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A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .?
Most Upvoted Answer
A motor of power 10 kW is used to pump water from a well 20 m deep. Ca...
Work done = mgh = (2400)(10)(20) = 480 KJ
Time taken = 1 minute = 60 seconds
Power Output = work done/time = (480/60) KW = 8 KW
Efficiency = power output/power input = 8 KW/10 KW = 0.8 = 80%
Community Answer
A motor of power 10 kW is used to pump water from a well 20 m deep. Ca...
Given:
- Power of the motor = 10 kW
- Depth of the well = 20 m
- Mass of water pumped per minute = 2400 kg
- Acceleration due to gravity = 10 m/s²
To calculate:
- Efficiency of the motor
Solution:
Step 1: Calculate the work done to pump the water:
The work done to pump the water from the well can be calculated using the formula:
Work = Force × Distance
The force required to lift the water can be calculated using the formula:
Force = Mass × Acceleration due to gravity
In this case, the mass of water being lifted is 2400 kg and the distance is 20 m. Therefore,
Force = 2400 kg × 10 m/s² = 24000 N
The work done to pump the water is:
Work = 24000 N × 20 m = 480000 J
Step 2: Calculate the input power:
The input power is the power supplied by the motor, which is given as 10 kW. To convert this to joules per second (Watts), we multiply by 1000:
Input Power = 10 kW × 1000 = 10000 W
Step 3: Calculate the efficiency:
Efficiency is defined as the ratio of output power to input power. In this case, the output power is the work done to pump the water. Therefore,
Efficiency = (Work / Time) / Input Power
Since the mass of water is given per minute, we need to convert the time to seconds:
Time = 1 minute = 60 seconds
Substituting the values:
Efficiency = (480000 J / 60 s) / 10000 W
= 8 J/s / 10000 W
= 0.0008
Therefore, the efficiency of the motor is 0.0008, or 0.08%.
- Power of the motor = 10 kW
- Depth of the well = 20 m
- Mass of water pumped per minute = 2400 kg
- Acceleration due to gravity = 10 m/s²
To calculate:
- Efficiency of the motor
Solution:
Step 1: Calculate the work done to pump the water:
The work done to pump the water from the well can be calculated using the formula:
Work = Force × Distance
The force required to lift the water can be calculated using the formula:
Force = Mass × Acceleration due to gravity
In this case, the mass of water being lifted is 2400 kg and the distance is 20 m. Therefore,
Force = 2400 kg × 10 m/s² = 24000 N
The work done to pump the water is:
Work = 24000 N × 20 m = 480000 J
Step 2: Calculate the input power:
The input power is the power supplied by the motor, which is given as 10 kW. To convert this to joules per second (Watts), we multiply by 1000:
Input Power = 10 kW × 1000 = 10000 W
Step 3: Calculate the efficiency:
Efficiency is defined as the ratio of output power to input power. In this case, the output power is the work done to pump the water. Therefore,
Efficiency = (Work / Time) / Input Power
Since the mass of water is given per minute, we need to convert the time to seconds:
Time = 1 minute = 60 seconds
Substituting the values:
Efficiency = (480000 J / 60 s) / 10000 W
= 8 J/s / 10000 W
= 0.0008
Therefore, the efficiency of the motor is 0.0008, or 0.08%.
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A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .?
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A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .?.
A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .?.
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