A petrol engine raises 200 kg of water in a well from a depth of 7 m in 6 s. Show that the engine is developing about 2.33 KW of power
power = work/time = force*distance/time = mgh/t
200*9.81 * 7 / 6 = 2289 W
2289
To determine the power developed by the petrol engine, we can use the formula:
Power = (Work Done) / (Time)
First, let's calculate the work done by the engine to raise the water:
Work Done = Force × Distance
The force required to raise the water can be calculated using the weight of the water:
Force = Mass × Acceleration
The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the force required to raise the water is:
Force = Mass × 9.8
The mass of the water can be calculated using its weight and the acceleration due to gravity:
Mass = Weight / Gravity
Weight = Mass × Gravity
The weight of the water can be calculated using the formula:
Weight = Density × Volume × Gravity
The density of water is approximately 1000 kg/m^3. The volume of water raised can be calculated using its height:
Volume = Area × Height
The area can be calculated using the radius of the well:
Area = π × Radius^2
Assuming a standard well radius of 1 meter, we have:
Area = π × 1^2 = π m^2
Now we can calculate the volume:
Volume = π × 7 m^2 = 7π m^3
Substituting the density and volume into the weight formula:
Weight = 1000 kg/m^3 × 7π m^3 × 9.8 m/s^2
Now we can calculate the mass:
Mass = Weight / Gravity
Mass = (1000 kg/m^3 × 7π m^3 × 9.8 m/s^2) / 9.8 m/s^2
Next, we substitute the mass into the force formula:
Force = Mass × 9.8
Force = [(1000 kg/m^3 × 7π m^3 × 9.8 m/s^2) / 9.8 m/s^2] × 9.8
Now we can calculate the work done:
Work Done = Force × Distance
Work Done = [(1000 kg/m^3 × 7π m^3 × 9.8 m/s^2) / 9.8 m/s^2] × 9.8 × 7 m
Finally, we can substitute the work done and time into the power formula:
Power = Work Done / Time
Power = {[(1000 kg/m^3 × 7π m^3 × 9.8 m/s^2) / 9.8 m/s^2] × 9.8 × 7 m} / 6 s
Simplifying the equation and doing the calculations, we find that the engine is developing about 2.33 kW of power.
To calculate the power developed by the engine, we need to find the work done by the engine and then divide it by the time taken.
The work done by the engine is given by the formula:
Work = force × distance
In this case, the force is the weight of the water being raised, and the distance is the height it is being raised.
The weight of an object is given by the formula:
Weight = mass × gravitational acceleration
Given that the mass of the water is 200 kg and the gravitational acceleration is approximately 9.8 m/s² (usually rounded to 10 m/s² for simplification), we can calculate the weight of the water:
Weight = 200 kg × 10 m/s² = 2000 N
The work done by the engine is then:
Work = 2000 N × 7 m = 14,000 J (Joules)
Since the time taken is given as 6 seconds, we can calculate the power developed by the engine using the equation:
Power = Work / Time
Power = 14,000 J / 6 s = 2333.33 W
Therefore, the engine is developing approximately 2.33 kW (kilowatts) of power.