A-Level Physics October/November 2024 Q2(b)(ii): Calculate the change in the total kinetic energy ΔEK of the balls due to the collision.

1 answer

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  accepted ✓

  The formula for kinetic energy is: $E_K = \frac{1}{2}mv^2$

  The change in kinetic energy is the final kinetic energy minus the initial kinetic energy: $\Delta E_K = E_{K, \text{final}} - E_{K, \text{initial}}$

  Substituting the values for the final and initial states: $\Delta E_K = \left(\frac{1}{2} \times 0.24 \times 16^2\right) - \left(\frac{1}{2} \times 0.48 \times 8.0^2\right)$

  $\Delta E_K = 30.72 - 15.36$

  $\Delta E_K = 15.36 \text{ J}$

  Rounding to two significant figures consistent with the data: $\Delta E_K = 15 \text{ J}$

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  How the marks are awarded

  • C1 — Correctly stating the formula for kinetic energy, $E_K = \frac{1}{2}mv^2$.
  • C1 — Correctly substituting the initial and final mass and velocity values into the change in kinetic energy formula, as shown by the line $\Delta E_K = (\frac{1}{2} \times 0.24 \times 16^2) - (\frac{1}{2} \times 0.48 \times 8.0^2)$.
  • A1 — Calculating the final correct answer of 15 J, which includes the correct unit and is given to an appropriate number of significant figures.

  Common mistakes

  • Calculating the initial kinetic energy minus the final kinetic energy, leading to an answer of -15 J. The change in a quantity is always final minus initial.
  • Forgetting to square the velocity term for either the initial or final kinetic energy calculation.
  • Providing the final answer to an incorrect number of significant figures, such as 15.36 J or 15.4 J, which is not appropriate given the precision of the input data.
  • Only calculating the final kinetic energy (e.g., 31 J) or the initial kinetic energy (e.g., 15 J) instead of the change between them.

  Examiner tip: For any question asking for the 'change' in a physical quantity, always calculate the final value and subtract the initial value (ΔX = X_final - X_initial).

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