Why is My Young's Modulus Calculation Giving a Different Result?

In summary, the equation states that the Young's modulus, E, is equal to the product of the wire's thickness, F, and the distance between the wires, A, divided by the wire's length, L.
  • #1
toforfiltum
341
4

Homework Statement


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Homework Equations


E= (F/A) x (L/ΔL)

The Attempt at a Solution


I know that since the material is the same, the Young modulus should be the same. However, when I try to find the ratio of the second wire to the first, I get the answer C. For the first wire, E= 4FL / d2Δl, since A = d2/4.
For the second wire, the value of E I obtain is F x ½L / (d2/16) x Δl , which is twice the first value. I can't see what's wrong with my working. Can someone point it out?
 
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  • #2
This is a conceptual question, so we know for a particular material at a certain temperature Young's modulus will be a constant. Using the above equation we see that area does not reduce linearly so you're probably wondering how do I compare a thicker wire to a thinner one. Remember that to get the same ratio of change in length from original length in the thinner wire will require less force. So while your area is a quarter of the size of the original wire, the force needed is also reduced.
 
  • #3
vanoccupanther said:
This is a conceptual question, so we know for a particular material at a certain temperature Young's modulus will be a constant. Using the above equation we see that area does not reduce linearly so you're probably wondering how do I compare a thicker wire to a thinner one. Remember that to get the same ratio of change in length from original length in the thinner wire will require less force. So while your area is a quarter of the size of the original wire, the force needed is also reduced.
Oh I see, so from the information given in the question above, there's no way of obtaining the same value of E as the first wire without knowing the change in the value of F is it?
 
  • #4
toforfiltum said:
Oh I see, so from the information given in the question above, there's no way of obtaining the same value of E as the first wire without knowing the change in the value of F is it?

Yes, its not meant to be solved numerically.
 
  • #5
vanoccupanther said:
Yes, its not meant to be solved numerically.
Ok, thanks.
 

FAQ: Why is My Young's Modulus Calculation Giving a Different Result?

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 describes how much a material will deform when a force is applied to it.

2. Why is Young's Modulus important?

Young's Modulus is important because it helps engineers and scientists understand and predict how a material will behave under different types of stress, such as tension or compression. This information is crucial for designing structures and objects that can withstand these forces without breaking.

3. How is Young's Modulus measured?

Young's Modulus is typically measured using a tensile test, where a sample of the material is subjected to increasing amounts of tension until it breaks. The amount of stress applied and the resulting strain (deformation) are measured, and Young's Modulus is calculated as the ratio of stress to strain.

4. What factors can affect Young's Modulus?

The Young's Modulus of a material can be affected by various factors, including temperature, humidity, and the presence of impurities or defects in the material's structure. Additionally, different materials have different Young's Moduli, so the composition of the material is also a significant factor.

5. How do we use Young's Modulus in real-world applications?

Young's Modulus is used in a wide range of real-world applications, such as designing bridges, buildings, and airplanes. It is also used in the manufacturing of everyday objects, such as cars and furniture, to ensure that they can withstand the stresses they will be subjected to during use.

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