Work, energy and power

Two identical scooters travel on the same path. Scooter B moves at twice the speed of Scooter A. How does B's kinetic energy compare with A's?

1. A

   It is the same.

2. B

   It is twice as large.

3. C

   It is four times as large.

4. D

   It is eight times as large.

1. a

   Select and explain Select the correct comparison and explain it using the kinetic-energy relationship.

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   Correct choiceC

   1. 1

      Selects option C: scooter B has four times the kinetic energy.

   2. 2

      States or uses Eₖ = ½mv².

   3. 3

      Explains that doubling v multiplies v², and therefore Eₖ, by four while mass is unchanged.

Three students climb the same vertical height of 3.0 m. Use g = 10 N kg⁻¹ and ignore energy transferred to the surroundings.

1. a

   Calculate Calculate the gravitational potential energy gained by each student.

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   1. 1

      Calculates Lina's gain as 48 × 10 × 3.0 = 1440 J.

   2. 2

      Calculates Marek's gain as 60 × 10 × 3.0 = 1800 J.

   3. 3

      Calculates Noor's gain as 54 × 10 × 3.0 = 1620 J.

2. b

   Determine Determine each student's average power and identify the greatest value.

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   1. 1

      Calculates Lina's power as 1440 ÷ 5.0 = 288 W.

   2. 2

      Calculates Marek's power as 1800 ÷ 6.0 = 300 W and Noor's as 1620 ÷ 4.5 = 360 W.

   3. 3

      Identifies Noor as producing the greatest average power.

3. c

   Explain Explain why the fastest time alone is not a fair comparison of power for these students.

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   1. 1

      Power depends on both energy transferred and time, and the students transfer different energies because their masses differ.

A school will replace 100 classroom lamps. Both options provide the required brightness. Lamp A uses 12 W, transfers 9.0 W as useful light, and lasts 15 000 h. Lamp B uses 8.0 W, transfers 6.8 W as useful light, and lasts 10 000 h. Lamps operate for 5.0 h per school day on 180 days each year.

1. a

   Calculate Calculate the efficiency of each lamp.

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   1. 1

      Calculates A: 9.0 ÷ 12 × 100% = 75%.

   2. 2

      Calculates B: 6.8 ÷ 8.0 × 100% = 85%.

2. b

   Determine Determine the annual electrical-energy saving if the school chooses B instead of A.

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   1. 1

      Finds total annual operating time per lamp = 5.0 × 180 = 900 h.

   2. 2

      Finds power difference for 100 lamps = 100 × 4 W = 400 W = 0.400 kW.

   3. 3

      Calculates saving = 0.400 × 900 = 360 kWh per year.

3. c

   Evaluate Recommend a lamp and explain what additional information could change the decision.

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   1. 1

      Makes a recommendation supported by efficiency, annual energy, and/or service-life evidence.

   2. 2

      Recognises the trade-off that B uses less energy but has a shorter stated life.

   3. 3

      Identifies decision-relevant missing evidence such as purchase cost, light quality, repair access, embodied energy, or local electricity emissions.