Why Isn't the Child's Pulling Force Shown in the Free Body Diagram?

[jack1234]

I have a question for the question
http://tinyurl.com/2mftmr

The following is the solution for the question, and you can see the free body diagram for child only, chair only and chair and child as one system
http://tinyurl.com/32ozt9

For the free body diagram of chair and child as one system, the downward force including the weight of chair and the weight of child.
My question is: the problem has specified that "Pat pulls on the loose end of the rope", but why there doesn't exist a downward arrow from the child's hand because he is pulling down the rope?

 

[PhanthomJay]

From Newton's 3rd law, since the child is pulling down on the rope with a force of 250N, then the rope is exerting an equal but opposite force on the child of 250N upward. Since you are looking in your FBD's for the forces acting on the child or child/chair system, it is the upward tension force you want to consider. Tension forces always pull away from the objects on which they act.

 

[ogb p]

Thank you for your question. In a free body diagram, we typically only show the external forces acting on the system, not the forces applied by the system itself. In this case, the child's hand pulling on the rope is considered an internal force within the system, and therefore is not shown in the free body diagram. The only external forces acting on the system are the weight of the child and the weight of the chair, as well as the tension in the rope from Pat pulling on it. I hope this clarifies any confusion.