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CALCULUS 265 Honors
Fall Semester 2000
8:00 to 8:50 MTTF
Carver 0002

Instructor: Hentzel
Office: 432 Carver
Office Hours: 9:00-10:00 MTTF

E-mail  hentzel@iastate.edu
phone  294-8141
Website

http://www.math.iastate.edu/hentzel/honors.265

Friday, October 20:    Section 14.6
p1048:27
p1049:35

previous assignment:
p1048:6,9,17,23

Main idea:  Weight each little surface fragment and add them up. 

Key words:   F.N dS, Flux, Flow, buoyancy, Mobius Strip.

Goal:  Compute a Surface integral. 

Mobius Strip:  Not Orientable Surface;

Hydrostatic pressure is perpendicular to the surface and

proportional to the depth.

The force of buoyancy is equal to the weight of water displaced

and passes through the centroid.

Consider a 1/2 sphere half way submerged.
               .....                 
               |       .       
               |         .
               |          .
               |          .
---------------|          .------------
               |          .
               |         .
               |       .
               |.....      
 
(a)  Find the volume submerged. 

(b)  Compute the centroid of the area below the water line.

(c)  Integrate the hydrostatic pressure over the surface.

(d)  Find the centroid of the whole half sphere.

(e)   Which way will it tilt?  Will it tend to rotate 

rounded part down or flat part down?  Explain why?