EBK MATHEMATICS FOR MACHINE TECHNOLOGY
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 63, Problem 11A

Solve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified.

A brass casting is in the shape of a right circular cone with a base diameter of 8.26 centimeters and a height of 18.36 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.

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2. Derive the component transformation equations for tensors shown be- low where [C] = [BA] is the direction cosine matrix from frame A to B. B[T] = [C]^[T][C]T 3. The transport theorem for vectors shows that the time derivative can be constructed from two parts: the first is an explicit frame-dependent change of the vector whereas the second is an active rotational change of the vector. The same holds true for tensors. Starting from the previous result, derive a version of transport theorem for tensors. [C] (^[T])[C] = dt d B dt B [T] + [WB/A]B[T] – TWB/A] (10 pt) (7pt)
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of prove- Let (X, Td) be aspace. show that if A closed set in X and r & A, thend (r,A) +0
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