Maximally Inelastic Collision

This topic covers Maximally Inelastic Collisions. claimed by apatel404

The Main Idea

A collision is a brief interaction between large forces. This could include two objects or several depending on the situation and how they collide is important. Collisions can be either inelastic,elastic, or maximally inelastic which is a subset of inelastic. Inelastic collisions occur when the object's kinetic energies are not conserved in the final and initial state. In maximally inelastic collisions, the objects in the system collide and stick together to form one object which has a new velocity and the mass of the object is the total mass of all the objects that have now combined into one.

A Mathematical Model

Maximally Inelastic Collisions can be based off the fundamental principle of momentum:

[math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}{Δt} }[/math]

where p is the momentum of the system, F is the net force from the surroundings, Δt is the change in time for the process.

Using the principle of momentum, one can derive the final velocity of the object where the two initial objects have combined to become one since the interaction between the objects is brief, [math]\displaystyle{ {Δt} ≈ {0} }[/math].

So rewriting the equation with the concept that the change in time is 0 yields:

[math]\displaystyle{ {ΔP_{system}} = {0} }[/math].

Breaking the change in momentum of the system to it's initial and final components we get:

[math]\displaystyle{ {P_{final}} = {P_{initial}} }[/math].

Now if we plug in the mass and velocity of object 1 and the mass and velocity of object 2 we see that: [math]\displaystyle{ m_1 v_1 + m_2 v_2 = \left( m_1 + m_2 \right) v \, }[/math] where v is the final velocity, which becomes

[math]\displaystyle{ v=\frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} }[/math]

A Computational Model

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