To determine Calculate the mass and center of mass x ¯ of the linear wire. Explanation Given information: The density of wire is δ ( x ) = 1 x + 1 . The interval is 0 ≤ x ≤ 3 . Calculation: Consider the typical piece of length dx . Calculate the mass of the piece as shown below. m = δ ( x ) d x Substitute 1 x + 1 for δ ( x ) . m = ( 1 x + 1 ) d x Calculate the mass of the linear wire as shown below. Mass = ∫ 0 3 ( 1 x + 1 ) d x = ( ln | x + 1 | ) 0 3 = ( ln | 3 + 1 | − ln | 0 + 1 | ) = ln 4 Hence, the mass of the linear wire is ln 4 _ . Calculate the moment about the origin as shown below. Moment = Distance × mass = x ( 1 x + 1 ) d x = ( x x + 1 ) d x Calculate the moment along the linear wire as shown below

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 6.6, Problem 3E

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Calculate the mass and center of mass x¯ of the linear wire.

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Chapter 6.6, Problem 2E

Chapter 6.6, Problem 4E

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