I very like classical mechanic You want to build model
I can not Understand problem ?
how many balls ? why it is impossible ?
The problem is the positive charges in the nucleus.
How are you going to get them so close together try doing this with magnets try and stick a whole pile of the same poles together.
Short of getting out rope and binding them all together they are never going to stay there.
To get the protons squeezed together like they are in a classic physics atom you need a force to push them together or pull them together
Now that force can only push or pull against space itself .. remember the charges repel
Ok you probably don't get the problem ... so reach down grab your ankles and pull your feet up off the ground please
See the problem gravity is outside the forces you can't do it gravity would always win and the atom would collapse.
Ok give me a minute and I will simplify down and show you how an atom really works.