Ten litre of water per second is lifted from well through 10m and delivered with a velocity of 10m/s if g=10m/s^2. The power of motor is
Answer 1.5Kw how ??
the energy to lift the water is
... m g h = 10 kg * 10 m/s^2 * 10 m
... = 1000 J
the kinetic energy of the water at delivery is ... 1/2 m v^2
... = 1/2 * 10 kg * (10 m/s)^2
... = 500 J
1500 J / s = 1500 watts = 1.5 kw
To find the power of the motor, we can use the formula:
Power = (work done) / (time taken)
First, let's calculate the work done:
Work done = force x distance
The force required to lift the water can be determined using the formula:
Force = mass x gravity
Given that 10 liters of water is lifted per second, we need to convert this to kilograms:
1 liter of water = 1 kg (since the density of water is 1 g/cm³ = 1 kg/L)
So, 10 liters of water = 10 kg
The distance lifted is given as 10 m.
Therefore, the force = 10 kg x 10 m/s² = 100 N
Now, let's calculate the work done:
Work done = 100 N x 10 m = 1000 J
Next, we need to determine the time taken to lift this quantity of water.
Since 10 liters of water is lifted per second, and the distance is 10 m, the time taken is 1 second.
Now, let's calculate the power:
Power = work done / time taken
Power = 1000 J / 1 s = 1000 W
Finally, converting this to kilowatts:
Power = 1000 W / 1000 = 1 kW
Therefore, the power of the motor is 1 kW (kilowatt).
To find the power of the motor, we need to calculate the work done per second, which is equal to the power.
First, let's find the weight of the water lifted. The weight of the water can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the acceleration due to gravity (g) is 10 m/s^2, and the mass of the water is given as 10 liters, we need to convert liters to kilograms:
1 liter of water = 1 kg
So, 10 liters of water = 10 kg
Therefore, the weight of the water lifted = 10 kg * 10 m/s^2 = 100 N (Newtons)
Next, let's calculate the work done in lifting the water. The work done is given by the formula:
Work = force * distance
In this case, the force is equal to the weight of the water (100 N) and the distance is given as 10 meters. Therefore, the work done in lifting the water is:
Work = 100 N * 10 m = 1000 J (Joules)
Finally, let's calculate the power. The power is equal to the work done per second:
Power = Work / Time
Since 10 liters of water is lifted per second, the time taken is 1 second. Therefore, the power is:
Power = 1000 J / 1 s = 1000 W (Watts)
To convert the power from Watts to kilowatts, we divide by 1000:
Power = 1000 W / 1000 = 1 kW
So, the power of the motor is 1 kW.
It seems like there was a mistake in the given answer. The correct power of the motor should be 1 kW, not 1.5 kW.