Solving Tension Ratio of Steel Wires with Hooke's Law

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The discussion focuses on calculating the tension ratio of two steel wires, P and Q, under the same extension using Hooke's Law. Wire P has a length l and area A, while wire Q has a length of 2l and area A/2. Participants emphasize that stress and strain must remain consistent for both wires, as dictated by Young's Modulus. The calculations indicate that the tension in wire Q should be four times that in wire P, leading to a tension ratio of 4:1. Clarifications are sought on how to ensure that the force applied results in equal stress and strain for both wires.
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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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