Question

State law of conservation of energy and prove it in the case of freely falling body.​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

IN Simple terms , Law of conservation of energy : Energy can neither be created nor destroyed . But it can be converted from one form into the another form so that the total energy will remains constant in a closed system .

Proof :In case of a freely falling body :

Let a body of mass is dropped from a height 'H' at point A.

Forces due to gravitational are conservation forces .so total mechanical energy (E= P.E +K.E) is constant i.e., neither destroyed created

Explanation:

The conversion of potential energy to kinetice energy for a ball of mass m dropped from a height H .

1 . At point H : Velcoity of body v = 0

⇒K=0 Potential energy (u) = mgH

where H = height above the ground

T.E = u + K = mgh ------ (1)

2. At point 0 : i.e., just before touching the ground :

A constant force is a special case of specially dependent force F (x) so mechanical energy is conserved .

So energy at H = Energy at 0 = mgH

Proof : At point '0' height h = 0 ⇒

⇒v=2gH−−−−√,u=0

K0=12mv2=12m2gH=mgH

Total energy E = mgH + 0 = mgH -------(2)

3 . At any point h : Let height above ground = h

u=mgH,Kh=12mV2

Where V=(2g(h−x))

∴ Total energy =mgh+12m2g(H−h)

⇒E=mgh+mgH−mgh=mgH ----- (3)

From eq . 1 , 2, & 3 total energy at any point is constant

Hence , law of conservation of energy is proved .

Conditions to apply law of conservation of energy :

1) work done by internal forces is conservative .

2) No work is done by external force .

When the above two conditions are satisfied then total mechanical energy of a system will remain constant .