A-Level Physics May/June 2024 Q3(c)(ii): the Young modulus of the material from which the sample is made.

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  The Young modulus, $E$, is the ratio of stress, $\sigma$, to strain, $\epsilon$.

  $E = \frac{\sigma}{\epsilon} = \frac{F/A}{x/L} = \frac{FL}{Ax}$

  From the question data, we have: Force, $F = 5.4$ N Original length, $L = 3.2$ m Cross-sectional area, $A = 4.0 \times 10^{-7}$ m$^2$ Extension, $x = 0.06$ m

  Substituting these values into the equation:

  $E = \frac{(5.4 \text{ N}) \times (3.2 \text{ m})}{(4.0 \times 10^{-7} \text{ m}^2) \times (0.06 \text{ m})}$

  $E = \frac{17.28}{2.4 \times 10^{-8}}$

  $E = 7.2 \times 10^8$ Pa

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  How the marks are awarded

  • C1 — Correctly stating the formula for the Young modulus, such as $E = FL/Ax$ or by defining it as stress divided by strain.
  • C1 — Correctly substituting the given values for force, length, area, and extension into the Young modulus formula.
  • A1 — Calculating the final correct answer of $7.2 \times 10^8$ Pa, including the correct unit (Pascals).

  Common mistakes

  • Forgetting to convert units, for example using an extension in millimetres or an area in mm² instead of converting to base SI units (m and m²).
  • Inverting the formula, for example calculating strain/stress ($Ax/FL$) instead of stress/strain ($FL/Ax$).
  • Making a calculator entry error, especially by not using brackets for the denominator, leading to an incorrect order of operations.
  • Using the gradient of a force-extension graph (the spring constant, k) incorrectly in the formula, for example as $E = kA/L$ instead of the correct $E = kL/A$.

  Examiner tip: Always begin by writing down the core defining equation, and then meticulously check that every quantity has been converted to its base SI unit before substituting and calculating.

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