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?
5.540*10^6
To calculate the power generated by the dam, we need to find the gravitational potential energy of the falling water and then divide it by the time it takes for the water to fall.
The gravitational potential energy (GPE) of an object can be calculated using the formula:
GPE = mgh
Where:
m = mass of the object (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height (in meters)
Given:
Mass of water falling per second (m) = 57,000 kg
Height of fall (h) = 19 m
Let's calculate the gravitational potential energy:
GPE = mgh
GPE = 57,000 kg * 9.8 m/s^2 * 19 m
GPE ≈ 10,771,200 J
Now that we have the gravitational potential energy, we can calculate the power using the formula:
Power = GPE / time
The problem does not specify the time it takes for the water to fall, so we can't calculate the power without that information.
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.
The gravitational potential energy (GPE) of an object near the Earth's surface is given by the formula:
GPE = mgh
Where:
m = mass of the object (in this case, the mass of the water)
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height through which the water falls (19 m in this case)
The mass of the water falling per second can be calculated using the formula:
Mass = flow rate × time
Given that the flow rate is 57,000 kg/s, and the time is 1 second, the mass of the water falling per second is 57,000 kg.
Now, let's plug in the values into the formula for GPE:
GPE = (57,000 kg) × (9.8 m/s²) × (19 m)
Simplifying this equation, we get:
GPE = 10,950,600 J (joules)
Since only half of the gravitational potential energy is converted to electrical energy, we divide this value by 2:
Electrical energy = 10,950,600 J / 2 = 5,475,300 J
To find the power, we divide the electrical energy by the time:
Power = 5,475,300 J / 1 s = 5,475,300 W (watts)
Therefore, approximately 5,475,300 watts of power would be generated by the dam.
mgh/time * .5= work
mass/time * g * h* .5= work
do the math.