Cross sectional area - Young Modulus

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SUMMARY

The discussion confirms that the cross-sectional area of a wire changes when a force is applied, specifically during stretching. As a wire elongates, its volume remains constant, leading to a decrease in cross-sectional area. This phenomenon is particularly evident in materials like steel, where the reduction in area becomes significant as the load exceeds the elastic limit and approaches the ultimate breaking strength. The example of a rubber band illustrates this behavior effectively.

PREREQUISITES
  • Understanding of Young's Modulus and material elasticity
  • Knowledge of tensile stress and strain concepts
  • Familiarity with the properties of materials such as steel and rubber
  • Basic principles of volume conservation in physics
NEXT STEPS
  • Research the mathematical relationship between stress, strain, and Young's Modulus
  • Explore the effects of different materials on cross-sectional area changes under load
  • Study the concept of elastic limit and ultimate tensile strength in materials science
  • Investigate practical applications of these principles in engineering and design
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Students and professionals in materials science, mechanical engineering, and physics, particularly those interested in the mechanical properties of materials under stress.

RCB
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out of interest does cross sectional area change when a force is applied (lets say I had a wire and I applied a force to it, the wire would stretch ) does its cross sectional area change
 
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Yes. During the stretching, the volume remains constant, so if the length increases, the area must decrease. Stretching a rubber band provides a good example of this. If the wire is steel, the stretch is relatively small under light loads, and thus the area reduction is small; as the load increases, then so does the elongation, and the reduction in area becomes significant beyond the wire's elastic limit as it approaches it's ultimate breaking strength.
 

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