Solve the Equilibrium of a Light Elastic String with Mass m

In summary, the conversation discusses a problem involving two light elastic strings with different modulus of elasticity and a particle of mass m hanging from them. The person solving the problem uses Hooke's law and a free-body diagram to determine the tension in the strings and ultimately find the length AD. However, they are unable to complete the solution without knowing the distance between the fixed point and AD.
  • #1
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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  • #2
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 ?
 

1. What is an equilibrium of a light elastic string with mass m?

An equilibrium of a light elastic string with mass m refers to a state in which the string is in a stable and balanced position, with no net force acting on it. This means that the string is not stretching or compressing, and the mass is not accelerating.

2. How is the equilibrium of a light elastic string with mass m determined?

The equilibrium of a light elastic string with mass m is determined by balancing the forces acting on the string. These forces include the weight of the mass, the tension force from the string, and any external forces such as friction or air resistance.

3. What factors affect the equilibrium of a light elastic string with mass m?

The equilibrium of a light elastic string with mass m can be affected by the length and elasticity of the string, the mass of the object attached to the string, and the presence of any external forces. Changes in these factors can alter the tension force and therefore the position of the equilibrium.

4. How is the equilibrium of a light elastic string with mass m calculated?

The equilibrium of a light elastic string with mass m can be calculated using Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. By setting the net force to zero, the equation can be solved to find the position of the equilibrium.

5. What is the significance of solving the equilibrium of a light elastic string with mass m?

Solving the equilibrium of a light elastic string with mass m is important in understanding the behavior of elastic materials and the forces acting on them. It is also essential in designing structures and machines that involve the use of elastic strings, such as musical instruments or bungee cords.

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