An automated vertical farming facility uses a motorized hoist system to raise planting trays from the germination floor up to the high-density growing racks.
A planting tray of mass 18 kg18\text{ kg}18 kg is placed on the hoist. The hoist lifts it through a vertical height of 4.5 m4.5\text{ m}4.5 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 planting tray is about 800 J800\text{ J}800 J (take g=10 N/kgg = 10\text{ N/kg}g=10 N/kg).
(iii) State the work done on the planting tray and give the unit.
The hoist system is powered by a 3.0 kW3.0\text{ kW}3.0 kW electric motor.
(i) State the equation linking efficiency, useful power output, and total power input.
(ii) The hoist lifts 808080 planting trays of mass 18 kg18\text{ kg}18 kg each minute. Calculate the efficiency of the hoist.
Another automated hoist has an efficiency of 45%45\%45%. Its input power is 8.0 kW8.0\text{ kW}8.0 kW. For this hoist:
(i) Calculate the useful power output.
(ii) Calculate the wasted power.
