referred to as a perfectly non-elastic (non-plastic) collision [20]. In the case of the latter
the two bodies do not separate after the collision but start moving as one body. For
actual real bodies deformation usually partially disappears and is partially retained. In
this case the collision is referred as imperfectly elastic.
a) When a point or a mechanical system is subjected to the action of regular
forces their value during the collision is disregarded. The ground for this lies in the fact
that their impact impulses are negligible.
b) The displacement of material objects during the collision is disregarded; i.e.
bodies are assumed to be stationary.
7.2 Collision of mechanical objects
7.2.1 Material particle collision
a) Basic equation for the dynamics of a particle during a direct collision.
If a particle having a mass m is subjected to an impact force at a certain moment
of time, then based on the theorem for the variation of the amount of movement we
can write down the following equation:
where v is the speed of this particle before the collision and u is the speed of the
same particle after the collision. This equation is called the basic equation for the
dynamics of a particle during collision. Considering the assumptions we made in the
previous paragraph, the action of the impact force can be evaluated by its impact
impulse, which in the impact theory plays a role that is similar to regular forces acting
during the movement of material objects [20].
b) A particle colliding in a stationary surface
Let us consider a falling material particle colliding in a stationary surface. The
task is to determine the speed of this particle u after the collision and its direction β
knowing the mass m of the particle, the speed v before the collision and the direction
of the impact relative to the normal drawn to the colliding surface α.
The following two Newton’s laws could be used to give a satisfactory answer to
these questions:
