Why did early americans write the constitution and the bill of rights?

The simplest answer is because they wanted to be ruled by a government that recognized the rights and power of the people being ruled. The bill of rights outlines and as much as possible guarantees what things are granted to everyone. It's not only freedom religion, assembly and speech. It is things like gun control, search and seizure, the right to trial, the right not to incriminate oneself by saying anything at all.

The constitution outlines how each of the governments divide up the power given to each of them. The most carefully written part has to do with the role of the federal government vs states rights.

elastic potential energy

could you go a bit more in depth with you question? it's quite hard to understand. as soon as you do that i will be glad to : )