An engineering team is testing a prototype regenerative braking system for an industrial warehouse lift. During a test run, a loaded lift cabin descends at a constant speed, driving an electrical generator that charges a backup battery system. The parameters recorded during this test descent are shown in the table below:
| Measurement | Value |
|---|---|
| Vertical distance descended | 12.0 m12.0\text{ m}12.0 m |
| Mass of the loaded cabin | 750 kg750\text{ kg}750 kg |
| Time taken for descent | 8.0 s8.0\text{ s}8.0 s |
| Average charging current | 15.0 A15.0\text{ A}15.0 A |
| Average voltage across battery terminals | 48.0 V48.0\text{ V}48.0 V |
State the equation linking gravitational potential energy (GPE\text{GPE}GPE), mass, ggg, and height.
Calculate the gravitational potential energy (GPE\text{GPE}GPE) lost by the lift cabin during the descent. (Take g=9.8 N/kgg = 9.8\text{ N/kg}g=9.8 N/kg, 9.81 N/kg9.81\text{ N/kg}9.81 N/kg or 10 N/kg10\text{ N/kg}10 N/kg)
Explain why only some of the gravitational potential energy lost by the cabin is transferred to the battery storage system.
Calculate the electrical energy transferred to the battery system during this descent.
