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

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SUMMARY

The discussion centers on the omission of the child's pulling force in the free body diagram (FBD) for a system involving a child and a chair. It clarifies that while the child exerts a downward force of 250N on the rope, the relevant force to consider in the FBD is the upward tension force exerted by the rope on the child, as per Newton's Third Law. The FBD for the child and chair system must account for the combined weight of both objects and the tension acting on the child, rather than the downward force from the child's hand.

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jack1234
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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?
 
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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.
 

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