Stress, Strain and the Young Modulus · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Stress, strain, and true stiffness

Science · Matter & Materials · ages 17-18
Name ______________________   Date ____________

  1. What are the units of strain?

    • No units
    • Pascals (Pa)
    • Newtons (N)

  2. What is stress?

    • Extension divided by original length
    • Force multiplied by cross-sectional area
    • Force divided by cross-sectional area

  3. A material can deform elastically even when its stress-strain graph is curved.

    Circle one:   True   False

  4. A 2 m wire stretches by 0.001 m. What is the strain?

    Answer: ______________

  5. A uniform circular wire has diameter 2 mm and carries a tensile force of 157 N. Use pi = 3.14. What is its tensile stress in pascals?

    Answer: ______________

  6. In the linear elastic region through the origin, how is Young modulus calculated, and what is its unit?

    • Strain/stress, in newtons
    • Stress/strain, in pascals
    • Force/extension, in joules

  7. Two equal-length wires from the same steel batch are tested at the same temperature and in the same direction. Both are linear elastic under the same force. One has twice the area and half the strain. How do their Young moduli compare?

    • The thicker wire has twice the modulus.
    • The thinner wire has twice the modulus.
    • The wires have the same modulus.

  8. A uniform wire is in its linear elastic region through the origin. Its original length is 2 m and area is 0.000002 m squared. A tension of 100 N produces extension 0.001 m. What is its Young modulus in pascals?

    Answer: ______________

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Answer key

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Stress, strain, and true stiffness W1-mt_uWdqhWGT7Y-s1

  1. No units · Strain divides extension by length, so the units cancel out.
  2. Force divided by cross-sectional area · Stress spreads the force over the cross section, in pascals.
  3. True · Elastic deformation disappears after unloading. A curved graph shows loss of proportionality, which need not mean permanent deformation.
  4. 0.0005 · Divide extension by length: 0.001 over 2 is 0.0005, with no units.
  5. 50000000 · Radius = 0.001 m. Area = 3.14 × 0.001 squared = 0.00000314 m squared. Stress = 157 / 0.00000314 = 50000000 Pa.
  6. Stress/strain, in pascals · Young modulus is the gradient of stress against strain. For the stated straight line through the origin, this equals stress/strain, in pascals.
  7. The wires have the same modulus. · At the same force, doubling area halves stress. Strain is also halved, so stress divided by strain stays unchanged.
  8. 100000000000 · Stress = 100 / 0.000002 = 50000000 Pa. Strain = 0.001 / 2 = 0.0005. Young modulus = 50000000 / 0.0005 = 100000000000 Pa.
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