Question

Water flows over a section of Niagara Falls at the rate of 1.1 × 106 kg/s and falls 50.0 m. How much power is generated by the falling water? The acceleration of gravity if 9.81 m/s 2 . Answer in units of W.

Answer 1

5.395 × 10^8 Watts

Step-by-step explanation:

We are given;

• Rate of flow is 1.1 × 10^6 kg/s
• Distance is 50.0 m
• Gravitational acceleration is 9.8 m/s²

We are required to calculate the power that is generated by the falling water

• Power is the rate of work done
• It is given by dividing the energy or work done by time

• Power = Work done ÷ time

But; work done = Force × distance

Therefore;

Power = (F × d) ÷ time

The rate is 1.1 × 10^ 6 Kg/s

But, 1 kg = 9.81 N

Therefore, the rate is equivalent to 1.079 × 10^7 N/s

Thus,

Power = Rate (N/s) × distance

= 1.079 × 10^7 N/s × 50.0 m

= 5.395 × 10^8 Watts

The power generated from the falling water is 5.395 × 10^8 Watts