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This question already has an answer here:

How can the action and reaction force be same.? And if so then how the colliding objects could further move as there net force is Zero. Since F1 = - F2, that means that the force act on both sides and as there magnitude is same then undoubtedly there is no such net or derived force for which one could move further.

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marked as duplicate by sammy gerbil, ACuriousMind, Wolpertinger, John Rennie newtonian-mechanics Aug 28 '16 at 4:47

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This is Newtons 3rd law: When body A exerts a force on body B, then body B will exert an equal but opposite force on body A.

The important thing to realise is that these forces act on different objects. As such, they cannot cancel each other out - unless it is the case of a contact force such as a book resting on a table.

Take a horse and cart for example. The horse exerts a force on the cart, and the cart exerts this force back. However, the horse also exerts a force on the ground, which is why the system does not remain at rest. If the horse and cart were in space, then you would be right - they would not move. However, it is important to realise that there are other forces involved.

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    $\begingroup$ Because as it hits you, your face resists the motion of the ball, exerting a force back on the ball. $\endgroup$ – Noah P Aug 24 '16 at 12:01
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    $\begingroup$ You do act upon the ball just by being present $\endgroup$ – Noah P Aug 24 '16 at 12:02
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    $\begingroup$ You have to assume that newtons second law and the conservation of momentum are true. Then: $\endgroup$ – Noah P Aug 24 '16 at 12:10
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    $\begingroup$ $F=\frac{dp}{dt}$, where $p$ is the momentum of the object $\endgroup$ – Noah P Aug 24 '16 at 12:10
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    $\begingroup$ If the objects exert forces $F_a$ and $F_b$, and they each have momentum $p_a$ and $p_b$, momentum conservation would give: $\endgroup$ – Noah P Aug 24 '16 at 12:11

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