A fire engine must lift 30 kg of water a vertical distance of 20 m each second. What is the amount of power needed for the water pump for this fire hose?
Is the answer 5880W? If yes, why so?
potential energy per second = m g h = work done per second = power
= 30 * 9.81 * 20
5886 Joules/second or Watts
=
To calculate the power needed for the water pump on the fire engine, we can use the formula:
Power = force × velocity
First, we need to calculate the force required to lift the water. The force can be found using the formula:
Force = mass × acceleration due to gravity
Given that the mass of water being lifted is 30 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force:
Force = 30 kg × 9.8 m/s^2 = 294 N
Next, we need to determine the velocity at which the water is being lifted. In this case, it is being lifted vertically, so we can consider the velocity to be the distance traveled (20 m) divided by the time taken (1 second):
Velocity = 20 m / 1 s = 20 m/s
Now, we can calculate the power:
Power = Force × Velocity = 294 N × 20 m/s = 5880 W
So, yes, the amount of power needed for the water pump for this fire hose is indeed 5880 W.