Calculate the power of a pump which can lift 100kg of water through a vertical height of 5m in 20s
To calculate the power of the pump, we will use the formula:
Power = (Work done) / (time)
First, we need to calculate the work done by the pump. The work done is given by the equation:
Work = force x distance
The force is the weight of the water being lifted, which is equal to its mass times the acceleration due to gravity:
Force = mass x gravity
Force = 100 kg x 9.8 m/s^2 (approximately)
The distance is the height that the water is lifted:
Distance = 5 m
Now we can calculate the work done:
Work = Force x Distance
Work = (100 kg x 9.8 m/s^2) x 5 m
Next, we need to convert the work to joules. 1 Joule (J) is equal to 1 Newton-meter (N*m). Therefore, the work done will be in Joules.
Work (in joules) = Work (in Newtons) x Distance
To convert from kg.m/s^2 to Newtons (N), we use the equation 1N = 1 kg.m/s^2:
Work (in joules) = (100 kg x 9.8 m/s^2) x 5 m
Finally, we can calculate the power:
Power = Work / (time)
Power = Work / 20s
Substitute the values:
Power = [(100 kg x 9.8 m/s^2) x 5 m] / 20s
Calculating this expression will give you the power of the pump in watts (W).
To calculate the power of a pump, you need to use the formula:
Power = Work / Time
In this case, the work being done by the pump is equal to the potential energy gained by the water. The potential energy can be calculated using the formula:
Potential Energy = Mass * Gravity * Height
where:
Mass = 100 kg (mass of water)
Gravity = 9.8 m/s² (acceleration due to gravity)
Height = 5 m (vertical height)
Let's calculate the potential energy first:
Potential Energy = 100 kg * 9.8 m/s² * 5 m
Potential Energy = 4900 J
Now, to calculate the power:
Power = Potential Energy / Time
Power = 4900 J / 20 s
Power = 245 W
Therefore, the power of the pump is 245 watts.