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If a hammer does work by driving a nail into a wooden board, how does the mechanical energy from right before the hammer hits the nail compare to the mechanical energy after the nail has been driven into the board?

Since mechanical energy is conserved, shouldn't it be the same before and after impact? I'm confused because if the hammer does positive work, it has lost kinetic energy. Before impact, it has some non-zero velocity $v_i.$ After impact, $v_f = 0,$ so the final kinetic energy is less than the initial kinetic energy, which indicates a decrease in mechanical energy. Doesn't this conclusion contradict the conservation of mechanical energy?

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  • $\begingroup$ I have never heard of the conservation of mechanical energy as a law of nature $\endgroup$ – user83548 Nov 13 '15 at 5:01
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There are different forms of energy. Energy can be converted from one form to another but cannot be destroyed. In this case the kinetic energy of the hammer is driving the nail into the wood which is breaking the molecular bonds in the wood fiber. The energy is converted to heat energy as a result of the breaking of the bonds and the friction of the nail in the wood.

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  • $\begingroup$ That's what I suspected as well. There must be a change in some other form(s) of energy that counteracts the decrease in kinetic energy. But ultimately, mechanical energy is conserved, so its initial state is equal to its final state, right? $\endgroup$ – A is for Ambition Nov 13 '15 at 5:09
  • $\begingroup$ conservation of mechanical energy is not a law of nature, but conservation of energy is. Some of the mechanical energy is converted into heat, which rises temperature, which is a rise in internal energy at the expense of mechanical energy. $\endgroup$ – user83548 Nov 13 '15 at 5:13
  • $\begingroup$ Okay, so then mechanical energy decreases. But then when is mechanical energy conserved? $\endgroup$ – A is for Ambition Nov 13 '15 at 5:19
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    $\begingroup$ when the forces involved are conservative, Read: en.wikipedia.org/wiki/Conservative_force $\endgroup$ – user83548 Nov 13 '15 at 5:27
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Conservation of Mechanical Energy Before and After Impact of a Hammer

The kinetic energy of a hammer of mass $m$ ans speed $v$ is equal to the work done by the resistance force , $F_r$ the nail faces while it travels the distance $d$ in the wood.

$mv^2 /2 = F_r * d$

$F_r * d$, like any work done by a friction force, converts mainly into heat.

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