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| 183_notes:collisions [2021/04/01 01:58] – stumptyl | 183_notes:collisions [2021/04/01 01:59] (current) – [Sometimes, you can approximate that the system's momentum is conserved] stumptyl | ||
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| - | 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): |
| $$\Delta \vec{p}_{sys} = \vec{F}_{surr} \Delta t \approx 0$$ | $$\Delta \vec{p}_{sys} = \vec{F}_{surr} \Delta t \approx 0$$ | ||