Introduction
Welcome to the FiveHive article for Unit 4.3 of AP Physics 1!
In this article, we will be exploring yet another major section of the applications of mechanics. Namely, we will explore the conservation of momentum.
As usual, we will only cover the topics included in the CED for unit 4.3.
Conservation of Momentum
Conservation of momentum simply states that the total momentum of a system of objects must always stay the same. The total momentum of a system is simply the sum of the momenta of the individual parts of the system.
The only time that this rule does not work is when a force outside of the system exerts an impulse on the system. Therefore, any change in momentum of the system is due to a transfer of momentum between the system and the surroundings.
When problem-solving in the AP exam, it is highly suggested you write at the start of any derivation involving the conservation of momentum with:
This is because the AP exam usually rewards points for foundational statements, such as the conservation of momentum.
Properties of the Center of Mass
Thus far, we have likely only seen the center of mass as a representation of a grouping of objects. However, there is a lot more we can do with this concept of a center of mass.
In some cases, you will have to find the position of the center of mass, as well as the acceleration of the center of mass. However, these equations simply replace the velocity term in the equation with either position or acceleration of each constituent part of the system. It is also worthwhile noting that the velocity of the centre of mass stays the same after any sort of collision.
Impact of Impulse
It is important to realize that the impulse that object A exerts on object B is equivalent to the impulse that object B exerts on object A.
Why is that? The answer is simple. Let’s go back to the ancient days of Newton’s Laws; according to Newton’s third law, the forces are going to be equivalent in magnitude, meaning the impulses will also be equivalent.
If an external force acts on the system, the change in momentum is equivalent to the impulse exerted on it. Using this principle, we can often figure out the velocity of the system and/or its constituent parts before or after a force is exerted.