# Math 204--Calculus III: Project 1, Fall 1998

## A Little Manufacturing...

### by Gavin LaRose (glarose@umich.edu), Nebraska Wesleyan University, September 1998

©1998 Gavin LaRose (glarose@umich.edu)
permission granted to use and distribute free in an academic setting.

PostScript version of project

### Chemproc, Inc.

20000 Ryan-ears Blvd.
Lonlinc, SK 08685

9 September 1998

Sophisticated and Independent Mathematical Contractors (SIMaC), Inc.
Suite 5, Strawmarket Business Plaza
Lonlinc, SK 04685

Dear SIMaC:

Continuing to be a leader in the manufacture of all manner of chemical products, Chemproc, Inc. is proud to be the sole creator of the anti-scratch conduction-enhancing microchip coating known by its development name ``ChipLess.'' As part of our contract to supply this to leading chip manufacturers such as Telin and MIB, we are also formulating an appropriate process by which the coating is to be applied to the chips in question, and it is to assist in this that we are contacting you.

In the process, rectangular chips will be coated by passing them through a vertical spray as shown in figure 1. To avoid complications with possible coating by the splashing of the spray from other surfaces the chips are to move through the line magnetically levitated at some height H above the surface of the process line, and to ensure that the coating is completely uniform the chips should pass through the spray at a precisely horizontal orientation.

 Figure 1: production process Figure 2: non-horizontal chip

Because of the requirement of the horizontal orientation, we need to be able to determine if the chip deviates from this, as shown in figure 2. We are able to measure the projected area B of the chip's area A on the process line, and would like to use this information to correct any errors in the chip's orientation---if this is insufficient to accomplish the correction, we need to know what additional measurements we could take that would allow it. Adjustments in the orientation of the chip produced by the levitation system are accomplished by describing how the vector normal to the chip, n, should change, and your work should therefore describe how this should be changed to right chips that are incorrectly oriented.

We look forward to receiving your final report of 3--7 pages on or before the 28th of September. To assure your success in your work, our not-so-senior scientist-with-an-attitude, Dr. P. Gavin LaRose, has agreed to answer any questions you may have in the course of your investigation. He has also suggested that it may be useful to initially consider the case in which the chip is tilted in only one direction. Please note that he will be unavailable to assist with this project over the weekend of the 25th--27th. You should plan on meeting with him during or before the week of the 14th of September to verify your initial progress. We have made available, through him, a number of sample reports that may prove useful as you develop your report.

Sincerely
E. Idu Pont
President, Chemproc, Inc.

eip:glr

Gavin's Calc III Project 1, Fall 1998
Last Modified: Thu Nov 12 22:19:40 CST 1998