To calculate the total mechanical energy in this system, we consider the gravitational potential energy (GPE) that the water possesses before falling.

Formula for Gravitational Potential Energy:

$\text{GPE} = m \cdot g \cdot h$ Where:

• $m = 1000 \, \text{kg}$ (mass of the water),
• $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity),
• $h = 30 \, \text{m}$ (height from which water falls).

Calculation:

$\text{GPE} = 1000 \cdot 9.8 \cdot 30$ $\text{GPE} = 294,000 \, \text{J} \, (\text{joules})$

Total Mechanical Energy:

In this case, since the energy is completely converted from gravitational potential energy to kinetic energy (ignoring losses like friction), the total mechanical energy of the system is simply the gravitational potential energy.

$\text{Total Mechanical Energy} = 294,000 \, \text{J}$

Thus, the total mechanical energy of the system is 294,000 joules (J).

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Would you like a breakdown of the energy transformation process or have any further questions?

Related Questions:

1. How is the total mechanical energy affected if the height is doubled?
2. How would energy losses like friction affect the total mechanical energy?
3. What is the velocity of the water when it reaches the ground?
4. How much power can the plant generate if this energy is converted over 5 seconds?
5. How does the mass of water influence the total energy?

Tip:

Always ensure to account for energy losses when analyzing real-world systems, as they affect the efficiency of energy conversion.