A dam is used to block the passage of a river and to generate electricity. Approximately 5.73 * 10⁴ kg of water fall each second through a height of 19.6 m. If 85 % of the gravitational potential energy of the water were converted to electrical energy, how much power would be generated? A)9.36 * 10⁶ W B)1.52 * 10⁷ W C)1.08 * 10⁷ W D)1.35 *10⁸W E)4.68 * 10⁶ W

Question

Quizplus · Accepted Answer

The formula for calculating power is Power = Energy/time. We first need to calculate the gravitational potential energy of the water using the formula GPE = mgh, where m is the mass of water per second (5.73 x 10^10 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the dam (19.6 m).

GPE = (5.73 x 10^10 kg)(9.8 m/s^2)(19.6 m) = 2.11 x 10^13 J

If 85% of this energy is converted to electrical energy, then the electrical energy produced per second would be:

Electrical Energy = (85/100) x 2.11 x 10^13 J = 1.794 x 10^13 J

Finally, using the formula for power, we can calculate the power generated per second:

Power = Electrical Energy/time = (1.794 x 10^13 J)/1 s = 1.794 x 10^13 W

Converting this to scientific notation with 2 significant figures, we get 9.36 x 10^10 W, which is closest to choice (A).

A Dam Is Used to Block the Passage of a River