ECE390_HW1 - F. A cylindrical coffee cup (8 cm in diameter...

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ECE390 Homework #1 A. Determine the gradient of the scalar field (in cylindrical coordinates): ) 2 cos( ) , , ( z r z r V B. Determine the divergence of the vector field (in Cartesian coordinates): z x P ˆ ˆ ) , , ( 2 xz yz x z y x C. Determine the curl of the vector field (in spherical coordinates): ˆ ) cos( ˆ ) cos( ) sin( ˆ ) cos( 1 ) , , ( 2 θ r P r r r D. Express the unit Farad in base SI units (i.e. m, kg, s, A). E. The flow of water in a pipe is faster in the middle than near the outside. For a 2 cm diameter pipe, given that the velocity of the water as a function of distance from the center of the pipe is: s m cm r r v / 48 . 1 ) / 1 ( ) ( 2 2 Determine the total flow in the pipe in liters/second.
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Unformatted text preview: F. A cylindrical coffee cup (8 cm in diameter and 10 cm tall) is filled to the brim with coffee. Neglecting the weight of the cup, determine the torque at the handle (2 cm from edge of cup) when lifted by a bleary-eyed student. Density of water is 1 gm/cm 3 . Gravity = 9.8 m/s 2 Use integration over the volume of the cup to get the answer. Note: an easier way is to use the center of mass of the cup but then you wouldn’t practice setting up your integral. 8 cm 10 cm 2 cm Find torque about this point....
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This note was uploaded on 01/18/2011 for the course ALS 161 taught by Professor Sfuiaf during the Spring '10 term at American InterContinental University Los Angeles.

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ECE390_HW1 - F. A cylindrical coffee cup (8 cm in diameter...

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