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AS Daily A Level Physics question

2026-06-22 OCR A Cross-topic problem solving (mechanics ↔ circuits energy; graphs & modelling) Module 3.3: Work, energy and power (AS) Module 4.2.1: Charge, current and potential difference (AS) Module 4.2.3: Internal resistance and emf; terminal pd under load (AS) Module 1: Practical skills — data handling and proportional reasoning

A 12 V DC bench supply with some internal resistance powers a small winch that lifts a 0.50 kg mass vertically at a steady 0.40 m s−1. The p.d. across the motor terminals during the lift is 9.0 V. Assume essentially all electrical power delivered to the motor becomes mechanical power m g v. The student now replaces the mass with 1.0 kg and tries to keep the same lifting speed using the same supply. Which statement must be true?

  1. A Not possible to keep 0.40 m s−1: initial data give r ≈ 13.5 Ω; doubling m needs 4.0 W at the motor, but even at I ≈ 0.44 A the terminal p.d. is ≈6.0 V so power ≈2.7 W < 4.0 W. (correct)
  2. B Possible by doubling current: the terminal p.d. stays about 9.0 V so motor power doubles to ≈4.0 W.
  3. C Possible because the source power 12 V × 0.44 A ≈ 5.3 W exceeds 4.0 W, so the motor can still get enough power.
  4. D Not possible because the current cannot exceed about 0.22 A with this source; the motor is already at its limit.

Answer

The correct answer is A.

Correct: A — Not possible to keep 0.40 m s−1: initial data give r ≈ 13.5 Ω; doubling m needs 4.0 W at the motor, but even at I ≈ 0.44 A the terminal p.d. is ≈6.0 V so power ≈2.7 W < 4.0 W. A uses energy–power balance and the fact that V = 12 − I r falls as I rises; substituting r from the first lift shows no VI can reach 4.0 W with this source. B assumes the terminal p.d. stays at 9.0 V when current doubles, ignoring the internal resistance drop that reduces V as I increases. C confuses source power (E I) with power at the motor (V I); the I^2 r loss is large (≈2.7 W at 0.44 A), leaving too little for the motor. D invents a hard current limit at 0.22 A; higher I is possible, but it drags the terminal p.d. down, so the motor still cannot receive 4.0 W.

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