The mechanical energy of a freely falling body under gravity is constant.

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Answer 2

Yes

when body is at height h

it's doesn't have any kinetic energy but it has potential energy which is equal to 'mgh' where m is mass of body ,g is acceleration due to gravity

and h is the height above the ground where body is situated

so mechanical energy at that point will be mgh

case 2 when body is at height h/2

for this kinetic energy is equal to 1/2 *m*(v)²

but v² - u²= 2as

since u is 0

so v² =2as

but a=g and s= h/2

so v² = 2* g* h/2= 2gh

so kinetic energy will be mgh/2

and potential energy is mgh/2

so mechanical energy is mgh

case 3 when body touches the ground

kinetic energy is 1/2m v²

but v²-u²=2as

but a =g and s=h and u= 0

so v²=2gh

so kinetic energy = mgh

but at ground potential energy is 0

so mechanical energy is mgh

from case 1 ,case2 and case 3

mechanical energy is conserved

(important note the h in kinetic energy is the height covered by body but in potential energy is the height at which body is situated)