Container of Water Work Problem

AI Thread Summary
To calculate the work required to pump water from a container with a volume defined by y=x^4, it's essential to express both force and distance correctly. The force can be determined using the formula F = VDg, where V is the volume of water, D is the distance the water needs to be lifted, and g is the acceleration due to gravity. The user struggles with integrating the volume and distance, specifically stating that they used VD = (pi/16)y^3dy, indicating a misunderstanding in the setup of the integral. Clarification on how to properly express these variables is needed to proceed with the calculation. Understanding the relationship between force, distance, and the volume of the tank is crucial for solving the work problem.
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!
 
W = FD
F = VDg
W = \int (1000)(9.8)(V)(D)


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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