183_notes:collisions

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183_notes:collisions [2021/04/01 01:57] – [Momentum is never conserved] stumptyl183_notes:collisions [2021/04/01 01:59] (current) – [Sometimes, you can approximate that the system's momentum is conserved] stumptyl
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 ====== Momentum is never conserved ====== ====== Momentum is never conserved ======
  
-In real situations that you have observed in your everyday life, the momentum of a system is never conserved. There are always external interactions that act to change the system's momentum. That is, the momentum before is not equal to the momentum after.+In real situations that you have observed in your everyday life, the momentum of a system is never conserved. There are always external interactions that act to change the system's momentum. That is, the momentum before is not equal to the momentum after. (Momentum uses SI units of **kg*m/s**)
  
 $$\Delta \vec{p}_{sys} = \vec{p}_{sys,f} - \vec{p}_{sys,i} =  \vec{F}_{surr} \Delta t$$ $$\Delta \vec{p}_{sys} = \vec{p}_{sys,f} - \vec{p}_{sys,i} =  \vec{F}_{surr} \Delta t$$
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 [{{ 183_notes:conservation_of_momentum2.png?300|The momentum of this system of two particles is approximately conserved before and after the collision.}}] [{{ 183_notes:conservation_of_momentum2.png?300|The momentum of this system of two particles is approximately conserved before and after the collision.}}]
-In some cases, the external interactions on the system can be neglected when compared to the internal interactions between particles in the system. Think of a system of two particles that are going to collide (Figure to the right). In this situation, the particles in the system exert huge contact forces on each other as compared to external interactions (gravitational force, air resistance, etc.). Moreover, the collision occurs over a very short time. In this situation, the impulse delivered by the surroundings can be neglected ($\vec{F}_{surr} \Delta t \approx 0$) because it's so small compared to the forces that the objects in the system experience due to each other. So, in this case, you have momentum conservation (to the extent we can say the external interactions don't really matter):+__In some cases, the external interactions on the system can be neglected when compared to the internal interactions between particles in the system.__ Think of a system of two particles that are going to collide (Figure to the right). In this situation, the particles in the system exert huge contact forces on each other as compared to external interactions (gravitational force, air resistance, etc.). Moreover, the collision occurs over a very short time. In this situation, the impulse delivered by the surroundings can be neglected ($\vec{F}_{surr} \Delta t \approx 0$) because it's so small compared to the forces that the objects in the system experience due to each other. So, in this case, you have momentum conservation (to the extent we can say the external interactions don't really matter):
  
 $$\Delta \vec{p}_{sys} =  \vec{F}_{surr} \Delta t \approx 0$$ $$\Delta \vec{p}_{sys} =  \vec{F}_{surr} \Delta t \approx 0$$
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