Solving Tension Ratio of Steel Wires with Hooke's Law

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Homework Help Overview

The discussion revolves around determining the tension ratio of two steel wires, P and Q, using Hooke's Law. The wires have different lengths and cross-sectional areas, and the problem involves analyzing their behavior under the same extension.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between stress and strain, referencing Young's Modulus. There are attempts to derive the tension ratio based on the properties of the wires, including their lengths and areas.

Discussion Status

Some participants have made attempts to solve the problem but express uncertainty about the correctness of their answers. Guidance has been offered regarding the relationship between stress and strain, and the need for the forces to be equal for both wires to maintain the same ratio.

Contextual Notes

Participants are reminded to show their attempts at solving the problem as per forum rules, indicating a structured approach to the discussion.

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Two steel wires P and Q have lengths l and 2l respectively and cross sectional areas A and A/2 respectively. Both wires obey Hooke's Law.

What is the ratio (tension in P/tension in Q) when both wires are stretched to the same extension?
 
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You must show an attempt at solving this before we can help you (forum rules).
 
Yeah, I got it but it's not the right answer...
 
cremedelacreme said:
Yeah, I got it but it's not the right answer...
If you post your attempt, perhaps we could help you out.
 
F/A divided by Difference in L/L

Since
Stress/Strain

Thus Fl/A(Difference in L)

L is doubled

Area is halved
hence in Q it should be 4
while in P it is 1

But the answer says that it is 4:1
 
That's a good attempt, you're very close.

Stress/Strain must be the same for both wires, since that is Young's Modulus for the material.

As you said, (L/A) is a factor of 4 larger for Q.

What must F be for wire Q, in order that the ratio
F L/(A ΔL)
be the same for both wires?
 

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