An environmental club builds a small-scale waterfall and reservoir in your schools central courtyard. Every minute, 5.20×103 kg of water falls 6.20 m. The efficiency of transforming gravitational potential energy to electrical energy is 78.0%. What power, measured in Watts, would the waterfall generate for the school?

Question

10-05-2025
Physics

High School

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An environmental club builds a small-scale waterfall and reservoir in your schools central courtyard. Every minute, 5.20×103 kg of water falls 6.20 m. The efficiency of transforming gravitational potential energy to electrical energy is 78.0%. What power, measured in Watts, would the waterfall generate for the school?

Answer :

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TaylorSmith48 TaylorSmith48 · Answer 1 · 2025-01-19T19:30:38-05:00

Final answer:

The power output of a waterfall can be calculated using the equation of gravitational potential energy (GPE = mgh), accounting for the efficiency of energy transformation, and converting from energy per minute to power output in watts.

Explanation:

This question is about harnessing the gravitational potential energy (GPE) of the falling water and transforming it into electrical energy. The equation used to compute gravitational potential energy is GPE = mgh, where m is mass in kilograms, g is gravitational acceleration (9.81 m/s² for Earth), and h is height in meters. The energy transformation efficiency is accounted for in the final step.

First, we calculate the waterfall's gravitational potential energy per minute: GPE = (5.20×10³ kg) * (9.81 m/s²) * (6.20 m). Then, to find the power output in watts, we multiply by the energy transformation efficiency (78.0%) and divide by 60 seconds (to convert from per minute to per second). This gives us the power output in Watts.

Learn more about Gravitational Potential Energy here:

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