Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is larger than the repulsive electrical force between two protons-hence its name. But the strong force quickly weakens as the distance between the protons increases. A well-established model for the potential energy of two nucleons interacting via the strong force is
U=U0[1−e−x/x0]
where x is the distance between the centers of the two nucleons, x0 is a constant having the value x0 = 2.0 × 10−15 m, and U0 = 6.0 × 10−11 J.
Quantum effects are essential for a proper understanding of nucleons, but let us innocently consider two neutrons as if they were small, hard, electrically neutral spheres of mass 1.67 × 10−27 kg and diameter 1.0 × 10−15 m. Suppose you hold two neutrons 2.0 × 10−15 m apart, measured between their centers, then release them. What is the speed of each neutron as they crash together? Keep in mind that both neutrons are moving.