183_notes:colliding_systems

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183_notes:colliding_systems [2016/08/14 00:41] – [Examples] waterso8183_notes:colliding_systems [2021/04/01 02:01] (current) – [Inelastic Collisions] stumptyl
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 +Section 10.1, 10.2, 10.3 and 10.4 in Matter and Interactions (4th edition) 
 +
 ===== Collisions ===== ===== Collisions =====
  
-Collisions occur everywhere around you. Right now, molecules of gas are constantly colliding with each other in the air that surrounds you as well as colliding with your clothes and skin. In the notes, you will read about how to analyze collisions using the [[183_notes:momentum_principle|momentum principle]] and [[183_notes:energy_cons|energy principle]]. You will also read about different kinds of collisions. Later you will read how collisions lead to the [[183_notes:discovery_of_the_nucleus|discovery of the nucleus]].+Collisions occur everywhere around you. Right now, molecules of gas are constantly colliding with each other in the air that surrounds you as well as colliding with your clothes and skin. **In the notes, you will read about how to analyze collisions using the [[183_notes:momentum_principle|momentum principle]] and [[183_notes:energy_cons|energy principle]].** You will also read about different kinds of collisions. Later you will read how collisions lead to the [[183_notes:discovery_of_the_nucleus|discovery of the nucleus]].
  
 ==== Lecture Video ==== ==== Lecture Video ====
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 {{youtube>ZEsAuTpQ7B8?large}} {{youtube>ZEsAuTpQ7B8?large}}
  
-==== Collisions & Conservation of Momentum & Energy ====+====== Collisions & Conservation of Momentum & Energy ======
  
 Collisions are brief interactions between objects that involve very large forces between the objects. That is, in a collision, you will often choose the system to be both colliding objects, so you can neglect the interactions of the system with its surroundings. By choosing a system of both particles in this way, you find that the momentum and total energy of the system are conserved. Collisions are brief interactions between objects that involve very large forces between the objects. That is, in a collision, you will often choose the system to be both colliding objects, so you can neglect the interactions of the system with its surroundings. By choosing a system of both particles in this way, you find that the momentum and total energy of the system are conserved.
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 Neglecting these external interactions can be done because (a) the interaction between the colliding objects occurs over a very short time, and because (b) the forces that the colliding objects exert on each other are much larger than the forces exerted by the surroundings. Neglecting these external interactions can be done because (a) the interaction between the colliding objects occurs over a very short time, and because (b) the forces that the colliding objects exert on each other are much larger than the forces exerted by the surroundings.
  
-=== The System Can Have Internal Energy ===+==== The System Can Have Internal Energy ====
  
 While the above discussion might make you conclude that the energy that is conserved is only kinetic (i.e., due to the motion), this is not the case. The total energy of the system is conserved, so you have to keep track of kinetic and [[183_notes:internal_energy|internal energy]] during a collision. In fact, whether the system changes its internal energy is a part of understanding collisions. While the above discussion might make you conclude that the energy that is conserved is only kinetic (i.e., due to the motion), this is not the case. The total energy of the system is conserved, so you have to keep track of kinetic and [[183_notes:internal_energy|internal energy]] during a collision. In fact, whether the system changes its internal energy is a part of understanding collisions.
  
-=== Collisions Can Occur Without Physical Contact ===+==== Collisions Can Occur Without Physical Contact ====
  
 When you think about the collision of systems, are the objects that collide touching? Probably so. But, collisions can occur without physical contact. The only properties we have used to define collisions are that they are (a) brief and (b) involve large forces. So, consider two positively charged atoms (e.g., a Helium nucleus impinging upon a Gold nucleus). When you think about the collision of systems, are the objects that collide touching? Probably so. But, collisions can occur without physical contact. The only properties we have used to define collisions are that they are (a) brief and (b) involve large forces. So, consider two positively charged atoms (e.g., a Helium nucleus impinging upon a Gold nucleus).
  
 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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