Each second, 1200 m^3 of water passes over a waterfall 100 m high. Three-fourths of the kineti

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Each second, 1200 m^3 of water passes over a waterfall 100...

Each second, $1200 \mathrm{~m}^{3}$ of water passes over a waterfall $100 \mathrm{~m}$ high. Three-fourths of the kinetic energy gained by the water in falling is transferred to electrical energy by a hydroelectric generator. At what rate does the generator produce electrical energy? (The mass of $1 \mathrm{~m}^{3}$ of water is $1000 \mathrm{~kg}$.)

Key Concepts

Gravitational Potential Energy

This is the energy that a mass possesses due to its position in a gravitational field, calculated using the formula E = mgh, where m is mass, g is the acceleration due to gravity, and h is the height. In the context of the waterfall, gravitational potential energy is converted into kinetic energy as water falls.

Mass Flow Rate

Mass flow rate is the amount of mass passing through a given point per unit time. When given the volume flow rate and the density of the fluid, the mass flow rate can be determined, which is essential for calculating the total energy transferred per unit time in hydropower systems.

Energy Conversion Efficiency

This is a measure of how effectively energy is converted from one form to another. In the scenario of a hydroelectric generator, not all the potential energy is converted into electrical energy. The efficiency factor (in this case, three-fourths or 75%) indicates the fraction of the energy that is successfully transformed into electrical energy.

Electrical Power Generation

Electrical power generation is the process of converting one form of energy into electrical energy per unit time, typically measured in watts. In hydroelectric systems, the power output is derived from converting the gravitational potential energy of falling water, factoring in the mass flow rate and efficiency of the conversion process.

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