When I raise a pen, the external work I do gets stored in the form of potential energy hence the mechanical energy is increased. When I leave the pen the pen starts falling and as the potential energy decreases the kinetic energy increases. No external force so no change in mechanical energy.

When the pen strikes the ground, it's kinetic energy is brought to zero and its potential energy is also decreased. Hence, its total mechanical energy is reduced. But the ground only exerted a normal force on the pen, it didn't do any work. No other external force acted upon the pen. There was a change in mechanical energy even though no external force did any work on it. the (7) point given in the image is contradicted. Where am I going wrong?

I even wanted to ask what we mean by non-conservative internal forces?

  • $\begingroup$ Non-conservative forces are those forces which cannot be expressed as the gradient of a scalar potential and thus have non-zero curl. $\endgroup$ – user36790 Jun 2 '16 at 10:55
  • $\begingroup$ @MAFIA36790 understand the concept of conservative and non-conservative forces but what is a non-conservative internal force? $\endgroup$ – oshhh Jun 2 '16 at 11:00
  • 1
    $\begingroup$ Internal forces are those between parts of a system. External forces are those between some part of the system and something that is not part of the system. A "non-conservative internal force" is an internal force that isn't conservative. $\endgroup$ – dmckee --- ex-moderator kitten Jun 2 '16 at 22:35

For a conservative force the work done in going from position $A$ to position $B$ is independent of the path taken.When the pen hits the ground the ground is deformed.
For a non conservative force the work done does depend on the path taken and the frictional force is an example of such a force. If you slide a block from position $A$ to position $B$ on a flat table the path you take will determine how much work you need to do to move the block.

If the deformation is perfectly elastic the ground will be compressed and the pen's kinetic energy will become elastic potential energy (the ground acting like a spring).
The pen will then reclaim all its original kinetic energy as the ground reverts to its original shape.
This is the internal forces being conservative you compress the ground and the ground then gives all that energy back. The work done on the ground compressing the ground is equal to the work done by the ground in expanding.
So going from not compressed to compressed and then from compressed to not compressed results in no net work being done on the ground.

However if the collision is no t elastic the phase where the ground is compressed will result in permanent deformation of the ground (bonds will be permanently broken), heat and sound also being produced so the spring potential energy will be less than before and so the rebound of the pen will not be as high if at all.
This is the internal forces being non-conservative.
So going from not compressed to compressed and then from compressed to not compressed results in net work being done on the ground.


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