Final answer:
The choice of the system of interest impacts which forces are considered external and affect the system's acceleration according to Newton's second law of motion. Internal forces are not included in the net force calculation, while external forces are. The system selected can change whether a force is internal or external, which alters the forces included in the analysis.
Step-by-step explanation:
The choice of the system of interest is critical when applying Newton's second law of motion because it affects which forces must be considered external and therefore influence the acceleration of the system. Internal forces are those that act between components within the chosen system, and these do not affect the center of mass motion of the system according to Newton's second law. In contrast, external forces are those that act on the system from the outside, and it is the net external force that is equal to the mass of the system multiplied by its acceleration.
For example, if our system of interest is a car being pushed by a person, and we consider both the car and the person to be part of the system, the force of the person pushing the car is internal. However, if we choose only the car as our system of interest, then the person's push becomes an external force. This illustrates how our choice of the system can change which forces we need to consider when applying Newton's laws.
Also, Newton's third law of motion tells us that forces occur in equal and opposite pairs, but the choice of system of interest affects whether these forces are considered internal or external. Two objects exerting forces on each other may be within the same system of interest, in which case these forces would cancel out in the net force calculation, or they might belong to different systems, making the forces external to each other.