Elastic Collision. The percussive force of the small ball and the buffer is P, and it is calculated according to Newton's second law of motion:
The force and deformation formulas of the elastic collision between the ball and the buffering device obtained in the elastic stage are substituted:
In these equations, e refers to elasticity or coefficient of restitution--the ratio of relative speeds after and before a collision--varying between 1, a perfectly elastic collision, and 0, a perfectly plastic collision.
Given a perfectly elastic collision (e = 1), then [U.sub.Last ball] = [V.sub.Launcher], the standard behavior of the Newton's cradle.
system indicate that the relative speeds of the particles do not change before and after collision as a result of an elastic collision
[absolute value of [v.sub.pb]] = [absolute value of [v'.sub.pb]] = [v.sub.pb].
In the present work, the elastic collisions
, [d-.sub.3][Li.sup.6], [d-.sub.6][C.sup.12], [d-.sub.8][O.sup.16], [d-.sub.12][Mg.sup.24], [d-.sub.16][S.sup.32], [d.sub.-20][Ca.sup.40], [d-.sub.23][V.sup.50], [d-.sub.28][Ni.sup.58], [d-.sub.32][Ge.sup.70] and [d-.sub.32][Ge.sup.72] have been studied according to their cluster and nucleon structures.
We consider identical particles of a unit mass with a diameter [sigma] > 0, interacting as hard spheres with elastic collisions. Every particle is characterized by its phase coordinates ([q.sub.i], [p.sub.i]) = [x.sub.i] [member of] [R.sup.3] x [R.sup.3], i [greater than or equal to] 1.
In the paper a new approach to the problem of the rigorous description of the kinetic evolution of a system of hard spheres with elastic collisions was developed.
The energetic ion when traverse through the material medium it losses its energy either in displacing atoms (of the sample) by elastic collisions
or ionizing the atoms by inelastic collision.
Furthermore, at these energies the particles will tend to move in straight lines as they lose energy until their energy becomes low enough for elastic collisions
to cause them to deviate from straight line paths.
Particles can undergo partially elastic collisions
with walls, and can be trapped or retained by certain surfaces.
Throughout this article I will consider elastic collisions
between point particles which move in one and the same unidimensional space, the axis X.