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Show in detail how the statement of conservation of mechanical energy derives from the work energy...

Show in detail how the statement of conservation of mechanical energy derives from the work energy theorem and the definition of a potential function. (asking for summrized clear answer)

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Answer #1

statement ;-

"the total mechanical energy of a system is constant if the internal forces are conservative and external forces do no work"

mechanical energy E=PE+KE

according to work energy therom ,work done by forces external and internal forces acting on the body is equal to change in kinetic energy

wext+Wef+Wnef=K2-K1

we know workdone by conservative force is equal to negative of change in potential energy

Wef=U1-U2

Wext+U1-U2+Wnef=k2-k1

wext+Wnef=(K2-K1)+(U2-U1)

=[K2+U2]-[K1+U1]

Wext+Wnef=E2-E1

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