So a car moves, because the wheels exert a force on the ground which exert an opposite force back on the wheels causing it to move forward. The car then exerts this force on the air and the air back onto the car. Shouldn’t the resulting force on the car be 0 Newton then? Because the force the ground exerts on the car is the same as the force the air exerts on the car, thus cancelling each ofher out?
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The air moves out of the way. The amount of equal-and-opposite force will match the force needed to move the air away.
Think about punching a piece of paper being held up in front of you. Because your hand will go through the paper, the entire force of your punch wouldn’t go back to your hand (like it would if you punched a hard wall). Only the amount you imparted to the paper before it tore.
> Because the force the ground exerts on the car is the same as the force the air exerts on the car, thus cancelling each ofher out?
Sure, but *at best* that should mean that the car should move forward with half of the force, with the other half propelling the ground. The car moves forward, though, because the ground weighs *waaaaaaaaaaaaaaaaaay* more than the car. The force is equal and opposite but since the ground ain’t gonna move much, the car moves a lot.
The same thing happens with the air. The car weighs *waaaaaaaaaay* more than the air bumping into it so although the force is equal and opposite, the car ain’t gonna stop moving much so the air moves a lot (out of the way).
When you are cruising on the highway at a constant speed, those forces do balance out to zero.
While you’re accelerating, the force pushing you forward exceeds air drag.
Air resistance increases the pressure needed to move forward. This is actually why you use less gas going 55 than you do at 70 even though it takes longer to get where you are going. The faster you go the more the air pushes back against you. Eventually if kept pushing speed you would get to a point where the engine cannot push any faster than the wind resistance built up, just like gravity reaches a terminal velocity because it can no longer overcome the air resistance.
The key thing to remember about the third law is that pairs of equal and opposite forces do _not_ have to act on the _same object_.
So you talk about the force that the ground exerts on the car – good. What do we pair that with? _Not_ the force that the air exerts on the car. No, it’s actually paired with the force that the _car_ exerts on the _ground_.
So yes, the earth is pushed back by the car! It’s just negligible, thanks to the earth’s enormous mass (see second law). The car is pushed forward by the same magnitude of force as the earth is pushed back, but because it’s so much smaller, it accelerates more.
Now let’s turn to the force that the air exerts on the car. This does _not_ have to be equal to what the ground exerts on the car. That is not the pair of equal and opposite forces. We’ve already paired that force (see above).
So what do we pair with the force that the air exerts on the car? You guessed it: the force that the car exerts on the air. And there is absolutely nothing to stop the magnitude of this pair of forces being less than that which the car and ground are exerting on each other.
In fact, at the very moment the car starts moving, it isn’t pushing the air at all, because it’s stationary. So the air doesn’t push back. So all that’s acting on the car is the force from the ground. This force has a twin, sure but it’s not acting on the car (see above).
As soon as the car is actually moving, then yes, it’s exerting a force on the air. But it’s not very much force, as the car is still slow. The air pushes back with the same small force, which still doesn’t match what the ground is exerting on the car, so it keeps accelerating.
(Bear in mind that the air is much lighter than the car, so will be getting absolutely buffeted by the force that the car exerts on it (second law again) – it’s the car’s turn to be the big guy!)
Eventually, the car will get so fast that it’s pushing the air forwards just as hard as it’s pushing the ground backwards. Which means the ground is pushing the car forwards just as hard as the air is pushing the car backwards. And now the car will just keep going at a constant speed (terminal velocity) because the forces acting _on the car_ are equal.
But notice that there are _four_ forces at work in this story. And newton’s third law never said they _all_ have to be equal. They’ve only just reached equilibrium at the end of the story, as a special case.
But they’ve always been two pairs, and each member of the pair has always been equal with the other. The ground has always pushed the car just like the car pushes the ground. And the car has always pushed the air just like the air pushes the car. _Those_ are the equal and opposite reactions. The ground and air _can_ push as hard as each other, but they don’t _have to_. So the car can accelerate.
Hope this helps.
> the wheels exert a force on the ground which exert an opposite force back on the wheels
Correct.
>The car then exerts this force on the air and the air back onto the car
Not completely. The car doesn’t exert “this” force (the one between tires and road) on the air. The aerodynamic drag (the resisting force that the air exerts on the car) depends on aerodynamic drag coefficient, front section of the car and speed. It does not directly depend on how strong the tires “push” on the ground. When you accelerate, the wheel force is bigger than the air force. Accordingly, you can’t say:
> the force the ground exerts on the car is the same as the force the air exerts on the car
There is however a specific situation where the first law applies: at constant speed. This situation is achieved by having the wheels and the ground exerting the same force on each other as the car’s body and the air.
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