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A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent?
Most Upvoted Answer
A pump can throw up 10 quintals of coal per hour from a coal mine 120m...
Calculation of Power
To calculate the power of the engine, we need to use the formula:
Power = Work done / Time
In this case, the work done is the amount of coal lifted by the pump, and the time is the duration of one hour.
Calculating the Work Done
The work done by the pump is given by the formula:
Work done = Force x Distance
In this case, the force is the weight of the coal being lifted, and the distance is the height of the coal mine.
The weight of the coal can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
Given that 1 quintal is equal to 100 kg, we can convert the weight of the coal to:
Weight = 10 quintals x 100 kg/quintal = 1000 kg
The acceleration due to gravity is approximately 9.8 m/s^2.
Therefore, the weight of the coal is:
Weight = 1000 kg x 9.8 m/s^2 = 9800 N
The distance the coal is lifted is given as 120 m.
Therefore, the work done is:
Work done = 9800 N x 120 m = 1,176,000 Nm
Calculating the Power
Now that we have the work done, we can calculate the power using the formula:
Power = Work done / Time
Given that the time is one hour, we need to convert it to seconds:
Time = 1 hour x 60 minutes/hour x 60 seconds/minute = 3600 seconds
Therefore, the power is:
Power = 1,176,000 Nm / 3600 s = 326.67 W
Considering Efficiency
The efficiency of the engine is given as 80 percent. This means that only 80 percent of the input energy is converted into useful work.
Therefore, the actual power output of the engine is:
Actual Power = Efficiency x Power = 0.80 x 326.67 W = 261.33 W
Hence, the power of the engine is 261.33 watts.
To calculate the power of the engine, we need to use the formula:
Power = Work done / Time
In this case, the work done is the amount of coal lifted by the pump, and the time is the duration of one hour.
Calculating the Work Done
The work done by the pump is given by the formula:
Work done = Force x Distance
In this case, the force is the weight of the coal being lifted, and the distance is the height of the coal mine.
The weight of the coal can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
Given that 1 quintal is equal to 100 kg, we can convert the weight of the coal to:
Weight = 10 quintals x 100 kg/quintal = 1000 kg
The acceleration due to gravity is approximately 9.8 m/s^2.
Therefore, the weight of the coal is:
Weight = 1000 kg x 9.8 m/s^2 = 9800 N
The distance the coal is lifted is given as 120 m.
Therefore, the work done is:
Work done = 9800 N x 120 m = 1,176,000 Nm
Calculating the Power
Now that we have the work done, we can calculate the power using the formula:
Power = Work done / Time
Given that the time is one hour, we need to convert it to seconds:
Time = 1 hour x 60 minutes/hour x 60 seconds/minute = 3600 seconds
Therefore, the power is:
Power = 1,176,000 Nm / 3600 s = 326.67 W
Considering Efficiency
The efficiency of the engine is given as 80 percent. This means that only 80 percent of the input energy is converted into useful work.
Therefore, the actual power output of the engine is:
Actual Power = Efficiency x Power = 0.80 x 326.67 W = 261.33 W
Hence, the power of the engine is 261.33 watts.
Community Answer
A pump can throw up 10 quintals of coal per hour from a coal mine 120m...
Answer should be 408.3 watt
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A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent?
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A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent?.
A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pump can throw up 10 quintals of coal per hour from a coal mine 120m deep. Calculate the power of the engine in watt assuming that efficiency is 80 percent?.
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