Theoretical information. For two colliding bodies, two equations based on the law of conservation of momentum and the law of conservation of kinetic energy can be considered

For two colliding bodies, two equations based on the law of conservation of momentum and the law of conservation of kinetic energy can be considered. Bodies motion descriptions after noncentral impact have difficulties. Motion characteristics in this case depend on initial conditions, interacting bodies mass relationship and interaction geometry.

A task is simplified, if bodies have a form of balls of identical diameter and one of them is immovable before the impact (fig. 1, where d is aimed parameter).

During interaction the component of momentum changes (fig. 2, where is the projection of momentum to direction O₁O₂).

Then the second ball acquires momentum , directed at the angle a₂ to the momentum , and the first ball acquires momentum (fig. 3) .

The momentum of the first ball is directed at the angle a₁ to the momentum .

Characteristics of interaction result are: a₁, P₁, E₁, a₂, P₂, E₂, where E₁ and E₂ are kinetic energies of balls.

2. Work fulfillment method

In this work, a computer experiment simulates an impact of two balls of the same diameter with masses m = 1... 5 kg and with initial velocity of balls v = 4... 10 m/s. However, using the criteria of similarity of processes, the experiment results can be applied for objects which are beyond these scopes. Fig. 2 demonstrates that angle a₂ depends only on the aimed parameter d and diameter of balls D:

The momentum of the second body depends on relation and initial velocity of the first ball v. From fig. 3 follows that:

, .

Then according to momentum conservation law we obtain:

Therefore moments , and angles a₁ and a₂ depend on the relationship between masses of balls (fig. 4, 5):

,

Energies are calculated according to the formulas:

, .

The program of experiment does not allow to change the diameter of balls. That is why the criteria of similarity are functions of relationship between parameters and :

Balls velocities and depend on relationship of the balls masses and parameters (fig. 6; 7):

Fig. 6 Fig. 7

Functions (1) — (4) change for selected values . Balls motion characteristics are determined by using functions (1) — (4) for the given values .

Дата добавления: 2015-10-26