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while i have tried reading explanations for why newtons third law doesn't mean objects can't move such as this one: With Newton's third law, why are things capable of moving? I still do not understand how to apply them to the system I'm about to describe:

(Suppose the system is in space so friction isn't present)

Force F is pushing object A, object A thus pushes object B with force equal to F. According to newtons third law object B will exert an equal force on object A in the opposite direction. So now on Object A, two equal forces are acting in opposite directions, so it should not move. my question is why does object A end up moving after all?

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marked as duplicate by sammy gerbil, ZeroTheHero, Jon Custer, peterh, Bill N Jun 9 '17 at 1:16

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  • $\begingroup$ It won't. The situation you're describing is basically that of a Newton's cradle, in which you can see this in action. If you push two objects on a table as shown, they will both move because the force applied (e.g. by a hand) is applied by pushing against something else, allowing the whole system (hand, objects) to move. $\endgroup$ – user122423 Jun 8 '17 at 21:06
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    $\begingroup$ A does not push B with force F. It pushes with a force less than F such that both accelerate at the same rate. The resultant force on A is not zero. $\endgroup$ – sammy gerbil Jun 8 '17 at 21:14
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Object B does not exert a force equal to F. By Newton's Third Law, Object B exerts a force on A equal to the force exerted by A on B. That's what Newton's Third Law states.

If the entire system were not moving, we could then point out that the force exerted by B must match F, but in reality, the system will accelerate. A will push on B with less force than F, and thus B will push on A with less force than F too. The two objects will accelerate together, and the forces will distribute such that if you look at the forces on B from A, it's just enough to accelerate block B at their combined acceleration rate. And if you look at A, you'll find the difference between the force F and the force of B on A will also be exactly the right amount to accelerate B at the same rate.

(We know this beacause we intuitively know the blocks will move together, accelerating at the same rate. Proving that this works without making that intuitive leap involves a bit more physics. You'll learn that eventually!)

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