Why does a magnet attract metal objects?

[withoutname]

Hi, there! I am studying magnetism right now and I can’t understand how does a magnet work. I read that the magnet has a magnet field, which influences only charged particles with velocity. But then how does magnet attracts metal objects, e.g iron nail? I read that in metals there are free electrons, which are moving outside of the atom shells. But the average velocity component of these electrons in any direction is zero, so then the magnetic force is also zero…

At all I want to design my own musical instrument, which uses only magnets and no electricity. So I tried to determine how a magnet would act on a metal guitar string eg. and what forces are acting in this configuration.

 

[Lnewqban]

Welcome, @withoutname !
Not all metal are attracted by a magnet.
Alloys based on iron, like the materials used in common magnets, respond the best.

Copied from:
https://en.wikipedia.org/wiki/Magnetism

"A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in addition to the electrons' intrinsic magnetic moment's tendency to be parallel to an applied field, there is also in these materials a tendency for these magnetic moments to orient parallel to each other to maintain a lowered-energy state"

 

[glappkaeft]

This is what a guitar pickup does.
https://en.wikipedia.org/wiki/Pickup_(music_technology)#Magnetic_pickups

Unfortunately for your project this requires amplification since this results in very little energy. Extracting more energy will at some point before you get a useful amount of energy out of it start to dampen the string too fast or otherwise effect the sound.