Explanation Given: The density of the material is 7 .85 Mg / m 3 . Subdivide the assembly into 3 parts: Part 1: Circular cone Part 2: Hemispherical segment Part 3: Circular cone As the part (3) is a hole, take it as a negative part. Show the free body diagram of the subdivided segments as in Figure 1. Calculations: From Figure 1, Use similar triangles to obtain the distance z . z 450 mm + z = 100 mm 300 mm z 0.45 m + z = 0.1 m 0.3 m 0.3 z = 0.1 ( 0.45 + z ) 0.3 z = 0.045 + 0.1 z z = 0.225 m Calculate the mass of first segment. m 1 = ρ V 1 = ρ [ 1 3 π r 2 h ] (I) Here, the density is ρ , the radius is r , the volume of mass 1 is V 1 and the height is h . Substitute 7 .85 Mg / m 3 for ρ , 0 .3 m for r , and ( 0.45 + 0.225 ) m for h in Equation (I). m 1 = ( 7 .85 Mg / m 3 ) [ 1 3 π ( 0.3 ) 2 ( 0.45 + 0.225 ) m ] = ( 7.85 × 10 3 kg / m 3 ) [ 1 3 π ( 0.3 ) 2 ( 0.675 m ) ] = ( 7.85 × 10 3 kg / m 3 ) ( 0.06361 m 3 ) = 499.395 kg Calculate the mass of second segment. m 2 = ρ V 2 = ρ [ 2 3 π r 3 ] (II) Here, the volume of mass 2 is V 2 . Substitute 7 .85 Mg / m 3 for ρ and 0 .3 m for r in Equation (II). m 2 = ( 7 .85 Mg / m 3 ) [ 2 3 π ( 0 .3 m ) 3 ] = ( 7 .85 × 10 3 kg / m 3 ) ( 0.05654 m 3 ) = 443.90 kg Calculate the mass of third segment

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 10.8, Problem 102P

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The mass moment of inertia of the assembly about the z-axis.

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Chapter 10.8, Problem 101P

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The mass moment of inertia of the assembly about the z- axis.

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