Tension of a rope between two trees

[Elphaba123]

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.

 

[Modulated]

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.

 

[Elphaba123]

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.

 

[PhanthomJay]

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.

 

[felper]

look at thous links

http://members.chello.nl/j.beentjes3/Ruud/catfiles/catenary.pdf

http://www.sc.ehu.es/sbweb/fisica/solido/din_rotacion/catenaria/catenaria.htm

the second one is in spanish, you can translate it :P

 

[PhanthomJay]

look at thous links

http://members.chello.nl/j.beentjes3/Ruud/catfiles/catenary.pdf

http://www.sc.ehu.es/sbweb/fisica/solido/din_rotacion/catenaria/catenaria.htm

the second one is in spanish, you can translate it :P

These links are far too complex and involve calculus and the hyperbolic functions. They are not necessary to solve this problem.