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

State the law of conservation of mechanical energy. Show that total me

1.	State the law of conservation of mechanical energy. Show that total mechanical energy of a body falling freely under gravity is conserved.
Answer» Solution :Energy can NEITHER be created nor destroyed but can be transformed into other forms of energy. Let a particle be at 'C'. Initially the particle will be zero velocity. Let 'h' be the HEIGHT of the particle. `P.E_(C)=mgh,""K.E_(C)=0`, `T.E_(C)` = mgh At B, `K.E_(B)=1//2mv_(B)` `=1//2m(2gx)` = mgx `P.E_(B)=mg(h-x)` Hence `T.E_(B)=(mgh-mgx)+(mgx)` = mgh At A, `v_(A)^(2)=2gh` So that `K.E_(A)=(1)/(cancel2)mcancel2gh` = mgh `P.E_(A)=0` Hence at all points. A, B and C, the total energy is CONSERVED.