Power and efficiencyEdexcel A-Level Physics: Subtopic test

1. 1
   A motor in a building site hoist lifts a load of mass 250 kg through a height of 12 m at constant speed in 30 s. The electrical power supplied to the motor during the lift is 1.4 kW. Take g = 9.81 N kg⁻¹.

   (a)

   Calculate the useful power output of the motor in raising the load.

   [1 mark]

   • A100 W
   • B2.9 × 10⁴ W
   • C981 W
   • D1400 W

   (b)

   What is the efficiency of the motor?

   [1 mark]

   • A143%
   • B70%
   • C30%
   • D98%

   (c)

   Calculate the energy wasted by the motor during the lift.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A householder compares two lamps that both give 3.0 W of light output. The filament lamp has an input power of 60 W. The LED lamp has an input power of 9.0 W.

   (a)

   What is the efficiency of the filament lamp?

   [1 mark]

   • A20%
   • B95%
   • C0.50%
   • D5.0%

   (b)

   What is the efficiency of the LED lamp?

   [1 mark]

   • A33%
   • B67%
   • C300%
   • D15%

   (c)

   The householder replaces a filament lamp with the LED lamp and uses it for 1000 hours. Calculate the energy saved, in joules.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A cyclist, with a bicycle, has a total mass of 85 kg and rides at a steady 4.0 m s⁻¹ up a road that rises 6.0 m for every 100 m travelled along the road. Resistive forces may be ignored. Take g = 9.81 N kg⁻¹.

   (a)

   Calculate the useful power the cyclist must produce to raise herself and her bicycle up the road.

   [3 marks]

   (b)

   The cyclist's body is 25% efficient at converting chemical energy into useful power. The climb lasts 20 minutes. Calculate the chemical energy she uses during the climb.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A pumped-storage scheme has an upper reservoir 300 m above a lower reservoir. At night, surplus electricity drives pumps that lift water from the lower to the upper reservoir. At times of high demand the water flows back down through turbines that drive generators. In each direction the water moves at 2.0 × 10⁴ kg s⁻¹. The pumps are 85% efficient and the turbines and generators together are 90% efficient. Take g = 9.81 N kg⁻¹.

   (a)

   Explain the energy transfers in the scheme, and why the electrical energy recovered is less than the electrical energy used to pump the water.

   [6 marks]

   (b)

   Calculate the overall efficiency of storing and then recovering energy in the scheme. Evaluate whether the scheme is worthwhile.

   [6 marks]

   Total for question 4: 12 marks

End of questions