Solving Tension Ratio of Steel Wires with Hooke's Law

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In summary, the ratio of tension in wire P to tension in wire Q is 1:4 when both wires are stretched to the same extension. This is due to Young's Modulus for the material, where the stress/strain must be the same for both wires. Since the length-to-area ratio is 4 times larger for wire Q, the tension in wire Q must be 4 times larger to maintain the same ratio for both wires.
  • #1
cremedelacreme
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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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  • #2
You must show an attempt at solving this before we can help you (forum rules).
 
  • #3
Yeah, I got it but it's not the right answer...
 
  • #4
cremedelacreme said:
Yeah, I got it but it's not the right answer...
If you post your attempt, perhaps we could help you out.
 
  • #5
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
 
  • #6
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?
 

1. What is Hooke's Law?

Hooke's Law is a principle in physics that describes the relationship between the force applied to an elastic material and the resulting deformation or change in length of the material. It states that the force is directly proportional to the change in length, as long as the material remains within its elastic limit.

2. How is Hooke's Law used in solving tension ratio of steel wires?

Hooke's Law can be used to determine the tension ratio of steel wires by measuring the amount of force applied to the wire and the resulting change in length. This information can then be used to calculate the tension ratio, which is the ratio of the force applied to the cross-sectional area of the wire.

3. What is the tension ratio of a steel wire?

The tension ratio of a steel wire is a measure of the amount of force that can be applied to the wire before it reaches its breaking point. It is calculated by dividing the force applied to the wire by its cross-sectional area.

4. How can Hooke's Law be applied to different types of steel wires?

Hooke's Law can be applied to different types of steel wires as long as they remain within their elastic limit. This means that the relationship between the force and the resulting change in length will remain consistent, regardless of the type of steel wire being used.

5. Are there any limitations to using Hooke's Law in solving tension ratio of steel wires?

While Hooke's Law is a useful tool for determining the tension ratio of steel wires, it does have some limitations. It assumes that the material remains within its elastic limit, and it does not take into account factors such as temperature and material defects that can affect the accuracy of the results.

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