An ore processing facility uses an automated vertical hoist system to lift extracted copper ore from a subterranean level up to the crushing unit.
A skip filled with ore has a mass of 150 kg150\text{ kg}150 kg. The hoist lifts it through a vertical height of 4.2 m4.2\text{ m}4.2 m.
(i) State the equation linking gravitational potential energy (GPE\text{GPE}GPE), mass, ggg, and height.
(ii) Show that the gravitational potential energy gained by the ore skip is about 6000 J6000\text{ J}6000 J (take g=10 N/kgg = 10\text{ N/kg}g=10 N/kg).
(iii) State the work done on the ore skip and give the unit.
The hoist system is powered by a 7.5 kW7.5\text{ kW}7.5 kW electric motor.
(i) State the equation linking efficiency, useful power output, and total power input.
(ii) The hoist lifts 303030 ore skips each minute. Calculate the efficiency of the hoist system.
Another hoist system has an efficiency of 45%45\%45%. Its input power is 8.0 kW8.0\text{ kW}8.0 kW. For this hoist system:
(i) Calculate the useful power output.
(ii) Calculate the wasted power.