A rectangular beam will be cut from a cylindrical log of radius 10 inches. (a) Show that
Question:
(a) Show that the beam of maximal cross-sectional area is a square.
(b) Four rectangular planks will be cut from the four sections of the log that remain after cutting the square beam. Determine the dimensions of the planks that will have maximal cross-sectional area.
(c) Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.
10 depth - width H
Step by Step Answer:
a dA dx y 0 x y 100 2 The crosssectional area of the rectangular beam is A 2x 2y 4xy 4x 100x0 x 10 ...View the full answer
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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