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There is a box on the surface of earth. The earth exerts a force to the box (black arrow). The box exerts a reaction force to the earth(brown arrow). But this reaction force is exerted to the earth not the box, so where is the normal force? If the reaction is the normal force then why they put the arrow starting in the box upwards and not starting in earth? (second diagram).

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  • $\begingroup$ Each force has a "line of action". So, for convenience, forces drawn on a diagram may be slid up or down along their lines as long as the magnitudes and directions are unchanged. One might, for example, want to slide forces along their lines of action to have all their tails coincide. $\endgroup$
    – robphy
    Commented Sep 25, 2022 at 0:36
  • $\begingroup$ The reaction force to the Force-on-B-by-A is the equal-magnitude and oppositely-direction Force-on-A-by-B and is of the same type. $\endgroup$
    – robphy
    Commented Sep 25, 2022 at 0:39

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There are two different third-law force pairs. One pair is the downward gravitational force on the box and the upward gravitational force on the earth. The other is the upward normal force on the box and the downward normal force on the earth.

In equilibrium, the gravitational and normal force are equal and opposite to each other, but that's due to the first law (no net force in equilibrium), not the third law.

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  • $\begingroup$ So in space, with gravity neglected, if you put together two equal dimension boxes with the same mass side by side, are there normal forces too? $\endgroup$
    – Carlitos_30
    Commented Sep 25, 2022 at 3:11
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    $\begingroup$ @Carlitos_30 In equilibrium, no, because there are no other forces, and the total force is zero, so the normal force is zero. In nonequilibrium situations there may be. If the boxes bounce off of each other, there is a normal force while they're in contact. $\endgroup$
    – benrg
    Commented Sep 25, 2022 at 3:46
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The best way to visualize and solve force problems like this is with a Free Body Diagram, in which you isolate each body and draw all forces acting upon it. That way it is easy to see what forces are acting where.

In this case, the block has two forces acting on it: gravity, and the normal upward force.

The ground also has two forces acting on it: the normal force downward from the block, and then the "offscreen" upward force from whatever is supporting it.

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