Inelastic collision of "particles" with structure

Two equal "particles" with structure move with opposite velocities of magnitude v along the same line on a smooth horizontal surface.

Each "particle" has two "microscopic" elements of masses m and αm, interacting through a massless spring of stiffness k and natural length L and they move on a smooth horizontal surface.

Initially the spring is unstretched and the two "particles" move with opposite velocities of magnitude v.At some point the two "particles" collide.

The collision between the two inner masses is elastic; but, since the oscillatory mode is excited, one can understand (from a "macroscopic" point of view) the transfer from the translational mode (identified with the motion of the center-of-mass) to the oscillatory mode as a transfer of kinetic energy to an internal elastic mode.

• The unit time is (m/k)^1/2 .
• The unit length is v (m/k)^1/2 .
• You can select the values for the parameters α and L, as well as the interval between animation frames (Δt).
  Press Enter after modifying these values.
• You can display the whole "particle" and/or its "microscopic" elements by checking Body and/or Elements.
• You can also display, optionally, the center-of-mass, as well as its velocity and those of the "microscopic" elements.
• Use the slider on the top of the window to select the displayed range.
• After each collision the program will display the coefficient of restitution (e ≡ V / |v|, where V is the velocity of the center-of-mass). With this definition e will be negative if the center-of-mass is approaching the center.
• To get information on the any element, put over them the mouse pointer to see the corresponding tooltip.

See: J. M. Aguirregabiria, A. Hernández and M. Rivas, "A simple model for inelastic collisions"

Activities

• Check that there is a qualititative difference between α = 0.5 and α = 1.
• Find the boundary between these two different behaviors.
• Can you find other cases in which the collision is also elastic from the "macroscopic" point of view?
• Which is the most inelastic case?