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Let us suppose a stone of $4$kg mass falls from $5$ meter above upon an iron rod of the same mass which was entering the ground. Consequently the rod entered $10$ cm more deep into the ground.

Now considering the head of the iron rod as reference level total energy initially is that of the stone which is $m_{1}gh_{1}=4\times10\times 5=200$. Now after the rod has hit the ground $0.1$ meter deep, both the stone and rod's velocity becomes $0$ and so final energy of the system is $m_{2}g(-h_{2})=4\times 10 \times (-0.1)$. As we can see the energy has not been conserved. Where did i go wrong in this problem?

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It is an example of inelastic collision, i.e., a collision where (mechanical) energy is not conserved. The missing energy went into work of pushing the ground and overcoming friction, that is, it was converted in other forms of energy - mainly heat in the ground particles, the rod and the stone.

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  • $\begingroup$ No i think the logic is something else. See the final energy of the system is negative,which is absurd. $\endgroup$
    – madness
    Oct 21, 2021 at 11:10
  • $\begingroup$ I think the stone's velocity might non-zero at that point,it then gives $\frac{1}{2}m_{1}v^2-m_{2}gh_{2}$ on the right hand side. $\endgroup$
    – madness
    Oct 21, 2021 at 11:12
  • $\begingroup$ @madness there is nothing wrong with energy being negative - it depends on the reference level. WHat matters is the change in energy. $\endgroup$
    – Roger Vadim
    Oct 21, 2021 at 11:19
  • $\begingroup$ But the stone might have velocity as well. $\endgroup$
    – madness
    Oct 21, 2021 at 17:27
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Part of the energy was turned to heat another part to deforming energy. You call this not energy loss but energy depreciation, in most cases of energy conversion partor all of the energy ist depreciated. If you go with your car for some instance and return home, all the energy in the fuel is first turned to kinetic energy, but in the end, the cars energy is 0 and all is depreciated to heat.

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