Final answer:
When a pump is required to lift 840 kg of water per minute from a well 14.5 m deep and eject it with a speed of 17.4 m/s is A) 217,260 J
Step-by-step explanation:
When a pump is used to lift water from a well, it needs to provide enough energy to overcome the gravitational potential energy of the water and also to give it a certain velocity as it is ejected. In this case, the pump needs to lift 840 kg of water per minute from a well that is 14.5 m deep and eject it with a velocity of 17.4 m/s. To calculate the work done by the pump, we can use the formula:
Work = force x distance
The force required to lift the water is equal to its weight, which can be calculated using the formula:
Force = mass x gravitational acceleration
Substituting the given values, we get:
Force = 840 kg x 9.8 m/s^2 = 8232 N
The distance the water needs to be lifted is 14.5 m. So, the work done by the pump is:
Work = 8232 N x 14.5 m = 119,364 J
Next, we need to calculate the kinetic energy of the water as it is ejected. The formula for kinetic energy is:
Kinetic Energy = 0.5 x mass x velocity^2
Substituting the given values, we get:
Kinetic Energy = 0.5 x 840 kg x (17.4 m/s)^2 = 248,256 J
Finally, we need to add the work done by the pump and the kinetic energy of the water to get the total energy required. So, the correct answer is: A) 217,260 J