What do we mean by "external" force? In light of Newton's third law of motion, why can't an internal force cause a net force?

When we explore the interactions within a physics problem, the concept of an external force is crucial. An external force is applied to an object or system from something outside of that system. Imagine pushing a box across the floor—the force from your hands is an external force on the box system. External forces can create a change in motion, or a net force, which is the overall force acting on an object after all the individual forces are combined.

It is the interaction with the environment or other systems that allows external forces to actually impact the motion. For example, if a ball is at rest and you kick it, the force from your foot is external to the ball's system and causes it to move. In this way, external forces are those responsible for providing energy or causing a change in velocity for an object or system.

On the flip side, internal forces are forces that act within a system, between components of that system. Using the human body as an analogy, muscles exerting force on bones during movement would be considered internal forces. In an engineering context, the forces holding a structure together are internal forces. These forces are essential for maintaining the integrity of the system but, interestingly, they do not contribute to the net force responsible for the motion of the system as a whole.

Since internal forces always come in action-reaction pairs, according to Newton's third law of motion, they effectively cancel each other out. Therefore, even though they are present and essential for structural reasons, internal forces do not create a net force that could cause acceleration of the system itself.

Building on the understanding of external and internal forces, the net force is the vector sum of all the forces acting upon an object or system. It is directly tied to one of Newton's most famous principles, expressed in his second law of motion, that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. The net force is crucial because it determines changes in the state of motion of the object.

In simplest terms, if you have several forces acting on an object, some of which may be external and some internal, you sum all these forces up considering their direction to determine the net force. If the overall sum equals zero, the object will remain at rest or move at a constant velocity. Only an unbalanced net force, which occurs when the sum of all forces is not zero, can change the object's velocity, meaning either speeding it up, slowing it down, or changing its direction.