Container of Water Work Problem

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Homework Help Overview

The problem involves calculating the work required to pump water out of a container shaped by the volume function y=x^4, specifically from y=0 to y=16 meters. The context is centered around understanding the relationship between force, distance, and work in a fluid mechanics scenario.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formulation of work as the integral of force times distance, with specific inquiries about how to express force and distance in this context. There are attempts to clarify the variables involved, such as the force and the volume of water.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the original poster's approach and the expressions used for force and distance. Some guidance has been offered regarding the formulation of work, but there is no explicit consensus on the correct method or resolution of the problem.

Contextual Notes

Participants note the need for more information about the original poster's calculations to identify potential errors. There is an emphasis on the importance of clearly defining the variables involved in the work calculation.

Richter915
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You have a container which has the volume of y=x^4 from y=0 to y=16. This tank is filled with water...how much work is required to pump all of the water out of this 16 meter tall tank. I'm not too sure where I went wrong here because I know work is the integral of Force times Distance. Please help, thanks.
 
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What is the force in this case? And what is the distance? How can you express the force and the distance?

Jameson
 
It is impossible for us to tell you where you went wrong if you don't tell us what you did!
 
[tex]W = FD[/tex]
[tex]F = VDg[/tex]
[tex]W = \int (1000)(9.8)(V)(D)[/tex]


This is where I run into a problem...I put that VD equals (pi/16)y^3dy. I really am not sure what to do from here because that's where my mistake is. Please help.
 

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