In Newtonian mechanics, how come the net force on an object in free fall is zero, yet it is accelerating??
Definition:
In physics, a force is any interaction that, when unopposed, will change the motion of an object.
Let us take a billiard ball, and hold it over a balcony. The instant the fingers are opened, the ball is at $(x_0,y_0,z_0)$ and has velocity $v$ zero. It starts falling, i.e. its motion changes, therefore by definition there must be a force. The velocity keeps changing because there is no force opposing the original force, and it has been determined experimentally that the force $F=ma$ where $m$ is the mass as measured on scales with standard weights and $a$ is the acceleration, change of velocity over time $dv/dt$.
So, your analysis is wrong, a falling object is subjected to a force, by definition of force.
@annav is correct, of course, but I think maybe missing the op's intuitive reasoning that's suggesting "no force" to him:
(a) Suppose you're sitting in an accelerating automobile. Then you >>feel<< a force that's responsible for accelerating you forwards.
(b) But suppose instead you're in free fall, in a gravitational field, accelerating downwards. Then you feel absolutely nothing, no force whatsoever. So, yes, there must be a force, but >>where is it???<<, so to speak.
Answer: (a) You feel a force while sitting in an accelerating car because the force acts directly on your back, but not directly on the rest of your body. The carseat presses your back, then your back presses on your internal organs, etc. And it's all this pressing of one part of your body on another part that you're feeling. (This is called a contact force -- one object pushing on another that it's in contact with.)
(b) But in a gravitational field, gravity acts >>directly on every part<< of your body simultaneously. Even on every cell, every molecule, of every internal organ. So no one part of your body is pressing against any other part. All your "parts" are moving together, in unison, so to speak. And so you >>feel nothing<< directly. But there nevertheless is an overall force, gravity, just like everybody else already explained. (And note that gravity is not a contact force -- it acts at a distance, without being in contact with the objects it's acting on. And that's why it can directly affect your internal organs, which the accelerating car can't do.)
Note that prior to Newton's discovery/explanation of gravity, everybody believed that all forces were contact forces. Nobody ever imagined that one body could exert a force on another body without being directly in contact with it. And at first blush, that indeed sounds pretty reasonable. So Newton's genius was not only explaining gravity, but also conjuring up the almost unimaginable idea of force-at-a-distance in the first place.
So your intuition is quite understandable -- you don't feel a force, so how can there possibly be a force??? Action(force)-at-a-distance is the answer. But don't feel too bad -- it took Isaac Newton to figure that out.
Does acceleration in free fall disprove Newtonian mechanics?
No. It shows that it doesn't always apply the way that you think.
In Newtonian mechanics, how come the net force on an object in free fall is zero, yet it is accelerating?
Like John and Anna said above, there is a force - the force of gravity. But it isn't like the force exerted by the accelerating car.
If F=(a)(m), and F=0, it follows that: a must equals 0. But in reality a falling object will accelerate with a = 9.8 m/s^2.
That's right, the falling body accelerates. Some will tell you that the non-falling body is the one that accelerates, but it isn't true.
Since a=/= 0, then either F =/= 0 or F =/= (a)(m). And because we know that for object in free fall F = 0, then F =/= a m (i.e. newton second law does not apply)
What doesn't apply is Work = Force x Distance. Gravity doesn't do any work on a falling body. Instead you do work on a body when you lift it up. You add energy to it. In similar vein if you took a billiard ball and strapped a rocket to it, then fired it horizontally such that it was moving at 1000m/s, you have done work on that billiard ball. You have given it kinetic energy. You added energy to it. The billiard ball has its mass-energy, and it has its kinetic energy too.
However when you drop the billiard ball from some super-high location up in space and take a look at it again when it's falling at 1000m/s, gravity has not done any work on that billiard ball. Instead gravity converted some of the potential energy of the billiard ball, some of its mass-energy, into kinetic energy. Check out binding energy and the mass deficit.
This is why people sometimes say "gravity is not a force in the Newtonian sense".
