Finding Extension of Rod with FcosQ and FsinQ Applied

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SUMMARY

The discussion centers on calculating the extension of a rod under tension, influenced by forces FcosQ and FsinQ. The user initially proposed using the resultant force F(cosQ-sinQ) for Hooke's Law, but recognized this was incorrect due to the net force being zero. The correct approach involves understanding that the extension is influenced by both forces, leading to the conclusion that the effective force for extension should be F(cosQ + sinQ) when considering the tension from both ends. The user also highlights the importance of recognizing static equilibrium in the system.

PREREQUISITES
  • Understanding of Hooke's Law (F = Ks * delta)
  • Basic principles of static equilibrium in structures
  • Knowledge of vector components in force analysis
  • Familiarity with tension forces in mechanical systems
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  • Study the application of Hooke's Law in multi-force systems
  • Learn about static equilibrium and force balance in structures
  • Explore vector decomposition of forces in physics
  • Investigate real-world applications of tension in materials
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Mechanical engineers, physics students, and anyone involved in structural analysis or material science will benefit from this discussion.

Yuppy
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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.

picture 1

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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Yuppy said:
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.
What other forces act on this rod? Assuming this is a static structure (is it?), there must be other forces balancing these two, else the rod will accelerate.
 

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