# Extension of a rod

Hi all,
I have a rod which is part of a greater structure and I resolved the forces along the rod. This rod is under tension with a force FcosQ on the left end (force direction towards left) and FsinQ on the other end (force direction towards the right). I need to find the extension of the rod and I am using hooks law F=Ks*delta where Ks is the stretching force constant and delta is the extension of the rod. Now the problem is what is the force F that I should use in Hooks law.

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At first I thought I should use the resultant force F*(cosQ-sinQ) so that the extension of the rod is delta=F(cosQ-sinQ)/Ks. But this is wrong because if I pull a spring with 1000 N on one end and 1000 N on the other. The net force is zero, but I trust you would agree that it will stretch.

Then I thought that the force acting on the rod that causes the extension is F*(cosQ+sinQ) because if you have a rubber band and pull it with a force FcosQ on one end and FsinQ on the other end, it will extend from both ends and hence the total extension is delta=F*(cosQ+sinQ)/Ks.
But I guess this is also wrong because when we have a mass attached to a string and string attached to the ceiling, the tension in the string is F not 2F and we say that the extension of string is delta=F/k

picture 2

I feel bit confused!!!!! Your help would be greatly appreciated.
Thanks a lot

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