in every minute a pump draws 6 metric cubed of water from a well and issues it at a speed of 5 meters per second from the nozzle situated 4 meters above the level from which the water was drawn. find the average rate at which the pump is working. (1 metric cubed =1000kg)
Well, well, well, looks like we have a water-related problem here! Let's dive into it and find the solution, shall we?
To find the average rate at which the pump is working, we'll need to consider the amount of water pumped and the time it takes. First, let's convert the rate from cubic meters to kilograms. Since 1 cubic meter equals 1000 kilograms, the pump draws 6 metric cubic meters, which means it's pumping 6,000 kilograms of water.
Now, we need to determine the time it takes for the pump to draw this water. At a speed of 5 meters per second, and considering the water is pumped from a nozzle situated 4 meters above the level, we can use a little bit of geometry. The water will have to travel a distance of 4 meters vertically, so it will take 4/5 = 0.8 seconds for the water to be drawn.
Finally, we can calculate the average rate at which the pump is working by dividing the amount of water (in kilograms) by the time it takes (in seconds). Therefore, the average rate is 6,000 kg / 0.8 s ≈ 7,500 kg/s.
So, the average rate at which the pump is working is about 7,500 kilograms per second. Keep those numbers flowing!
To find the average rate at which the pump is working, we need to calculate the total amount of work done by the pump in a given time interval.
First, let's convert the volume of water pumped per minute from metric cubes to kilograms. Since 1 metric cube is equal to 1000 kg, the pump draws 6 x 1000 = 6000 kg of water per minute.
Next, we need to calculate the height the water is lifted. The nozzle is situated 4 meters above the level from which the water was drawn. Therefore, the height lifted is 4 meters.
Work is defined as the product of force and distance. In this case, the force is the weight of the water lifted, which is equal to the mass of the water multiplied by the acceleration due to gravity (9.8 meters per second squared).
So, the work done by the pump per minute is equal to the weight of the water lifted multiplied by the height lifted. Mathematically, this can be written as:
Work = (mass of water) x (acceleration due to gravity) x (height lifted)
Substituting the given values:
Work = 6000 kg x 9.8 m/s^2 x 4m
Now, we can calculate the total work:
Work = 235,200 joules
Since this calculation is done per minute, the average rate at which the pump is working is equal to the total work divided by the total time. In this case, the total time is 1 minute.
Average rate = 235,200 joules / 1 minute
Therefore, the average rate at which the pump is working is 235,200 joules per minute.
To find the average rate at which the pump is working, we need to calculate the total work done by the pump and divide it by the total time taken.
The work done by the pump can be calculated using the formula:
Work = Force x Distance
In this case, the force exerted by the pump is the weight of the water being lifted, and the distance is the height the water is lifted.
Force = Mass x Acceleration due to gravity
Distance = Height
Let's break down the calculation:
1. First, we need to calculate the mass of water being lifted in one minute. Given that 1 metric cubic meter of water weighs 1000 kg:
Mass = Volume x Density
= 6 metric cubic meters x 1000 kg/metric cubic meter
= 6000 kg
2. Next, we calculate the force exerted by the pump:
Force = Mass x Acceleration due to gravity
= 6000 kg x 9.8 m/s^2
= 58800 N
3. Now, we calculate the work done by the pump in one minute:
Work = Force x Distance
= 58800 N x 4 m
= 235200 J (Joules)
4. Since the problem states that the pump operates at a speed of 5 meters per second, we can assume that it takes 4 seconds to lift the water to the nozzle (distance/velocity).
5. Finally, we calculate the average rate at which the pump is working:
Average Rate = Work / Time
= 235200 J / 240 s
≈ 980 J/s (Watts)
Therefore, the average rate at which the pump is working is approximately 980 Watts.