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 momentum principle and energy principle. You will also read about different kinds of collisions. Later you will read how collisions lead to the discovery of the nucleus.

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.

From the multi-particle momentum principle,

$$\Delta \vec{p}_{sys} = \vec{F}_{ext}\Delta t$$ $$\Delta \vec{p}_{sys} = \underbrace{\vec{F}_{ext}\Delta t}_{\approx 0}$$ $$\vec{p}_{sys,f} - \vec{p}_{sys,i} = 0$$ $$\vec{p}_{sys,f} = \vec{p}_{sys,i}$$

From the energy principle,

$$\Delta E_{sys} = W_{surr} + Q$$ $$\Delta E_{sys} = \underbrace{W_{surr}}_{\approx 0} + \underbrace{Q}_{\approx 0}$$ $$E_{sys,f} - E_{sys,i} = 0$$ $$E_{sys,f} = E_{sys,i}$$

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.

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 internal energy during a collision. In fact, whether the system changes its internal energy is a bit part of understanding collisions.

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 in due 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.

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