# What is the force of collision of different materials between themselves?

Let think in two particles(A, B) for example. The particle A is moving with a constant velocity towards B and the particle B is still(not moving). Now, the particle A hits the particle B, let assume an elastic collision. Let think this two particles are in space and there is no other Forces acting on them.

What will be the Force of A hitting B?

We know that there is conservation of momentum(in this case linear) and conservation of kinetic energy. Now, If there is any Force at the collision, then there is acceleration, and this happens in a fraction of time.

I say now, that this fraction of time must be a function of the mass, either qualitatively or quantitatively.

Are there any way to identify those properties of matter?

• No. It depends on the elasticity of the particles. Commented Oct 30, 2016 at 2:16

I believe your question relates to the idea of impulse and how that relates to momentum and energy conservation. The definition of impulse gives:

$$F\Delta t = \Delta p = m\Delta v$$

A force applied over some time interval equals the change in momentum.

So take the case of an elastic collision between two particles, one moving, one stationary.

The force that each one experiences on impact relies on the interval of time in which the collision occurs, which relates to the elasticity of the particles.

Let's examine what happens when two objects collide, and the collision lasts 1 second (1 second passes before the objects are finished colliding). The first object has momentum $p_1$, and the second $p_2 = 0$

We can compare the momentum after the objects collide to find the change in momentum for each object. This is $m\Delta v$. Then the force that each object experienced during collision is simply the change in momentum of each object, as $\Delta t = 1$

$$F = \frac{m\Delta v}{\Delta t} = \frac{m\Delta v}{1} = m\Delta v$$

Of course, the time interval that collisions occur can vary, and this depends on the elasticity of the objects. If the time interval is very small, for very elastic objects, the force experienced is larger. For more inelastic collisions (for instance, a car crash where the vehicles spend time deforming before separating, or even sticking together), the force experienced is much less than in the elastic case. This is what led to the idea of implementing crumple zones in vehicles, so that during a collision, more energy is used in deforming the vehicles, lowering the impulse and the force which drivers would experience.

What will be the Force of A hitting B?

Newton's 2nd law tells us that: $$\sum F=\frac{dp}{dt}$$

And as shows, we do not have enough information. You need to know something about the duration of this impact - or alternatively about the speeds before and after, as the other answer shows, because we can do some rewriting.

We know that there is conservation of momentum(in this case linear) and conservation of kinetic energy. Now, If there is any Force at the collision, then there is acceleration, and this happens in a fraction of time.

Exactly. The $dt$ in the formula above will be tiny, so the force will be large.

But it's not always very tiny - when a tennisball hits a wall, it looks fast but is in fact a much longer collision duration than if a stone hits a wall. Which is why you can damage walls by throwing stones at them but not tennisballs; there is simply excerted a larger force on the wall.

I say now, that this fraction of time must be a function of the mass, either qualitatively or quantitatively.

No.

You can find a tennisball and a stone with the same mass. Or a big pillow for that matter with the same mass. The collision duration depends not on their mass but on how elastic they are - on their elasticity, which is a material property that depends on parameters like atomic bonding, microstucture (grains lattice defects) etc., but not mass.

Are there any way to identify those properties of matter?

This is a huge question because many parameters have influence.

• The elasticity $E$ (called Young's modulus) as an example can be found in simple pull-tests. You simply make a machine pull a piece of the material until it breaks and record how much it elongated linearly (elastically) along the way. Wikipedia has some examples of such stress-strain curves, where $E$ is the slope of the linear part of the curve in the beginning.

• Microstructure of materials is something you can see in electron microscopes and types, composition, orientation etc. can be measured with methods like x-ray diffraction etc.

• Was my error to say that the fraction of time is a function of mass, I meant a function of matter. Mass can only be a quantity but has no quality. Commented Oct 30, 2016 at 18:46
• @Andre Yes, ok. I'm not really sure how to grasp "a function of matter", though. Matter as the general term is not a parameter. But yes, we are talking about a function of matter's properties, and I guess that's what you meant all along. Commented Oct 30, 2016 at 20:19