Free-Body Diagram: Force Vector Explained

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The discussion focuses on the representation of the Force vector in a free-body diagram for two objects, m1 and m2. It highlights that the Force vector is only applicable in the context of the entire system or when analyzing the forces on m1. When considering m2, the normal force calculation becomes incorrect if the Force vector is improperly included. The applied force directly influences m1, which in turn affects the normal force m1 exerts on m2. Understanding these relationships is crucial for accurate free-body diagram analysis.
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For the following scenario: http://i14.tinypic.com/6jnvi3p.gif
why is the Force vector coming from the left only represented only in two of the three separate cases you can take. That is, te Force vector can only be represented in the case where you are considering a the system as a whole and the forces acting on the first object m1. However, if you do this for object m2 you obtain an incorrect normal force.
 
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The applied force only acts on m1. Of course, it affects the normal force that m1 exerts on m2.
 

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