Explanation Given information: The thickness ( t ) of sheet steel is 2 mm The density ( ρ ST ) of steel is 7 , 850 kg / m 3 . Calculation: Sketch the sheet steel as shown in Figure 1. Find the mass of rectangular section 1 as shown in below: m 1 = ρ V 1 (1) Here, V 1 is volume of rectangular section 1. Express the volume of rectangular section 1 as follows: V 1 = l w t Substitute 120 mm for l , 200 mm for w , 7 , 850 kg / m 3 for ρ , and 2 mm for t in Equation (1). m 1 = 7 , 850 × [ 120 mm ( 1 m 10 3 m ) × 200 mm ( 1 m 10 3 m ) × 2 mm ( 1 m 10 3 m ) ] = 7 , 850 ( 0.120 × 0.200 × 0.002 ) = 7 , 850 ( 0.000048 ) = 0.3768 kg Find the mass of rectangular section 2 as shown in below: m 2 = ρ V 2 (2) Here, V 2 is volume of rectangular section 2. Express the volume of rectangular section 2 as follows: V 2 = l w t Substitute 120 mm for l , 100 mm for w , 7 , 850 kg / m 3 for ρ , and 2 mm for t in Equation (2). m 2 = 7 , 850 × [ 120 mm ( 1 m 10 3 m ) × 100 mm ( 1 m 10 3 m ) × 2 mm ( 1 m 10 3 m ) ] = 7 , 850 ( 0.120 × 0.100 × 0.002 ) = 7 , 850 ( 0.000024 ) = 0.1884 kg Find the centroid of section 1 about x axis ( x 1 ) as shown below: ( x 1 ) = 100 mm = 100 mm ( 1 m 10 3 mm ) = 0.1 m Find the centroid of section 2 about x axis ( x 2 ) as shown below: ( x 2 ) = 200 mm = 200 mm ( 1 m 10 3 mm ) = 0.2 m Find the centroid of section 1 about y axis ( y 1 ) as shown below: ( y 1 ) = − 120 2 = − 60 mm ( 1 m 10 3 mm ) = − 0.06 m Find the centroid of section 2 about y axis ( y 2 ) as shown below: ( y 2 ) = − 120 2 = − 60 mm ( 1 m 10 3 mm ) = − 0.06 m Find the centroid of section 1 about z axis ( z 1 ) as shown below: ( z 1 ) = 100 mm ( 1 m 10 3 mm ) = 0.1 m Find the centroid of section 2 about z axis ( z 2 ) as shown below: ( z 2 ) = 50 mm ( 1 m 10 3 mm ) = 0

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 9.6, Problem 9.154P

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Find the mass products of inertia Ixy,Iyz, and Izx of the machine component.

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Chapter 9.6, Problem 9.153P

Chapter 9.6, Problem 9.155P

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A section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass products of inertia Ixy, Iyz, and Izx of the component.

A 2-mm-thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass moment of inertia of the component with respect to each of the coordinate axes.

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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - Prob. 9.3P Ch. 9.1 - Prob. 9.4P Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.7P Ch. 9.1 - Prob. 9.8P Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P

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Find the mass products of inertia I x y , I y z , and I z x of the machine component.

Solution Summary: The author calculates the mass products of inertia of the machine component.

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Find the mass products of inertia Ixy,Iyz, and Izx of the machine component.

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