Work done to lift a mass of water

[henry3369]

Homework Statement

A pump is required to lift 800 kg of water (about 210 gallons) per minute from a well 14.0 m deep and eject it with a speed of 18 m/s
(a) How much work is done per minute in lifting the water?
(b) How much work is done in giving the water the kinetic energy it has when ejected?

Homework Equations

Work = change in energy

The Attempt at a Solution

I don't understand the different between part a and part b.
Wouldn't the work done to lift it also be the work done to give it the final kinetic energy?

W = -ΔU or ΔK

 

[Doc Al]

I don't understand the different between part a and part b.
Wouldn't the work done to lift it also be the work done to give it the final kinetic energy?

They are breaking the total work required into two pieces:
(a) How much work is required just to lift the water? (Without imparting any kinetic energy.)
(b) How much additional work is needed to give it some kinetic energy?

 

[henry3369]

They are breaking the total work required into two pieces:
(a) How much work is required just to lift the water? (Without imparting any kinetic energy.)
(b) How much additional work is needed to give it some kinetic energy?

(a) W = mgh
(b) W = (1/2)mv^2

Ok so I got those two. The next question asks for the total power output of the pump.
It seems that the answer comes from adding (a) and (b) then dividing by 60 seconds.
I'm confused because:
P = Net Work / time
Net Work = -ΔU or ΔK, and the former gives (a) while the latter gives (b).

Additionally, I tried using conservation of energy with nonconservative forces:
Ki + Ui + Wnc = Kf + Uf
Wnc = Kf + Uf. Using this for the power equation gives the correct answer, but this is the work due to ONLY the nonconservative forces. If I want to find the total power output, wouldn't I need net work?

 

[henry3369]

They are breaking the total work required into two pieces:
(a) How much work is required just to lift the water? (Without imparting any kinetic energy.)
(b) How much additional work is needed to give it some kinetic energy?

I found another post that explained that work is actually the change in total mechanical energy. So does that mean Wnc = Net Work?

 

[Doc Al]

If I want to find the total power output, wouldn't I need net work?

So does that mean Wnc = Net Work?

Yes and yes.

I would put it this way: The net work done must equal the change in mechanical energy (ΔU + ΔKE) of the water. (We are ignoring details like friction and so on.)

 

[ElainaJeansonne]

Think about it this way, it is not just lifting that water and then moving it, the pump performs a constant process in which it is both lifting some water while pushing the last water it lifted at the same time... if it was just talking about a specific 800kg of water it would be different, but the pump has water constantly moving, i had the same question in my study guide and that is how i thought about it after we went over the answers

 

[kuruman]

Thank you for your contribution. Please note that this thread is 8 years old.