A roller-coaster car travels in a complete vertical loop. Explain, using the concept of energy transfer, why the car must be moving faster at the bottom of the loop than at the top of the loop.

WJEC A-Level Physics (Wales) — 1.5 Circular motion (A-Level only) · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A roller-coaster car has a mass of 500 kg. It travels in a complete vertical circular loop. The bottom of the loop is at ground level and the top of the loop is 20 m above the ground.

Model answer (5 marks)

The car has gravitational potential energy at the top of the loop because it is raised above the bottom. By conservation of energy, as the car rises, kinetic energy is transferred to gravitational potential energy. At the top of the loop the car has less kinetic energy than at the bottom. Since kinetic energy is directly proportional to the square of velocity, less kinetic energy means a lower speed. Therefore the car moves faster at the bottom than the top because kinetic energy is greatest at the lowest point (where gravitational potential energy is least).

Examiner tips

  • Use the phrase "conservation of energy" to link potential and kinetic energy.
  • Show the proportionality KE ∝ v² to justify the speed difference.
  • Mention the change in height (20 m) to emphasise the energy transfer.
  • Keep the explanation concise and directly tied to the marks scheme.

Common mistakes

  • Confusing kinetic energy with potential energy; forgetting that KE decreases as height increases.
  • Failing to state that KE is proportional to v², so not linking energy to speed.
  • Using vague terms like "more energy" without specifying which type of energy changes.

Mark scheme (5 marks)

  1. The car has gravitational potential energy at the top of the loop (because it is raised above the bottom)
  2. By conservation of energy, as the car rises, kinetic energy is transferred to gravitational potential energy
  3. At the top of the loop the car has less kinetic energy than at the bottom
  4. Since kinetic energy is directly proportional to the square of velocity, less kinetic energy means a lower speed
  5. Therefore the car moves faster at the bottom than the top because kinetic energy is greatest at the lowest point (where gravitational potential energy is least)

Related

More Circular motion (A-Level only) questions

▶ Try answering this question with AI marking (free) →