Collision

A shock is a process in which two or more bodies exert force on each other briefly. As a result, change the body of their state of motion, possibly also their shape and composition. In an inertial system applies to all shock processes conservation of momentum - the sum of all pulses remains constant. However, the conservation of energy includes not only the mechanical forms of energy, such as inelastic and reactive collisions show.

The basic laws of impact and their mathematical description were established in the period 1651-1655 by Christiaan Huygens. Their empirical validity are essential to the concept of inertial mass.

Classification of mechanical collision processes

At the point of contact of the two bodies can create a tangent plane, which is called the contact plane. The corresponding normal line is the surge line. The masses of the two bodies are and their initial velocities and the initial speeds and. The common speed at the time of contact should be.

There are two ideal limiting cases, the elastic collision and the plastic shock (also inelastic or inelastic ). In the elastic collision kinetic energy of the body is transmitted to the body, but is retained as a total kinetic energy because they come away from one another. When plastic shock, however, some of the kinetic energy is transferred into internal energy and the body come not from each other. Therefore, at the end both have the same speed. All intermediate stages called real shock.

For a straight shock the two momentum vectors are parallel to the joint line, otherwise it is an oblique shock. If the common center of gravity of the two bodies on the joint line, then one speaks of a central collision, otherwise by an eccentric shock.

In addition, the smooth surge of non-smooth shock (also harsh shock ) delimits. During harsh impact contact friction forces at the contact surface and the pulse transmission are no longer perpendicular to the contact plane. For further analysis - in consideration also of the rotational energy and the angular momentum - a suitable vector decomposition into the tangential and normal component.

• Classification

Ditto, gravity moves transversely to the direction of impact

Eccentric shock

Rough shock

For simplicity, it is assumed for the following calculations that the shock in an infinitely short time runs out and while not change the positions of the collision partners. The velocities of the collision partners are changing by leaps and bounds. In addition, the free movement of the collision partners is assumed, so only take place straight movements.

Elastic Collision

( Ideal Elastic Collision / fully elastic collision )

Two bodies collide, without compromising energy into internal energy, such as heat or deformation converted. According to the energy conservation law ie the sum of kinetic energy (kinetic energy) before the collision is equal to the sum of the kinetic energy ( motion energy) after the collision. The same is true according to the momentum conservation law for the vectorial sum of the pulses.

The ideal elastic shock in macroscopic objects is an ideal model concept. Due to friction and other factors the system kinetic energy is lost in fact. However, very close to the model, for example, billiard balls or a rubber ball.

An impact to the atoms and / or elementary particles ( see also kinematics ( particle impingement ) ) there is in each case a minimum energy required for excitation of an atom or particle, or the production and conversion of the particles in particle physics. If this energy is not achieved, it comes to a perfect elastic collision.

According to the definition of "elastic" must before the sum of the kinetic energy and be the same after the collision.

This includes the squares of the vectors as well as the products of the difference and sum vectors scalar.

At the same time the momentum conservation law holds:

The last line means that the momentum changes are opposite to equal. In the following, only the velocity components are seen in the direction of the momentum transfer (one-dimensional, vector without arrows). Orthogonal to not change the pulses and speeds. By comparing the equations (1) and (2) we see that the average speed of which is of the same. This is just the velocity u of the common center of gravity ( component in the impact direction, transverse to the comparison is unproductive, 0 = 0):

It follows

For the special case we have:

Two-dimensional elastic collision

( Shale, central, elastic collision )

The two-dimensional elastic collision is based in principle on the above -mentioned one-dimensional elastic collision. First, the so-called central slope must be calculated. This describes the slope of the. Straight line through the centers of the balls The slope of the tangent line through the point of contact of the balls then be calculated by

If we decompose the motion vectors and into two components parallel to the tangent and orthogonal thereto, so you can simplify the two-dimensional shock to a one-dimensional. It then applies the above formula, but only for the components in the central direction.

( From here on, to be dispensed with in favor of a simpler representation of the indices '1 'and '2'. )

It follows:

For (similarly for and ), the second equation can be simplified:

One thus gets the system of equations

Rearranging we obtain:

For you and sets accordingly.

Finally, the new vectors and as stated above must be calculated even now. In the simplest case, namely applies to:

Otherwise, the above formula must be applied.

The new velocity vectors and are then calculated by vector addition of the vectors and and or:

Inelastic collision

( Perfectly inelastic collision / plastic impact / fully plastic impact / inelastic collision)

When inelastic collision some of the kinetic energy into internal energy (U) is converted. In the simplest case this is done by plastic deformation of the body involved in, but also a shock absorber generates mechanical losses. In the ideal inelastic collision, the maximum possible proportion of the kinetic energy is converted into internal energy, this "stick" the two masses after the collision, and they operate at the same speed, hereinafter referred to further. An example are two Plastilinkugeln that stick together after the collision.

Again, the two conservation laws apply:

• Before the collision:

• After the collision:

From the momentum conservation law, one can derive the following:

From the conservation of energy, the internal energy can be calculated:

Real shock

(Part Elastic Collision / part plastic impact )

A real collision between two masses is always a mixed form of ideal elastic and ideal plastic shock dar. This hybrid form is represented by the coefficient of restitution k The number of collisions is also called coefficient of restitution.

The collision frequency can be set using a drop test to determine:

For a partially elastic collision with the collision number k, the following speeds result:

The strain energy = conversion of the kinetic energy can be determined from:

With

Can be simplified elastic and plastic impact, the equations for the strain energy and the equations of the velocities after the collision to the above equations in the section.

Momentum transfer at real bodies

In a real body, the momentum transfer does not proceed more rapidly. Where a rubber ball on the floor, it deforms initially and then pushes off again as it forms because of its elasticity back. The entire sequence corresponds to an impulse, in which only one collision partners is considered. Furthermore, Newton's third law applies " action equals reaction ":

For an impact that is experienced both collision partners a power surge in opposite directions.

Super Elastic Collision

When super elastic collision internal energy is given by at least one of the collision partners in kinetic energy. The kinetic energy after this shock greater than before the collision. The mathematical treatment is carried out as for the general inelastic collision, only.

Reactive collision

In reactive shock reactions occur, such as chemical reactions or for the production of new particles by collisions of high energy particles in particle physics. It must be remembered that before and after the impact of different particles contribute to energy and momentum. It therefore change besides the speed and mass, and possibly the number of particles.

A kind of the reactive impact of the charge transfer, for example, an atomic physical process, in which exchanged during a collision between atoms, molecules or ions of one or more electrons. In all probability this, the electrons are transferred to the collision partner with the positive charge. Thus, positive ions, for example, in the solar wind contained (see also highly charged ion ) during passage through the thin gas atmosphere surrounding a comet capture electrons and this radiation, including in X-rays, which emit.

Scattering

In particle physics, nuclear physics, nuclear physics, or when photons are involved, it is also called scattering. Here is inelastic scattering ( inelastic collision) that the kinetic energy is not conserved as such, but partially transformed eg in excitation energy or the bond-breaking is used. When a photon is involved in a non-elastic scattering, generally changes its wavelength. For details, see scattering and scattering theory.