Solving Tension Ratio of Steel Wires with Hooke's Law

[cremedelacreme]

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?

 

[Redbelly98]

You must show an attempt at solving this before we can help you (forum rules).

 

[cremedelacreme]

Yeah, I got it but it's not the right answer...

 

[Hootenanny]

Yeah, I got it but it's not the right answer...

If you post your attempt, perhaps we could help you out.

 

[cremedelacreme]

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

 

[Redbelly98]

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?