Why is strain greater in longer wires?

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SUMMARY

The discussion centers on the relationship between strain and stress in long, thin wires when measuring Young's Modulus. Participants emphasize that stress is greater in thinner wires due to their reduced cross-sectional area, which leads to higher stress values under the same applied force. Additionally, strain, defined as the deformation per unit length, is influenced by the wire's dimensions, making longer wires more susceptible to greater strain under tension. Understanding these concepts is crucial for accurately measuring material properties using Young's Modulus.

PREREQUISITES
  • Understanding of Young's Modulus
  • Knowledge of stress and strain definitions
  • Familiarity with the concepts of force and extension
  • Basic principles of material mechanics
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  • Research the mathematical relationship between stress and strain in materials
  • Study the effects of wire diameter on tensile strength
  • Explore experimental methods for measuring Young's Modulus
  • Learn about the significance of cross-sectional area in material science
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Students studying physics, particularly those focusing on material mechanics and Young's Modulus, as well as educators seeking to clarify concepts of stress and strain in practical applications.

God of War 90
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I'm doing A-Level physics and I've been answering questions on Young's Modulus. I need to be able to explain why a long, thin wire is used when measuring the Young's Modulus of a material. I can give an explanation of why stress due to the wire being thinner is greater but I don't know why stress is greater in a thinner wire. Any help in understanding this would be much appreciated.

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First take a look at the heading for your question in the light of your definition for strain.

What is your definition for strain?

Then look at your definition for stress.

Hint
Stress and strain are both relative to (depend on) the dimensions of the body concerned.

Force and extension are not.
 

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