A-Level Physics May/June 2025 Q4(b)(ii): the percentage of the total initial kinetic energy of the two objects that is transferr…

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  Step 1: Calculate the total initial kinetic energy ($KE_{initial}$)

  The total initial kinetic energy is the sum of the kinetic energies of the two individual objects.

  $KE_{initial} = (\frac{1}{2} m_1 v_1^2) + (\frac{1}{2} m_2 v_2^2)$

  $KE_{initial} = (0.5 \times 4.0 \times 6.0^2) + (0.5 \times 2.0 \times 3.0^2)$

  $KE_{initial} = 72 \text{ J} + 9.0 \text{ J} = 81 \text{ J}$

  Step 2: Calculate the final kinetic energy ($KE_{final}$)

  After the collision, the two objects move together as a single mass ($m_1 + m_2$) with a common final velocity.

  $KE_{final} = \frac{1}{2} (m_1 + m_2) v_{final}^2$

  $KE_{final} = 0.5 \times (4.0 + 2.0) \times 5.0^2$

  $KE_{final} = 0.5 \times 6.0 \times 25 = 75 \text{ J}$

  Step 3: Calculate the percentage of energy transferred

  The energy transferred is the difference between the initial and final kinetic energies. The percentage is this difference divided by the initial energy, multiplied by 100.

  Energy transferred = $KE_{initial} - KE_{final} = 81 - 75 = 6.0 \text{ J}$

  Percentage transferred = $\frac{\text{Energy transferred}}{KE_{initial}} \times 100$

  Percentage transferred = $\frac{6.0}{81} \times 100 = 7.407...\%$

  Percentage transferred $\approx 7.4\%$ (2 s.f.)

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  How the marks are awarded

  • C1 — Correctly calculating the total initial kinetic energy by summing the individual kinetic energies of both objects, resulting in 81 J.
  • C1 — Correctly calculating the final kinetic energy of the combined mass after the collision, resulting in 75 J.
  • A1 — Correctly calculating the percentage of energy transferred by finding the loss in KE and dividing by the initial KE, giving a final answer of 7% or 7.4%.

  Common mistakes

  • Calculating the energy loss (6 J) but forgetting to express it as a percentage of the initial energy.
  • Forgetting to square the velocity term (v) in the kinetic energy formula, i.e., using KE = 0.5mv.
  • Dividing the energy loss by the final kinetic energy (6/75) instead of the initial kinetic energy (6/81).
  • Incorrectly adding velocities or masses before calculating the initial kinetic energy, instead of calculating the KE for each object separately and then summing them.

  Examiner tip: For any 'percentage change' or 'percentage transferred' question, always clearly calculate the initial total and the final total before substituting them into the percentage formula.

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