Young's Modulus Question: stretch of a wire

The total stretch is 2mm+2mm = 4mm.In summary, the question asks what the stretch of a second wire, with the same material and cross-sectional area but twice the length, will be when subjected to the same force as a first wire that stretches by 2mm. By setting up and solving an equation using the formula F= (YA/L)ΔL, it is determined that the second wire will also stretch by 4mm. An alternative method is to consider the second wire as two copies of the first wire end to end, each stretching by 2mm for a total stretch of 4mm.
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DanT
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Homework Statement


A force stretches a wire by 2mm. A second wire of the same material and with the same area of cross-section and twice the length is also stretched by the same force. What will its stretch be?

Homework Equations


F= (YA/L)ΔL

The Attempt at a Solution



F, Y, and A are all equal

First wire:
F =(YA/L1)*2 mm

Second wire:
F =(YA/2L1)ΔL

1. I set them equal to each other to solve for ΔL
(YA/2L1)ΔL = (YA/L1)*2

2. I canceled out YA
ΔL/2L1 = 2/L1

3. I multiplied both sides by 2L1 to isolate ΔL

ΔL = 4 mmDid I do this correctly? I'm unsure because I've received notes from a friend and they got a different answer for the same problem. Thanks in advance.
 
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  • #2
You did it right.
An easier route to the answer considers the longer wire as two copies of the first wire end to end. Each copy is subject to the same tension as the original, so each stretches 2mm.
 
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Related to Young's Modulus Question: stretch of a wire

1. What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It is defined as the ratio of stress to strain, and is a constant value for a given material.

2. How is Young's Modulus calculated?

Young's Modulus is calculated by dividing the stress (force applied per unit area) by the strain (the change in length per original length) of a material. The resulting value is expressed in units of pressure, such as Pascals (Pa) or pounds per square inch (psi).

3. What is the significance of Young's Modulus?

Young's Modulus is an important property of materials, as it describes how much a material will stretch or compress under a given amount of stress. It is used in engineering and material science to predict the behavior of materials under different conditions, and is also important in the design of structures and machinery.

4. How does the stretch of a wire relate to Young's Modulus?

The stretch of a wire is directly related to Young's Modulus, as the modulus determines how much a material will stretch or compress under a given amount of stress. A wire with a higher Young's Modulus will have less stretch than a wire with a lower modulus, when subjected to the same amount of stress.

5. What factors can affect Young's Modulus for a material?

The factors that can affect Young's Modulus for a material include its composition, temperature, and microstructure. Different materials have different modulus values, and the modulus can also change with temperature and the structure of the material on a microscopic level.

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