1. 1
   A student pulls a loaded sledge 40 m across level snow at a constant speed. The rope is held at 30° above the horizontal and the tension in it is 60 N. The journey takes 50 s.

   (a)

   How much work is done on the sledge by the tension in the rope?

   [1 mark]

   • A1.2 kJ
   • B2.4 kJ
   • C0 J
   • D2.1 kJ

   (b)

   How much work is done on the sledge by friction during the journey?

   [1 mark]

   • A−2.1 kJ
   • B+2.1 kJ
   • C0 J
   • D−2.4 kJ

   (c)

   Determine the average power developed by the tension force.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A toy of mass 0.50 kg sits on top of a vertical spring of spring constant 800 N m⁻¹ that has been compressed by 5.0 cm. When the spring is released, the toy is launched vertically upwards. Take g = 9.81 m s⁻².

   (a)

   What is the elastic potential energy stored in the compressed spring?

   [1 mark]

   • A2.0 J
   • B1.0 J
   • C40 J
   • D1.0 × 10⁴ J

   (b)

   Assuming no energy is dissipated, what is the maximum height the toy rises above its starting position?

   [1 mark]

   • A0.10 m
   • B0.41 m
   • C0.20 m
   • D2.0 m

   (c)

   In practice the toy rises only 0.16 m above its starting position. Determine the efficiency of the energy transfer from the spring to gravitational potential energy, and state where the rest of the energy goes.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An electric motor raises a lift of total mass 800 kg through a height of 24 m in 16 s at constant speed. The electrical power supplied to the motor is 18 kW. During a power cut, the building's electricity is supplied by a diesel generator of efficiency 35%. The energy density of diesel is 45 MJ kg⁻¹. Take g = 9.81 m s⁻².

   (a)

   Determine the useful output power of the motor and its efficiency.

   [3 marks]

   (b)

   During the power cut the lift makes 200 identical journeys. Determine the mass of diesel burned, and comment on the overall efficiency of turning the fuel's chemical energy into gravitational potential energy of the lift.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A roller-coaster car and its riders have a total mass of 450 kg. The car starts from rest at the top of a first drop 32 m high and travels 60 m along the track to the lowest point, where a sensor records its speed as 23.0 m s⁻¹. From there it travels 45 m along the track to the top of a second hill, 18 m above the lowest point. Take g = 9.81 m s⁻².

   (a)

   Determine the average resistive force acting on the car during the first drop, and use your answer to predict the speed of the car at the top of the second hill.

   [6 marks]

   (b)

   The designers want to add a third hill, 30 m above the lowest point, reached after a further stretch of track. They claim the car will get over it 'provided the track is smooth enough'. Evaluate this claim using energy principles, and discuss the validity of treating the resistive force as constant in your answer to (a).

   [6 marks]

   Total for question 4: 12 marks

End of questions