Solve the Equilibrium of a Light Elastic String with Mass m

AI Thread Summary
The discussion revolves around solving for the length AD in a system involving two elastic strings with different moduli of elasticity. The participant sets up equations based on the tensions in the strings and applies Hooke's law to relate the tensions to the extensions of the strings. They derive the equation 2x - 4y = l but express uncertainty about the missing distance between the fixed point and AD. The conversation highlights the need for clarification on the equilibrium conditions and the derivation of the tension relationship. Overall, the participant seeks guidance on completing the solution.
aurao2003
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Homework Statement




Hi
Can anyone please help with this question?
A light elastic string AB has natural length l and modulus of elasticity 2mg. Another light elastic string CD has natural length l and modulus of elasticity 4mg. The strings are joined at their ends B and C and the end A is attached to a fixed point. A particle of mass m is hung from the end D and is at rest in equilibrium. Find the length AD.

this is what I did

Let Tension AB is T2 and tension CD be T1. since system is at rest
T2-T1 = mg (Equation 1)
AD = l +x +y +l (Where x and y are the extensions of AB and CD respectively)
So, AD = 2l +x+y
Using Hookes law
T2 = 2mgx/l

Similarly, T1 = 4mgy/l

substituting the above into equation 1
2x-4y =l
This is as far as I can go. I wasn't given the distance between the the fixed point and AD. Am I missing something? Kindly comment.

Homework Equations





The Attempt at a Solution

 
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Draw a free-body diagram for the particle of mass m. What does the diagram tell you about the tension T1?

Also, what is your justification for claiming T2-T1 = mg ?
 
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