Why Is There No Normal Force on the Second Block in Contact Systems?

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If there are 2 blocks beside each other and a force is applied to the first block, the first block will push the second block has well. This means that the two blocks are in contact. So why isn't there a normal force drawn perpendicular to the side of the second block if it is in contact with another surface other than the ground?
 
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The blocks interact at the sides in contact. There is a normal force from the first block to the second one, and also a normal force, of equal magnitude and opposite direction, from the second block on the first one.

ehild
 
Ok so if the blocks were A and B, then F(A on B) and F(B on A) are actually the normal forces from the contact?
 
Yes, they are the normal forces exerted by one block to the other because of the contact. ehild