Motion System Design
Fun With Fundamentals: Problem 222

Fun With Fundamentals: Problem 222

Braggin' Wagon
Problem 222
– Has Louie's luck run out? You decide according to this month's problem submitted by Richard Lewison of Pocahontas, Ia.

"Lucky" Louie just finished rebuilding the engine of his infamous "Draggin' Wagon," and he drove down to the Frosty Mug rootbeer stand to show it off to his buddies. As a crowd gathered, Louie boasted "How many other cars can produce 5000 lb-in. of front axle torque?" Just then, Walter W. Wussmeister II, employee of the month at the Frosty Mug, steps forward and says: "That sounds impressive Louie, but $50 says your ride doesn't have enough muscle to climb over these trays." As Louie's face reddens, he grabs the money out of Walter's hand and tells him to put the trays on the pavement. The trays are 3/4 in. thick. Is Louie making a smart bet? See the diagram for further information. What is the maximum thickness of trays Louie's "Draggin' Wagon" can climb over? (Neglect flattening or deflection of the tire and use the full 12 in. diameter).

Solution to November's problem 221 – You read the ending if you answered 1176 pages and 50 covers. Here's the final chapter:

The figure shows how the books were stacked side-by-side. You can see that the page at the extreme left end is page 100 of the A volume, not page 1. Similarly, the page at the extreme right end is page 1 of the Z volume, not page 100.

It is stated in the problem that the bookworm starts out on page 1 of the A volume and finishes at page 100 of the Z volume. Remember, the pages in a book are double-sided. When the worm eats through page 1, it also eats through page 2 on the other side, in other words, pages 1 and 2 make up one page.

The total number of pages and covers, then, that the worm eats through include the front cover of the A volume, all the pages and all covers (2 each) of volumes B through Y, and the back cover of volume Z. Mathematically, 2 covers + (2 x 24 volumes) = 50 covers total. Also, the worm eats all of the pages in volumes B through Y, so, 24 volumes x (98 page numbers per volume ÷ 2 page numbers per page) or 1176 pages.

Wurme's next book sale was greatly discounted.

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