A certain rain cloud at an altitude of 1.90 km contains 3.20 107 kg of water vapor. How long would it take for a 2.18-kW pump to raise the amount of water from Earth's surface to the cloud's position?
change in potential energy = m g h
= work done = 2180 Joules/second * t
To calculate the time it would take for a 2.18-kW pump to raise the amount of water from Earth's surface to the cloud's position, we need to consider the work done by the pump, the amount of water to be lifted, and the power of the pump.
1. Calculate the work done:
The work done is given by the equation: work = force x distance. In this case, the force is the weight of the water and the distance is the height difference between Earth's surface and the cloud's position.
The weight of the water can be calculated using the equation: weight = mass x acceleration due to gravity. In this case, the mass is given as 3.20 x 10^7 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
weight = (3.20 x 10^7 kg) x (9.8 m/s^2)
Next, we need to convert the height difference from km to meters:
distance = 1.90 km x 1000 m/km
2. Calculate the time taken:
Now that we have the work done and the distance, we can calculate the time taken using the equation: work = power x time.
Substituting the values we know, we can rearrange the equation to solve for time:
work = power x time
work / power = time
Substituting the calculated work and the given power, we can find the time it would take for the pump to raise the water:
time = (weight x distance) / power
Now, you can substitute the calculated values into the equation and calculate the time.