Final answer:
Internal forces within a system cancel each other out according to Newton's third law, which is why we can neglect them when applying Newton's second law of motion, focusing solely on external forces that actually cause changes in the system's motion.
Step-by-step explanation:
When applying Newton's second law of motion, we can neglect forces such as those holding a body together, because these are considered internal forces. Internal forces come in pairs according to Newton's third law of motion, where each force in a pair applies to different parts of the same system, thus they cancel out when considering the system as a whole. This is why only external forces need to be considered, as they do not cancel out within the system and are responsible for changes in the motion of the system.
To illustrate this, imagine a car accelerating down the road. The engine exerts forces on various parts of the car to make it move, but these forces are internal and cancel out. However, the external force of the ground pushing on the tires is what actually moves the car forward, and this external force would be considered in a free-body diagram and in the application of Newton's second law to analyze the car's motion.