Water is lifted out of a well 38.0m deep by a motor rated at 1.00hp. assuming70% efficiency, how many kilograms of water can be lifted in 1 min?
To find out how many kilograms of water can be lifted in 1 minute, we need to calculate the work done by the motor, taking into account its efficiency and the depth of the well.
First, let's convert the power rating of the motor from horsepower (hp) to watts (W), since efficiency is usually expressed as a decimal value in the international system. We know that 1 horsepower is equal to 746 watts, so:
1.00 hp * 746 W/hp = 746 W
Given that the motor has a 70% efficiency, we need to calculate the actual power output:
Power Output = Efficiency * Power Input
Power Output = 0.70 * 746 W
Power Output = 522.2 W
Next, let's determine the work done by the motor to lift the water out of the well. The work done is given by the equation:
Work = Force * Distance
We need to calculate the force exerted by the motor to lift the water. The force is determined by the weight of the water, which can be calculated using the formula:
Weight = Mass * Gravity
The mass of the water can be found by dividing the work done by the motor's power output:
Mass = Work / (Power Output * Time)
Since we are interested in finding the mass lifted in 1 minute, we'll use Time = 1 min = 60 s.
Now, let's calculate the mass of the water:
Mass = Work / (Power Output * Time)
Mass = (Force * Distance) / (Power Output * Time)
Mass = (Weight * Distance) / (Power Output * Time)
We know that the distance lifted is 38.0 m, so:
Mass = (Weight * 38.0 m) / (Power Output * 60 s)
Finally, let's calculate the weight of the water:
Weight = Mass * Gravity
The acceleration due to gravity is approximately 9.8 m/s^2. So:
Mass = Weight / Gravity
Now we can calculate the mass of the water:
Mass = (Weight * 38.0 m) / (Power Output * 60 s)
Mass = (Mass * Gravity * 38.0 m) / (Power Output * 60 s * Gravity)
Mass * Power Output * 60 s = Mass * 38.0 m
Mass * Power Output * 60 s / 38.0 m = Mass
Mass = (Power Output * 60 s) / 38.0 m
Substituting the known values:
Mass = (522.2 W * 60 s) / 38.0 m
Now we can calculate the mass of the water lifted in 1 minute by dividing the power output by 38.0:
Mass = (522.2 W * 60 s) / 38.0 m
Mass = 819.090 W*s/m / 38.0 m
Mass = 21.55 kg
Therefore, the motor can lift approximately 21.55 kilograms of water in 1 minute.