1. 1
   A stagehand pushes a heavy stage piano 5 m across a flat theatre stage by applying a constant horizontal force of 200 N, overcoming friction from the stage floor.

   (a)

   Which equation correctly gives the work done by the stagehand in pushing the piano?

   [1 mark]

   • AW = F / d
   • BW = F + d
   • CW = F x d
   • DW = d / F

   (b)

   As the piano is pushed, work is done against friction between the piano and the stage floor. Which statement correctly describes this energy transfer?

   [1 mark]

   • AWork done against friction transfers energy usefully to gravitational potential energy
   • BWork done against friction destroys energy
   • CWork done against friction increases the piano's elastic potential energy
   • DWork done against friction transfers energy to the surroundings by heating

   (c)

   Calculate the work done by the stagehand in pushing the piano 5 m.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A go-kart of mass 180 kg, including its driver, accelerates from rest to a speed of 12 m/s on a test track in 6 s.

   (a)

   Which equation is used to calculate the go-kart's kinetic energy at a given speed?

   [1 mark]

   • AEk = 1/2 x m x v^2
   • BEk = m x v
   • CEk = m x v^2
   • DEk = 1/2 x m x v

   (b)

   If the go-kart's speed were doubled while its mass stayed the same, what would happen to its kinetic energy?

   [1 mark]

   • AIt would double
   • BIt would stay the same
   • CIt would halve
   • DIt would quadruple (multiply by 4)

   (c)

   Calculate the kinetic energy of the go-kart when it is travelling at 12 m/s.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student investigates a rubber ball, of mass 0.06 kg, dropped from a height of 2 m onto a hard floor. After bouncing once, it rises to a maximum height of 1.5 m.

   (a)

   Calculate the gravitational potential energy of the ball when it is held at a height of 2 m before release (g = 10 N/kg), and state the law of conservation of energy.

   [3 marks]

   (b)

   Calculate the gravitational potential energy of the ball at its maximum rebound height of 1.5 m, and explain, in terms of energy dissipation, why this is less than the potential energy it had before it was dropped.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A homeowner compares two options for heating water in an off-grid cabin: an electric immersion heater powered by a small wind turbine, or a wood-burning stove with a back boiler. The immersion heater system transfers 3000 J of electrical energy to heat 2 kg of water, of which 2400 J is usefully transferred to the water; the rest is dissipated by heating the surroundings.

   (a)

   Calculate the efficiency of the immersion heater system as a percentage, and explain, in terms of useful and wasted energy, what happens to the energy that is not usefully transferred to the water.

   [6 marks]

   (b)

   The cabin owner is deciding between relying on the wind turbine to power the immersion heater, or using the wood-burning stove instead. Evaluate the advantages and drawbacks of each of these two energy resources for heating water in this off-grid cabin.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   A product designer tests a suspension spring for a mountain bike with a spring constant of 8000 N/m. During a test, the spring is compressed by 0.05 m, within its limit of proportionality.

   (a)

   Which equation is used to calculate the elastic potential energy stored in the compressed spring?

   [1 mark]

   • AEe = k x e
   • BEe = 1/2 x k x e^2
   • CEe = k x e^2
   • DEe = 1/2 x k x e

   (b)

   The elastic potential energy equation for a spring is only valid under which condition?

   [1 mark]

   • AThe spring must be stretched, not compressed
   • BThe spring must be compressed beyond its limit of proportionality
   • CThe spring must remain within its limit of proportionality
   • DThe spring must be made of metal

   (c)

   Calculate the elastic potential energy stored in the spring when it is compressed by 0.05 m.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   An electric bike motor transfers 45000 J of energy to the bike and rider in 30 s while climbing a hill at a steady speed.

   (a)

   Which equation is used to calculate the power output of the motor?

   [1 mark]

   • AP = E / t
   • BP = E x t
   • CP = t / E
   • DP = E + t

   (b)

   Some of the energy transferred by the motor is dissipated rather than being usefully transferred to the bike's kinetic and gravitational potential energy stores. Which of the following is most likely to be responsible for this dissipation?

   [1 mark]

   • AElastic potential energy stored in the frame
   • BThe chemical energy store of the battery
   • CSound energy released by the rider's voice
   • DFriction in the motor and gears, and air resistance, transferring energy by heating

   (c)

   Calculate the power output of the motor.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A research station located in a geologically active region is deciding between drilling a geothermal well to tap heat from underground rocks, or installing a solar photovoltaic array, to generate its electricity supply.

   (a)

   Describe how a geothermal power system generates electricity, and state one reason why geothermal power is classed as a renewable energy resource.

   [3 marks]

   (b)

   Evaluate the advantages and drawbacks of using solar power compared with geothermal power for this research station's electricity supply.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   An off-grid eco-lodge uses a small hydro turbine on a fast-flowing stream to charge batteries. Water flows through the turbine at a rate that delivers 2400 J of gravitational potential energy to the turbine every second, and the turbine's generator has an efficiency of 75%.

   (a)

   Calculate the useful electrical power output of the turbine generator, given that gravitational potential energy is delivered to it at a rate of 2400 J every second and the generator is 75% efficient. Then describe the energy transfers taking place, from the water's gravitational potential energy store to useful electrical energy, including where energy is dissipated.

   [6 marks]

   (b)

   The lodge previously used a diesel generator before installing the hydro turbine. Evaluate the advantages and drawbacks of using the hydro turbine instead of the diesel generator to supply the lodge's electricity, considering both energy resource type and reliability of supply.

   [6 marks]

   Total for question 8: 12 marks

End of questions