Explanation Work is referred to as the amount of energy that is required to perform any substantial task. If constant force is applied, then the work is simply given by the following equation W = F × d Where W = W o r k d o n e F = C o n s t a n t F o r c e d = d i s t a n c e t h r o u g h w h i c h t h e f o r c e a c t s If the force applied is not constant and changes over time, then integral equation is used to calculate the work done. W = ∫ x = a x = b f ( x ) d x Where, W = W o r k d o n e f ( x ) = f o r c e a s a f u n c t i o n o f d i s t a n c e x = d i s t a n c e t h r o u g h w h i c h t h e f o r c e a c t s Given: Given a hemispherical tank having radius as 10 m. Also, the density of water is 1000 k g / m 3 Formula Used: We know that force is given as F = m a or F = m g , where is acceleration due to gravity. Also, Mass, m = V D , where V is the volume of the object and d is the density. Thus, force is given as F = D V g Calculation: Let us place the origin at the center of the hemispherical tank, such that positive y-axis points downward. The radius of a layer of water at any depth y is given as 100 − y 2 Thus, the volume of one layer of water is given as V o l u m e = π ( 100 − y 2 ) Δ y m 3 Hence, the force required to lift each layer of water is F o r c e = ( 1000 ) ( π [ 100 − y 2 ] Δ y ) ( 9...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.5, Problem 19E

To determine

The work done (in Joules) required to pump all of the water out of the full tank if the density of the water is $1000 k g / m^{3}$ . Given that tank has the hemispherical shape and water exits through the spout.

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Chapter 6.5, Problem 18E

Chapter 6.5, Problem 20E

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The work done (in Joules) required to pump all of the water out of the full tank if the density of the water is 1000 k g / m 3 . Given that tank has the hemispherical shape and water exits through the spout.

Solution Summary: The author explains that the work required to pump all of the water out of a hemispherical tank through the spout is 1.18 10 8 J o u l e

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The work done (in Joules) required to pump all of the water out of the full tank if the density of the water is $1000 k g / m^{3}$ . Given that tank has the hemispherical shape and water exits through the spout.

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Chapter 6 Solutions

The work done (in Joules) required to pump all of the water out of the full tank if the density of the water is 1000 k g / m 3 . Given that tank has the hemispherical shape and water exits through the spout.

Solution Summary: The author explains that the work required to pump all of the water out of a hemispherical tank through the spout is 1.18 10 8 J o u l e

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The work done (in Joules) required to pump all of the water out of the full tank if the density of the water is 1000 kg/m3. Given that tank has the hemispherical shape and water exits through the spout.

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Chapter 6 Solutions

The work done (in Joules) required to pump all of the water out of the full tank if the density of the water is $1000 k g / m^{3}$ . Given that tank has the hemispherical shape and water exits through the spout.