Collisions, elastic velocity changing

The relative velocity changes from the value g2i before the collision to the value g2i after the collision. Since the collision is assumed to be elastic so that the internal energies of the molecules remain unchanged, the total kinetic energy Ec remains unchanged in a collision. 

Figure 4.2 Two common interactions between light and matter, (a) At certain angles, light is refracted when passing from one medium to another (at dashed line), changing direction and velocity, (b) When light hits a particle, elastic collisions result in changes in direction and phase (Rayleigh scattering), whereas inelastic collisions result in frequency changes (Raman effect).

If a particle collides elastically with the wall, it bounces off the wall with no loss of energy. For a straight-line collision, the change in velocity is 2v (the particle s velocity was V before the collision and —v after the collision therefore, the change is 2v). The force per collision is given by ... 

Such measurements have been performed with polarized laser pulses to measure the orientation relaxation [12.22] and to measure the total rate of inelastic collisions [12.23]. With single-mode lasers even velocity changing elastic collisions can be investigated [12.24]. 

Suppose we imagine a single molecule bouncing back and forth across a surface between two restraining barriers. If we define the direction of this motion to be the x direction and the velocity of the molecule to be vx, then the change in momentum at each collision (if we assume they are elastic) is... 

The quantity mu is the momentum of the particle (momentum is the product of mass and velocity), and the expression F = A(mu)/At means that force is the change in momentum per unit of time. When a particle hits a wall perpendicular to the x axis, as shown in Fig. 5.13, an elastic collision occurs, resulting in an exact reversal of the x component of velocity. That is, the sign, or direction, of ux reverses when the particle collides with one of the walls perpendicular to the x axis. Thus the final momentum is the negative, or opposite, of the initial momentum. Remember that an elastic collision means tjiat there is no change in the magnitude of the velocity. The change in momentum in the x direction is ... 

Figure 4.11 depicts the space-time plot of a head-on quasi-elastic collision with positive phase shifts between two waves of unequal velocity. The slower wave experiences the larger change in wave velocity. Both waves travel with higher velocities after the collision. This situation is reminiscent... 

According to the relevant power and momentum balance, Eqs. (38) and (39), the electron kinetics in steady-state plasmas is characterized by tbe conditions that at any instant the power and the momentum input from the electric field are dissipated by elastic and inelastic electron collisions into the translational and internal energy of the gas particles. This instantaneous complete compensation of the respective gain from the field and the loss in collisions usually does not occur in time-dependent plasmas, and often the collisional dissipation follows with a more or less large delay—for example, the temporally varying action of a time-dependent field. Thus, the temporal response of the electrons to certain disturbances in the initial value of their velocity distribution or to rapid changes of the electric field becomes more complicated, and the study of kinetic problems related to time-dependent plasmas naturally becomes more complex and sophisticated. Despite this extended interplay between the action of the binary electron collisions and the action of the electric field, the electron kinetics in time-... 

For simplicity we consider first the elastic scattering of two particles with masses m and m2t in which only the directions of motion of the particles change during the collision. In a center-of-mass coordinate system the scattering process is described by the motion of a mass point with an effective (reduced) mass p = m m2/(m-j+m2) in a potential field V(r) depending on the interparticular distance r. For a given initial relative velocity, the scattering direction, i.e., the direction of the final velocity relative to 1, is de-... 

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