Air Resistance and the Third law


According to Newton's third law action and reaction forces are always equal and in opposite direction. Then how come some objects falling through the air or falling through water move with acceleration? Is it true that in every moment the action force of the body's weight is equal to the reaction force of the water or air resistance, and hence the net force acting on the body being zero? If not Why?


Remember that the reaction/reaction forces are equal and opposite but they each apply to a different body. If they applied to the same body then nothing could ever change its velocity since all forces would add to zero.

In the case of an object falling through a fluid medium like air or water, there are multiple action/reaction pairs involved. The object and the Earth are one pair and the object and the medium are another pair. The force of gravity on the object is equal and opposite to the force of gravity on the Earth. The force of fluid friction on the object is equal and opposite to the force of fluid friction on the medium. The third law does not require that the force of fluid friction on the object be equal and opposite to the force of gravity on the object.

Looking at a falling object in terms of an action/reaction force pair is not the most logical way to analyze the motion. Since the Earth is huge relative to most falling bodies the reaction of the Earth to the gravitational attraction of the ball is negligible.

If we next consider the fluid medium through which the object is falling, in terms of the third law, there are an enormous number of action/reaction pairs consisting of the individual atoms on the surface of the falling object and the atoms of the fluid with which they interact through the electrical forces which keep atoms from occupying the same space at the same time. Life is too short to analyze the details of these interactions.

Fortunately, Newton's second law provides a way to analyze the motion of falling objects in terms of the net effects of all these forces without knowing the details of trillions of interactions. The acceleration of any object is the sum of all the forces acting on it divided by the object's mass. The force due to the Earth's gravity produces a constant acceleration of 9.8 meters per second per second near the surface of the Earth, over distances small compared to the Earth's radius. The sum of all the forces resulting from the interaction with the fluid through which the object is falling can be expressed in terms of the properties of the object and the fluid through which it is falling. The mathematical expression relating the net fluid resistance force to the properties of the fluid and the object must be determined experimentally.

It is possible that, as you suggest, the net force on a falling object may be zero if the weight is exactly balanced by the force of the fluid on the object. In that case the acceleration of the object is zero and it falls with a constant velocity. The particular velocity for which this condition holds is called the terminal velocity. In general however, there will be some net unbalanced force so that the object travels in a curved path with varying speed reflecting the acceleration resulting from the unbalanced force.

I hope this helps. Let me know what you think.