Let's say we have a meter stick with a single rope attached to it. One end of the rope is attached to one end of the meter stick, the other end of the rope is attached to the opposite end of the meter stick. By hanging the rope from a beam in the center of the rope, the meter stick (which is attached to the rope) balances perfectly flat in equilibrium as it hangs from the rope. Now, say the rope is not hung perfectly in its center, and as a result the meter stick accelerates from its perfectly horizontal position to an almost vertical position. (Does this make sense so far?) At this point where the meter stick is now at rest at an angle which is at a diagonal (the actual angle is irrelevant, we could say perhaps 5 degrees off the vertical, just to clarify to the reader), is the tension in the rope still constant among the two halves of the rope? How can it be, when it appears that so much more of the meter stick's weight is being held up by one end of the rope?
[Physics] Is tension always constant throughout a massless rope in equilibrium
forcesfree-body-diagrammassnewtonian-mechanicsstring
Best Answer
I'd like to put forth an answer which directly addresses the title of your post, but not the particular situation in which you put forth with the meter stick and rope.
Consider instead a massive rope hanging vertically from a ceiling.
Give the rope a total mass of, say, $M$. Then use Newton's second law on the lower half of the rope to find the tension at the midpoint. Compare this value to the tension at the top of the rope by using Newton's second law for the entire rope. This should let you answer your question.