Tension of a rope between two trees

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Homework Help Overview

The discussion revolves around the tension in a rope of mass m that hangs between two trees, with both ends at the same height and forming an angle with the trees. Participants are exploring how to determine the tension at different points along the rope, particularly at the ends and in the middle.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive the tension at the ends of the rope using a formula but expresses uncertainty about finding the tension in the middle without using integrals. Other participants question the validity of the original poster's approach and suggest drawing free body diagrams to analyze the forces acting on the rope.

Discussion Status

Participants are actively engaging with each other's reasoning, with some providing suggestions for visual aids like force diagrams. There is acknowledgment of the complexity of the problem, particularly concerning the tension in the middle of the rope, and some participants express doubt about the outcomes derived from their calculations.

Contextual Notes

There is mention of imposed homework rules that restrict the use of integrals at this stage, which may limit the methods available for solving the problem. Some participants also note that external resources provided may involve advanced concepts that are not necessary for the current discussion.

Elphaba123
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1. Suppose a rope of mass m hangs between two trees. The ends of the rope are at the same height and they make an angle ! with the trees.



I believe the tension at either end of the rope is T=(mg)/(2cos(theta)) but I don't know how to solve the for the middle. The only way I can think of doing it is by using integrals but my teacher told me we won't be using integrals till later in the year.
 
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How did you get the answer at the ends? The same working may help for the middle.

If you haven't already, try drawing a force diagram for just, say, the left half of the rope.
 
To find the rope at the end, I drew a free body diagram. From that I found the sum of the forces to be Tcos(theta)-(1/2)mg=0 because there is no movement. From this I found the tension. The problem is if I use this way I end up with the force in the middle being zero which I don't think is true.
 
Elphaba123 said:
To find the rope at the end, I drew a free body diagram. From that I found the sum of the forces to be Tcos(theta)-(1/2)mg=0 because there is no movement. From this I found the tension. The problem is if I use this way I end up with the force in the middle being zero which I don't think is true.
As Modulated suggests, draw a free body diagram of the left half of the rope, and sum forces in the x and y directions to solve for the unknown tension at the middle of the rope.
 

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