Explanation Draw the free body diagram of the steel housing as in Figure 1. Express the volume of the steel housing using the theorem of Pappus and Guldinus. V S = θ × ∑ r ¯ A (I) Here, the generating area is A , perpendicular distance from the axis of revolution to the centroid of the generating area is r ¯ , volume of revolution is V , and angle of revolution measured in radians is r . Since the angle of revolution is measured in radians, θ = 2 π rad Substitute 2 π rad for θ in Equation (I). V S = 2 π × ∑ r ¯ A (II) The complete volume of the full circular part is as follows: V T = V S − n V H (III) Here, volume of the housing is V H and number of holes in the steel housing is n . Express the volume of housing. V H = π r 2 h Here, radius of the steel housing is r and height of the steel housing is h . Substitute π r 2 h for V H in Equation (III). V T = V S − n ( π r 2 h ) (IV) Calculate the total mass of the steel housing. m = ρ V T (V) Therefore, the density of the steel is ρ . Conclusion: Refer to Figure (1) and use spreadsheet to calculate the value of A , r ¯ , and r ¯ A for three segments as shown in Table 1. Segment A ( mm 2 ) r ¯ ( mm ) r ¯ A ( mm 3 ) 1 40 ( 10 ) = 400 40

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 9.3, Problem 111P

To determine

The total mass of the steel housing (m) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.3, Problem 110P

Chapter 9.3, Problem 112P

Students have asked these similar questions

6-49. Determine the distance 7 to the centroid of the shape that consists of a cone with a hole of height h - 50 mm bored into its base. 500 mm 50 mm 150 min

Locate the mass center of the homogeneous solid body whose volume is determined by revolving the shaded area through 360° about the z-axis. Answer: 330 mm 7-4₂²³ 230 mm mm

9-53. Determine the location y of the centroid C of the "roll-formed" member. Neglect the thickness of the material and any slight bends at the corners. Problem 9-53 40 mm 20 mm 40 mm 150 mm

Chapter 9 Solutions

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

Ch. 9.1 - In each case, use the element shown and specify...Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid of the shaded area. Prob....Ch. 9.1 - Locate the center of mass x of the straight rod if...Ch. 9.1 - Locate the centroid of the homogeneous solid...Ch. 9.1 - Locate the centroid z of the homogeneous solid...Ch. 9.1 - Locate the center of mass of the homogeneous rod...Ch. 9.1 - Determine the location (x,y) of the centroid of...Ch. 9.1 - If the rod has a weight per unit length of 100...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The total mass of the steel housing ( m ) .

Solution Summary: The author explains how to express the volume of the steel housing using the theorem of Pappus and Guldinus.

Videos

The total mass of the steel housing (m) .

Want to see the full answer?

Chapter 9 Solutions