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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Solve Exercise 24 if the tank is half full of oil that has a density of 900  kg/m 3 .

To determine

To find:

The work required to pump the water out of the spout.

Explanation

1) Concept:

The work is calculated by using the formula W=abf(x)dx

And weight=gravity·volume

2) Given:

3) Calculation:

Let the circular disk slice of water have thickness x m .

It is lying at the coordinate x with radius r=9-x2 m

The given tank is half full of oil, therefore, the lower limit changes from -3 to 0 and the density of oil is 900 kg/m3

Volume of the slice of oil  =πr2 x m3=π9-x22x m3=π9-x2x m3

Therefore, the weight of the slice is =g·density·volume=9.8×900π9-x2x  N

This weight is lifted by the pump about x+4m.

Therefore, the work needed to pump the water out of the spout is

=9.8×900x+4π9-x2x J

Therefore, the total work reqiured is

W=abf(x)dx

W039

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