Explanation Given Information: The figure shows a non-uniform rod with varying linear density. Concept Used: Use the definition of the center of mass for a continuous object to find the location of center of mass of the non-uniform rod. If the mass is continuously distributed, the center of mass is, M r → c m = ∫ r → d m Here, M is the mass of the rod. Length of the non-uniform rod in centimeters is, x = 0.40 m = ( 0.40 m ) ( 100 cm 1 m ) = 40 cm Consider a small mass d m of length d x of non-uniform rod. The linear density of the non-uniform rod is, μ ( x ) = d m d x The x-coordinate of the center of mass of me non-uniform rod is, x c m = ∫ x d m ∫ d m = ∫ x μ ( x ) d x ∫ μ ( x ) d x By symmetry, the y-coordinate of the center of mass of the non-uniform rod is y c m = 0 The linear variation in the density of the non-uniform rod is μ ( x ) = 1.00 g/cm + ( 5.00 g/cm − 1.00 g/cm 0.40 m ( 100 cm 1 m ) ) ( x − 0 ) = 1.00 g/cm + ( 0.10 g/cm 2 ) x Substitute 1.00 g/cm + ( 0.10 g/cm 2 ) x for μ ( x ) in equation x c m = ∫ x μ ( x ) d x ∫ μ ( x ) d x . x c m = ∫ 0 40 c m x μ ( x ) d x ∫ 0 40 c m μ ( x ) d x = ∫ 0 40 cm x [ 1

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ISBN: 9781429281843

Author: Tipler

Publisher: MAC HIGHER

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Chapter 5, Problem 110P

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To Find:The location of the center of mass.

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Chapter 5, Problem 109P

Chapter 5, Problem 111P

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The location of the center of mass.

Solution Summary: The author explains that the figure shows a non-uniform rod with varying linear density.

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