nuclear physics - Mass defect- From where mass is being lost?

As a school student, I have wondered while studying mass defect the following mysterious problem

My assumption

1. 
   

   Just like a car's mass is constituted by each part of it(i.e total mass of car will be equal to mass of body+engine etc..), I assume that the mass of nucleus is the sum total of the mass of the particles the nucleus contains, i.e mass of nucleus =mass of protons +mass of neutrons

   
   


2. 
   
   

   I assume all the protons, neutrons are exactly the same, they have (each kind) exactly same mass

   
   


3. I assume the charge of proton is distributed uniformly.

Details

A quote from Wikipedia: http://en.wikipedia.org/wiki/Binding_energy

It is observed experimentally that the mass of the nucleus is smaller than the number of nucleons each counted with a mass of 1 a.m.u.. This difference is called mass excess.

The mysterious problem I encounter

There is no change in the number of neutrons or protons in the nucleus of the atom. And my idea was as the mass of nucleus is the total mass of protons and neutrons, if the mass of nucleus is to change what I can think about the possibilities are

1. Either the number of neutrons or number of protons should change


2. In order to fit the 2nd assumption, some part of the mass of every neutron and every proton will go (probably as energy) so that all the protons are same and all the neutrons too are same.

The 1st possible explanation is obviously wrong as we don't see any change in the number.

The 2nd possible explanation is just 'like a reason for the sake of giving a reason' logically difficult to convince myself. If that were true there should have been many types of protons and different types of neutrons (both classified according to their mass), which again is un-intuitive.

The question

• What's the possible explanation to the question from where the mass is being lost?



• Either one of my assumption is wrong (but isn't my assumption just logical?) or there should be some other reason how the mass can vary (may be we should better define what is the mass of the nucleus). In that case, another question , If my assumption 1 is false What constitute the mass of a nucleus?


• Isn't there something like a standard proton or a standard neutron (By standard I mean a fixed mass fixed charge etc)


• By my third assumption, If the proton loses some mass shouldn't it lose some of it's charge. And suppose we forget E=mc^2 can't we say the difference in the potential energy of electron-proton (as it changes when the charge changes) is an explanation of how the nucleus gets binding energy.