Okay so, this question is pretty simple. When two objects of constant velocity collide, is there a constant deceleration upon contact? or does it follow some unique function that can only be evaluated by testing it? Furthermore, if it is in fact constant, how do we know and how did we originally test it? (Assuming that we knew before the age of slow-mo video, etc.)
Thanks!
Think of the objects as not solids, but as small masses connected with little springs. All the of the masses move with the same speed initially.
As soon as they objects come in contact some of the masses change speed compressing some of the springs. This starts to decelerate the object. But at every time frame more and more springs add to the deceleration. Until the objects bounce off each other.
The shape of the contact force is non-linear with position due to the fact the contact area increases with force, resulting in a force curve with time which increases, plateaus and then decreases.
In general, Newtonian mechanics, that is taught at high school and at university in introductory level, considers objects as point particles or at most uncompressible solids. Therefore, in most cases, collisions are considered as elastic, where both kinetic energy and momentum are conserved.
However, in reality this is far from being the case. There is almost no point particles and any solid can be compressed. In other words, in reality there is almost no elastic collision; some of the kinetic energy is spent for deforming the shape and eventually is lost as heat.
There are a few materials properties (such as bulk modulus) involved in such calculations and I believe, analytical solutions only exists for certain geometrical shapes and for certain collision directions. For example, it could be possible to come up with such a function say for a spherical plastic ball or an iron cylinder etc. and I doubt that such a function will be constant for different shapes, materials and even collison directions. In other cases, that is, for complicated shapes and inhomogenoius materials, there might be some computer based numerical solutions that engineers apply.
Here is an example of a such non-elastic collision, as you mentioned, in slow motion.
