183_notes:colliding_systems

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183_notes:colliding_systems [2021/04/01 02:00] – [Collisions & Conservation of Momentum & Energy] stumptyl183_notes:colliding_systems [2021/04/01 02:01] (current) – [Inelastic Collisions] stumptyl
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 In this case, the interaction between these two objects is due to their electrical interaction. They repel each other. As the atoms get closer together, the electric force gets larger and larger. This interaction is brief, but would cause the nuclei to change their individual momenta (the total remains the same) because of the large forces involved. This is a collision, but the nuclei are never in physical contact. In this case, the interaction between these two objects is due to their electrical interaction. They repel each other. As the atoms get closer together, the electric force gets larger and larger. This interaction is brief, but would cause the nuclei to change their individual momenta (the total remains the same) because of the large forces involved. This is a collision, but the nuclei are never in physical contact.
-==== Elastic Collisions ====+===== Elastic Collisions =====
  
-An collision is called ``elastic'' if the internal energy of the system doesn't change. That is, before and after the collision the system experiences no new deformations (i.e., no new compressions of atomic bonds), no new rotations or vibrations, and no thermal energy changes (i.e., no new increased random motion of atoms). +A collision is called ``elastic'' if the internal energy of the system doesn't change. That is, before and after the collision the system experiences no new deformations (i.e., no new compressions of atomic bonds), no new rotations or vibrations, and no thermal energy changes (i.e., no new increased random motion of atoms). 
  
 In this case, the system conserves kinetic energy during the collision.  In this case, the system conserves kinetic energy during the collision. 
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 $$K_{sys,f} = K_{sys,i}$$ $$K_{sys,f} = K_{sys,i}$$
  
-==== Inelastic Collisions ====+===== Inelastic Collisions =====
  
 In contrast to elastic collisions, "inelastic" collisions are ones in which the internal energy of the system can change. These internal energy changes can be manifest in permanent deformations of the system, temperature changes, or other new vibrational and rotational changes of the atoms or the system. In this case the total kinetic energy of the system is not conserved because the initial kinetic energy is transformed into internal energy of the system. In contrast to elastic collisions, "inelastic" collisions are ones in which the internal energy of the system can change. These internal energy changes can be manifest in permanent deformations of the system, temperature changes, or other new vibrational and rotational changes of the atoms or the system. In this case the total kinetic energy of the system is not conserved because the initial kinetic energy is transformed into internal energy of the system.
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 $$K_{f,sys} \neq K_{sys,i}$$ $$K_{f,sys} \neq K_{sys,i}$$
  
-Although the kinetic energy is not conserved, inelastic collisions still conserve momentum. +__**Although the kinetic energy is not conserved, inelastic collisions still conserve momentum.** 
 +__
 $$\vec{p}_{f,sys} = \vec{p}_{sys,i}$$ $$\vec{p}_{f,sys} = \vec{p}_{sys,i}$$
  
-=== Maximally Inelastic Collisions ===+==== Maximally Inelastic Collisions ====
  
 Certain types of collisions result in the maximum internal energy change that a system can experience given its initial conditions. Such collisions are referred to as "maximally inelastic". A simple case to think of is when two objects with equal masses, and equal speeds are directed towards each other and collide. This system has zero total momentum. To conserve momentum, the system must have zero momentum after, which is satisfied by the objects stopping after their collision. The system goes from having some positive kinetic energy to having none. The total internal energy change is equal to the initial kinetic energy.  Certain types of collisions result in the maximum internal energy change that a system can experience given its initial conditions. Such collisions are referred to as "maximally inelastic". A simple case to think of is when two objects with equal masses, and equal speeds are directed towards each other and collide. This system has zero total momentum. To conserve momentum, the system must have zero momentum after, which is satisfied by the objects stopping after their collision. The system goes from having some positive kinetic energy to having none. The total internal energy change is equal to the initial kinetic energy. 
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