Set 14 Solutions.pdf

# Set 14 Solutions.pdf - ESE 318-02 Fall 2018 Homework Set#14...

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ESE 318-02, Fall 2018 Homework Set #14 Due Dec.11, 2018 1 . Zill9.14.6. (The curl is a bit tedious to take, but it simplifies a lot.) 2 . Zill9.14.8. 3 . Zill 9.14.10.(Note: both the upward and downward curves are along z = 9 - y 2 . Use a calculator to do the final piece of arithmetic.) 4 . Find the work integral over the closed path as indicated. 1 and 4 : , 3 , 3 2 2 z y x C z x y d C F r F 5. Find the work integral over the closed path as indicated. 0 , 1 , 0 to back 0 , 1 , 1 to 1 , 0 , 1 to 1 , 0 , 0 to 0 , 1 , 0 : 0 , sin , cos C y y d C F r F 6 . Let xz x z 2 , , 2 2 F . Let C be the curve that goes in straight line segments from (0,0,3) to (4,2,2) to (4,4,0) to (0,2,1) and back to (0,0,3). (These 4 points are coplanar and the curve C traces out a parallelogram.) Find the workintegral C d r F . 7 . Zill9.16.4. 8 . Zill9.16.5. 9 . Zill9.16.6. 10 . Zill9.16.8. 11 . Zill9.16.9. 12 . Zill 9.16.14. 13 .(This is a standard flux integral, for review purposes.) Find the flux of yz yze x y , , 16 3 3 F out of the portion of the surface 4 4 : 2 2 y x S , where 1 0 and 0 , 0 z y x .What is the (general) direction of that flux?

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ESE 318-02, Fall 2018 1 . Zill 9.14.6. (The curl is a bit tedious to take, but it simplifies a lot.) k j i F xy z xy x z xy y z sin 2 cos 1 cos 2 2 The curve is the wire frame. The surface is the slanted rectangular region. But the region of integration is the flat rectangle in the xy plane. 3 2 3 1 1 0 3 3 1 1 0 2 2 0 1 0 2 0 2 0 0 2 2 2 2 2 2 2 2 2 0 2 1 2 1 1 ˆ ˆ ˆ curl 1 ˆ 0 ˆ 2 ˆ , 0 , 2 cos sin cos 1 sin cos 2 cos 2 cos 1 2 cos 2 sin 2 cos 1 cos curl 1 0 1    y dy y dx dxdy y dxdy R y z Q x z P dS d y z R Q xz P z xz xy z xy yx z xy z xy y x z xy yz xy yz xy zx xy zx xy z xy x z xy y z z y x y z x z y z R S C n F r F k j i k j i F (You could have noticed that , and not bothered to find . But that still left a lot of tedium to find and especially .) 0 x z P ˆ Q ˆ R ˆ
ESE 318-02, Fall 2018 2 . Zill9.14.8.        36 4 9 4 9 2 4 9 9 Also 36 2 4 9 Area 9 9 3 4 2 3 2 2 3 , 2 , 2 3 2 2 2 3 2 curl 2 1 2 4 , 2 , 3 , 2 2 0 2 2 0 2 0 2 4 0 2 1 triangle       y y dy y dxdy dA dxdy dxdy y z x z dS curl d z y y x z x z y x y z x z y x y x f z z y y x z x y R R R S C n F r F k j i k j i F F

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ESE 318-02, Fall 2018 3 . Zill 9.14.10.(Note: both the upward and downward curves are along

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