A dam blocks the passage of a river and generates electricity. Approximately 57,000 kg of water fall each second through a height of 19 m. If one half of the gravitational potential energy of the water were converted to electrical energy, how much power would be generated?
didn't I just outline this?
To calculate the power generated by the dam, we need to find the amount of gravitational potential energy that is converted to electrical energy per second.
First, let's calculate the gravitational potential energy of the water using the formula:
Gravitational Potential Energy = mass × acceleration due to gravity × height
= m × g × h
Given that 57,000 kg of water fall each second through a height of 19 m:
Gravitational Potential Energy = 57,000 kg × 9.8 m/s² × 19 m
Now, we need to find half of this gravitational potential energy since only half is converted to electrical energy:
Converted Gravitational Potential Energy = 0.5 × (57,000 kg × 9.8 m/s² × 19 m)
Finally, to calculate the power generated, we divide the converted gravitational potential energy by the time taken, which is 1 second in this case:
Power Generated = Converted Gravitational Potential Energy / Time
= (0.5 × 57,000 kg × 9.8 m/s² × 19 m) / 1 s
Now, we can simplify and calculate the power:
Power Generated = 0.5 × 57,000 kg × 9.8 m/s² × 19 m
Calculating the above expression gives us the power generated by the dam.