dam is used to block the passage of a river and to generate electricity. Approximately 58.4 x 103 kg of water falls each second through a height of 20.1 m. If one half of the gravitational potential energy of the water were converted to electrical energy, how much power (in MW) would be generated

Question

Cheyenne Melton

Physics

12 November, 23:57

dam is used to block the passage of a river and to generate electricity. Approximately 58.4 x 103 kg of water falls each second through a height of 20.1 m. If one half of the gravitational potential energy of the water were converted to electrical energy, how much power (in MW) would be generated

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Answers (1)

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Magdalena Hess · Answer 1

8.049 MW

Explanation:

The expression for gravitational potential energy is given as

Ep = mgh ... Equation 1

Ep = gravitational potential energy, m = mass of water, h = height, g = acceleration due to gravity.

Given: m = 58.4*10³ kg, h = 20.1 m, g = 9.81 m/s²

Substitute into equation 1

Ep = 58.4*10³ (20.1) (9.81)

Ep = 1.6098*10⁷ J.

If one half the gravitational potential energy of the water were converted to electrical energy

Electrical energy = Ep/2

Electrical energy = (1.6098*10⁷) / 2

Electrical energy = 8.049*10⁶ J

In one seconds,

The power generated = 8.049*10⁶ W

Power generated = 8.049 MW