Material Science: Stress and Strain

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Questions and Answers

What is the radius of the spring in meters?

  • 0.02
  • 0.004
  • 0.002 (correct)
  • 0.01

Strain is a measured quantity with specific units.

False (B)

What is the formula for calculating stress?

Stress = Force / Area

Young's Modulus is calculated as the ratio of _____ to _____ .

<p>stress, strain</p> Signup and view all the answers

Match the terms with their definitions:

<p>Stress = Force acting per unit area Strain = Deformation of a material due to stress Young's Modulus = Stiffness or resistance to deformation Area = Cross-sectional area of the spring</p> Signup and view all the answers

What is the calculated area of the spring?

<p>12.56 x 10^-6 m² (A)</p> Signup and view all the answers

The stress on the spring is 15.92 x 10^6 N/m².

<p>True (A)</p> Signup and view all the answers

What is the change in length of the spring?

<p>0.02 meters</p> Signup and view all the answers

The Young's Modulus of the spring is _____ x 10^6 N/m².

<p>1592</p> Signup and view all the answers

Which of the following statements is true regarding stress?

<p>Stress is measured in Newtons per square meter. (C)</p> Signup and view all the answers

Flashcards

Stress

The force acting per unit area of a material.

Strain

The deformation of a material due to applied stress.

Young's Modulus

A material property that describes its stiffness or resistance to deformation.

Young's Modulus

The ratio of stress to strain, representing the stiffness of the material.

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Strain

The change in length divided by the original length.

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Stress

The force divided by the area over which it acts.

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Area of a Circle

The area of a circle, calculated using the formula π * r².

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Stress

The force applied to an object divided by the cross-sectional area.

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Strain

The change in length of an object divided by its original length.

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Young's Modulus

A measure of a material's stiffness, calculated by dividing stress by strain.

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Study Notes

Problem Description

  • A spring with a 4 mm diameter and an original length of 2 meters is stretched by a 200 Newton force.
  • The final length is 2.02 meters.
  • The purpose is to calculate stress, strain, and Young's modulus.

Calculations

  • Area:
    • The spring's area is calculated using π * r², where r is the radius.
    • The radius is 2 mm (0.002 meters).
    • The area is 12.56 x 10⁻⁶ square meters.
  • Stress:
    • Stress is force divided by area: Stress = Force / Area
    • Calculated stress is 15.92 x 10⁶ Newtons per square meter.
  • Strain:
    • Strain is change in length divided by original length: Strain = (Change in Length) / (Original Length)
    • The change in length is 0.02 meters (2.02 meters - 2 meters).
    • Strain is 0.01.
    • Strain is dimensionless.
  • Young's Modulus (Modulus of Elasticity):
    • Young's modulus is stress divided by strain: Young's Modulus = Stress / Strain
    • Calculated Young's modulus is 1592 x 10⁶ Newtons per square meter.

Key Concepts

  • Stress: Force per unit area of a material, measured in Newtons per square meter (N/m²).
  • Strain: Material deformation from applied stress, a dimensionless quantity (change in length divided by original length).
  • Young's Modulus (Modulus of Elasticity): Measures a material's stiffness—resistance to deformation, calculated as stress divided by strain, and also measured in N/m².

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