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
mass1.67 × 10−27 kg and
diameter 1.0 × 10−15 m.Suppose you hold two
neutrons 5.0 × 10−15 mapart, measured between
their centers, then release them.
What is the speed of each neutron as they crash
together? Keep in mind that bothneutrons are
moving.
Express your answer with the appropriate units.