Work done to lift a mass of water

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Homework Help Overview

The discussion revolves around a physics problem involving the work done by a pump to lift water from a well and impart kinetic energy to it. The specific context includes lifting 800 kg of water from a depth of 14.0 m and ejecting it at a speed of 18 m/s.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the distinction between the work done to lift the water and the work done to give it kinetic energy. There is confusion regarding whether these two components of work can be considered separately or if they are part of a total work calculation.

Discussion Status

Participants are actively questioning the separation of work into lifting and kinetic energy components. Some have suggested that the net work done should equal the change in mechanical energy, while others are exploring the implications of nonconservative forces in the context of power output.

Contextual Notes

There is an ongoing discussion about the assumptions related to the continuous operation of the pump and how this affects the interpretation of work done over time. Participants are also considering the implications of ignoring factors such as friction in their calculations.

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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
 
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henry3369 said:
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?
 
Doc Al said:
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?
 
Doc Al said:
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?
 
henry3369 said:
If I want to find the total power output, wouldn't I need net work?

henry3369 said:
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.)
 
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
 
Thank you for your contribution. Please note that this thread is 8 years old.
 
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