An engineer tests a prototype gravity energy storage system designed to store and release energy. During discharging, a heavy block is allowed to descend down a vertical mine shaft. The descending block is connected to a cable wound around a winch drum, which drives an electrical generator connected to a load resistor representing a micro-grid dump load.
The parameters recorded during a discharge test are shown in the table below:
| Parameter | Value |
|---|---|
| Vertical distance block falls | 12.5 m12.5\text{ m}12.5 m |
| Mass of the block | 45.0 kg45.0\text{ kg}45.0 kg |
| Duration of the descent | 8.0 s8.0\text{ s}8.0 s |
| Average current through load resistor | 2.40 A2.40\text{ A}2.40 A |
| Average voltage across load resistor | 115 V115\text{ V}115 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 block during this 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 block is transferred to the load resistor.
Calculate the electrical energy transferred to the load resistor.
