Explanation Work is defined as the amount of energy needed to perform any physical 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 an upward conical tank having the radius as 5 m and height as 10m 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 vertex of the inverted conical tank, such that positive y-axis points upward. The radius of a layer of water at the height of y The area of the layer of water in the conical tank is given as A r e a = π ( y 2 ) 2 m 2 Thus, the volume of one layer of water is given as V o l u m e = π ( y 2 ) 2 Δ y m 3 Hence, the force required to lift each layer of water is F o r c e = ( 1000 ) ( π [ y 2 ] 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 20E

To determine

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

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Chapter 6.5, Problem 19E

Chapter 6.5, Problem 21E

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

Solution Summary: The author explains that the work required for pumping all of the water out of a conical tank through the spout is 1.155 10 7 J o u l e

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

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Chapter 6 Solutions

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

Solution Summary: The author explains that the work required for pumping all of the water out of a conical tank through the spout is 1.155 10 7 J o u l e

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

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Chapter 6 Solutions

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