Contradictory FBD's for simple pulley problem

AI Thread Summary
The discussion revolves around a basic pulley problem involving a massless pulley and a suspended mass. Two free-body diagrams (FBDs) were analyzed, leading to contradictory conclusions about the tension in the ropes. Initially, it was thought that the tension in the top rope was equal to the tension in the bottom rope, but upon reevaluation, it was clarified that the top rope's tension is actually twice that of the bottom rope when considering the weight of the mass. The confusion arose from neglecting to account for the mass's weight in the first FBD. Ultimately, the participant recognized their oversight in applying basic physics principles.
mordechai9
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I have a basic pulley problem which has been troubling me.

Consider the system as shown in the attached picture. We have a massless pulley attached to the ceiling and a mass suspended from one side of the pulley.

If we take the free-body-diagram by 'cutting' where the red box is, we find the tension in the bottom rope is equal to the tension in the top rope. But if we take the free-body-diagram by 'cutting' at the green box, then we find the tension in the top rope is twice the tension in the bottom rope, since the tension in the rope is everywhere the same.

What is going wrong here?
 

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Nevermind. I just forgot for the red-box FBD you still have to include the weight of the mass, so actually it just says the tension in the top rope is equal to twice mg again. Doh. Too long since I did basic physics.
 

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