Water is lifted out of a well 30.0m deep by a motor rated at 1.00hp. Assuming 90% efficiency, how many kilograms of water can be lifted in 1 min?
Answer is 137kg but can not figure it out.
mgh/60sec=1hp(.9)(746watts/hp)
mass= 60sec/(9.8N*30m)*747n-m/sec)*.9
=137
Well, well, well... looks like you need some help with this water lifting conundrum! Let's dive right in and calculate it together.
First, let's convert the power rating from horsepower to watts because we love to keep things in the same units! One horsepower is equal to 746 watts. So, 1.00hp is equal to 746 watts. Got it?
Now, to calculate the work done to lift the water, we need to multiply the power by the time. Since we're given the time of 1 minute, we have 746 watts * 1 minute. This gives us 746 joules.
By the way, the efficiency of 90% means that only 90% of the power is actually used to lift the water. So, we multiply the work done by the efficiency: 746 joules * 0.9 efficiency.
Next, we need to calculate the gravitational potential energy of the water lifted. This is equal to the mass of water multiplied by the acceleration due to gravity (g) multiplied by the height lifted. Since the height lifted is given as 30.0m, we know that the gravitational potential energy is equal to the work done: 746 joules * 0.9 efficiency.
Keeping all these calculations in mind, we can rearrange the formula to calculate the mass of water lifted. It's equal to the work done divided by (g * height): (746 joules * 0.9 efficiency) / (9.8 m/s^2 * 30.0m).
And when you plug in these numbers into a calculator, you'll find that you can lift approximately 136.53 kilograms of water in 1 minute.
So, the answer is approximately 137 kilograms. Ta-daaa! Now that's some waterlifting wizardry!
To calculate how many kilograms of water can be lifted in 1 minute, we can use the power and efficiency of the motor.
1 horsepower (hp) is equivalent to 746 watts. So, 1.00 hp is equal to 746 watts.
First, let's calculate the power used by the motor:
Power (P) = 746 watts * 0.90 (efficiency) = 671.4 watts
Now, let's calculate the work done by the motor to lift the water out of the well:
Work (W) = Force (F) * Distance (d)
The force required to lift the water can be calculated using the weight of the water. The weight can be found using the formula:
Weight (W) = mass (m) * gravity (g)
Here, gravity (g) is approximately 9.8 m/s².
If we assume the mass of the water to be "m" kg, then the weight of the water is "m" kg * 9.8 m/s².
The distance (d) is given as 30.0 m.
Therefore:
Work (W) = m * 9.8 * 30.0 = 294 m * kg * s²
The work done (W) is equal to the power (P) multiplied by the time (t):
Work (W) = P * t
Therefore:
671.4 watts * t = 294 m * kg * s²
Simplifying:
671.4 watts * t = 294 m * 1 kg * 1 m²/s²
To convert from watts (W) to joules (J), we know that 1 watt = 1 joule/second.
So, 671.4 watts multiplied by t seconds is equal to 294 m * kg * m²/s², which simplifies to:
671.4 * t = 294 m * kg
Divide both sides of the equation by 671.4 to solve for t:
t = (294 m * kg) / 671.4
To lift the water in 1 minute, t is equal to 60 seconds:
60 seconds = (294 m * kg) / 671.4
Rearranging the equation:
294 m * kg = 60 seconds * 671.4
294 m * kg = 40284
Finally, solving for mass (m):
m = 40284 / 294 = 137 kg
Therefore, the motor can lift approximately 137 kilograms of water in 1 minute.
To calculate the amount of water that can be lifted in 1 minute, you need to determine the power required to lift the water and then relate it to the power output of the motor.
First, let's find the power required to lift the water. The work done to lift an object against gravity can be calculated using the formula:
Work = Force * Distance,
where Work is in joules (J), Force is in newtons (N), and Distance is in meters (m).
In this case, the force required to lift the water can be calculated using the formula:
Force = mass * gravity,
where mass is in kilograms (kg) and gravity is approximately 9.8 m/s².
The distance, in this case, is given as 30.0 m.
So, the work done can be calculated as:
Work = Force * Distance = (mass * gravity) * Distance.
Now, let's calculate the power required to perform this work in 1 minute. Power is defined as the rate of doing work and is given by the formula:
Power = Work / Time,
where Power is in watts (W) and Time is in seconds (s).
Since we want the final answer in kilograms, we need to convert the time to seconds. There are 60 seconds in 1 minute.
Now, let's calculate the power required:
Power (in watts) = Work / Time = (Force * Distance) / (Time).
The next step is to convert the power from watts to horsepower. 1 horsepower (hp) is equal to approximately 746 watts.
Finally, we can relate the power output of the motor to the required power, taking into account the motor's efficiency.
Power output of the motor = Efficiency * Power required.
In this case, the motor's efficiency is given as 90%.
Once we have the power output of the motor, we can calculate the mass of water lifted.
Mass = Power output * Time / (gravity * Distance).
Now, let's plug in the values:
Distance = 30.0 m
Time = 60 seconds
Efficiency = 0.90
Power output of the motor = 1.00 hp * 746 W/hp
Gravity = 9.8 m/s²
Mass = (Efficiency * Power output * Time) / (gravity * Distance).
Plugging in these values, we can calculate the mass of water lifted in 1 minute. The result is approximately 137 kg.
Therefore, the answer is 137 kg.