A-Level Physics May/June 2024 Q4(b)(i): Calculate the increase in gravitational potential energy of the ball when the spring re…

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  The increase in gravitational potential energy ($\Delta E_p$) is given by the formula:\

  $\Delta E_p = mg\Delta h$\

  Where $\Delta h$ is the vertical change in height. The ball moves a distance $d = 8.0 \times 10^{-2}$ m along a slope at an angle $\theta = 15^{\circ}$ to the horizontal. The vertical height change is therefore:\

  $\Delta h = d \sin \theta$\

  Substituting the values into the energy equation:\

  $\Delta E_p = mg(d \sin \theta)$
  $\Delta E_p = (4.5 \times 10^{-2}) \times 9.81 \times (8.0 \times 10^{-2} \sin 15^{\circ})$
  $\Delta E_p = 0.00913...$ J\

  Rounding to two significant figures:\

  $\Delta E_p = 9.1 \times 10^{-3}$ J

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  How the marks are awarded

  • C1 — States the correct formula for the change in gravitational potential energy, $\Delta E_p = mg\Delta h$.
  • C1 — Correctly substitutes all values, including resolving the distance along the slope to find the vertical height change using $\sin 15^{\circ}$.
  • A1 — Calculates the final answer correctly as $9.1 \times 10^{-3}$ J (or 0.0091 J), which is stated to two significant figures.

  Common mistakes

  • Using the distance moved along the slope ($8.0 \times 10^{-2}$ m) for the height change 'h' instead of the vertical height.
  • Using cosine instead of sine to calculate the vertical height change (i.e., calculating the horizontal component of displacement by mistake).
  • Stating the final answer to an incorrect number of significant figures, such as 0.009 J (1 s.f.) or 0.00913 J (3 s.f.), which loses the final accuracy mark.
  • Forgetting to include the acceleration of free fall, g (9.81), in the calculation.

  Examiner tip: Always remember that for gravitational potential energy calculations, the height change 'h' must be the vertical component of the displacement, which often requires using trigonometry on inclined planes.

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