A-Level Physics October/November 2024 Q4(b)(i): Determine the cross-sectional area of wire X.

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  The Young modulus, $E$, is given by the formula:

  $E = \frac{FL}{Ax}$

  Where $F$ is the force, $L$ is the original length, $A$ is the cross-sectional area and $x$ is the extension.

  Rearranging for the cross-sectional area, $A$:

  $A = \frac{FL}{Ex}$

  Substituting the given values:

  $A = \frac{(9.0 \text{ N})(0.84 \text{ m})}{(1.9 \times 10^9 \text{ Pa})(0.47 \times 10^{-3} \text{ m})}$

  $A = 8.475... \times 10^{-6} \text{ m}^2$

  $A = 8.5 \times 10^{-6} \text{ m}^2$ (to 2 s.f.)

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  How the marks are awarded

  • C1 — Correctly stating the formula for Young's modulus, $E = FL/Ax$, or its correct rearrangement for area, $A = FL/Ex$.
  • C1 — Correct substitution of all values into the formula, ensuring the extension is correctly converted to metres ($0.47 \times 10^{-3}$ m).
  • A1 — A final correct answer of $8.5 \times 10^{-6} \text{ m}^2$, rounded to two significant figures.

  Common mistakes

  • Incorrectly rearranging the formula, for example getting $A = Ex/FL$, which inverts the final answer.
  • Forgetting to convert the extension from millimetres to metres, leading to an answer that is $10^3$ times too large.
  • Using the diameter instead of the radius to calculate area if a diameter were given, or vice-versa.
  • Rounding the final answer to an incorrect number of significant figures, such as one or four.

  Examiner tip: For any calculation question, always write down the initial formula, show your algebraic rearrangement, and then substitute the values to maximise the chance of earning method marks.

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