In the book I'm studying, there is a graph for the potential energy of a system made by a free proton and a free neutron, the graph shows that the potential energy of the system as a function of the distance between the particles is zero for large distances, it has a minimum(aprox. -40MeV) at about 1fm, increases with the distance between 1fm and 3 fm and is very large for distances smaller than 0.5fm. As I understood this happened because of the nuclear force and i think that the large value of the potential energy for distances smaller than 0.5fm wasn't explained(in the book I'm studying), but that for now i don't care. After explaining nuclear force the book explains the binding energy, and it states that a nucleus as a smaller mass than the sum of the masses of it's constituents if they were apart, it also says that because the mass is a measure of energy, the total energy of the nucleus is less than the combined energy of the separated nucleons. And that this difference in energy is called the binding energy. And that I could calculate the binding energy using E=m(c^2). What i don't understand is this: Does the graph includes solely the change in the potential energy caused by the existence of the nuclear force?, or it includes too the binding energy?, or is the binding energy related with the nuclear force?, if so why does the mass changes with the union of the nucleons?. The book also says that the binding energy is the energy that must be added to the nucleus to break it apart, and with this statement it looks like that the binding energy is caused by the nuclear force, because as i understood the nuclear force is what keeps the nucleus together. What really confuses me is, as i look at the graph i would expect that if a proton and a neutron were apart and then joined together, the potential energy of the system would be changed from zero to a minimum, the variation of the energy of the system would be released somehow, don't see why should exist any change of the mass, and the energy required to take the particles apart then would be the -40MeV as i referred, that i would expect to be the binding energy.