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 gavitational are conservation forces .so total mechanical energy (E= P.E +K.E) is constant i.e., neither destroyed created
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
`rArr 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 `rArr`
`rArrv=sqrt(2gH),u=0`
`K_(0)=(1)/(2)mv^(2)=(1)/(2)m2gH=mgH`
Total energy E = mgH + 0 = mgH .......(2)
3 . At any point h : Let height above ground = h
`u=mgH,K_(h)=(1)/(2)mV^(2)`
Where `V=(2g(h-x))`
`therefore ` Total energy `=mgh+(1)/(2)m2g(H-h)`
`rArrE=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 .
