Young's Modulus, Stress, and Strain

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Questions and Answers

What does the area, $A$, represent in the Young's modulus equation $Y = \frac{FL}{A\Delta L}$?

  • The change in length of the material.
  • The cross-sectional area of the material. (correct)
  • The force applied to the material.
  • The original length of the material.

If a wire's radius is doubled, how does this affect the stress experienced under the same applied force?

  • Stress is quadrupled.
  • Stress is reduced to one-quarter. (correct)
  • Stress remains the same.
  • Stress is doubled.

A metal rod is subjected to a tensile force. Which of the following changes would result in the greatest increase in strain?

  • Decreasing the rod's original length.
  • Increasing the rod's cross-sectional area.
  • Decreasing the applied force.
  • Increasing the rod's original length. (correct)

What does 'B' represent in the equation $B = -P/(\Delta V/V)$?

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

A material with a high Young's modulus is most accurately described as:

<p>Difficult to stretch or compress. (D)</p> Signup and view all the answers

In the context of stress, what does $F$ represent in the equation $\sigma = F/A$?

<p>The applied force. (D)</p> Signup and view all the answers

How is 'Strain' defined in relation to a material's deformation?

<p>The ratio of change in length to original length. (C)</p> Signup and view all the answers

If a material experiences a small strain under high stress, what can be inferred about its Young's modulus?

<p>The Young's modulus is high. (B)</p> Signup and view all the answers

Which of the following best describes the physical quantity represented by 'Stress'?

<p>The force acting per unit area within a material. (D)</p> Signup and view all the answers

The equation Stress = $\rho$lg is used to calculate stress due to:

<p>Hydrostatic Pressure (C)</p> Signup and view all the answers

Flashcards

Young's Modulus

A measure of a material's stiffness, representing the ratio of stress to strain.

Stress (σ)

Force applied per unit area on a material.

Strain

The fractional change in length (ΔL/L) of a material under stress.

Young's Modulus Formula

The ratio of stress to strain.

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Bulk Modulus (B)

A measure of a fluid's resistance to compression.

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Stress Formula (plg)

Stress is equal to the density times gravity times height.

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A = πr²

Area of a circle.

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Study Notes

  • Young's Modulus (Y) is defined as: Y = (Force x Length) / (Area x Change in Length) or Y = FL / A∆L.
  • Young's Modulus can also be expressed as Stress/Strain.

Stress

  • Stress (σ) is calculated as Force (F) per unit Area (A): σ = F/A.

Strain

  • Strain is defined as the Change in Length (∆L) divided by the original Length (L): Strain = ∆L/L.

Area

  • Area (A) is calculated using the formula: A = πr², where r is the radius.

Bulk Modulus

  • Bulk Modulus (B) is defined as: B = -P / (∆V/V), where P is pressure, ∆V is the change in volume, and V is the original volume.

Stress Calculation

  • Stress can be calculated as: Stress = ρlg, where ρ is density, l is length, and g is the acceleration due to gravity.

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