Explanation Given: The centroid of the differential element along the x , y , and z axis are x ˜ , y ˜ , and z ˜ , respectively. The mass of each segment is represented by m . The density of material 1, ρ 1 = 2.70 Mg m 3 . The density of material 2, ρ 2 = 5.70 Mg m 3 . The density of material 3, ρ 3 = 7.80 Mg m 3 . Convert the unit of density for material 1 from Mg m 3 to kg mm 3 . ρ 1 = 2.70 Mg m 3 = 2.70 Mg m 3 × ( 10 3 mm ) 3 m 3 × 10 3 kg Mg = 2.70 × 10 − 6 kg mm 3 . Convert the unit of density for material 2 from Mg m 3 to kg mm 3 . ρ 2 = 5.70 Mg m 3 = 5.70 Mg m 3 × ( 10 3 mm ) 3 m 3 × 10 3 kg Mg = 5.70 × 10 − 6 kg mm 3 . Convert the unit of density for material 3 from Mg m 3 to kg mm 3 . ρ 3 = 7.80 Mg m 3 = 7.80 Mg m 3 × ( 10 3 mm ) 3 m 3 × 10 3 kg Mg = 7.80 × 10 − 6 kg mm 3 . Show the block is divided into three segments as shown in Figure (1). Determine the location of the center of gravity of the steel and aluminum plate along the x axis ( x ¯ ) using the relation, x ¯ = ∑ x ˜ m ∑ m (I) Here, the total mass is ∑ m . Determine the location of the center of gravity of the steel and aluminum plate along the y axis ( y ¯ ) using the relation, y ¯ = ∑ y ˜ m ∑ m (II) Determine the location of the center of gravity of the steel and aluminum plate along the z axis ( z ¯ ) using the relation, z ¯ = ∑ z ˜ m ∑ m (III) Conclusion: Refer to Figure (1) and use the spreadsheet to calculate the value of x ˜ m for the three segments as shown in Table (1). Materials m ( kg ) = ρ A d x ˜ ( mm ) x ˜ m ( kg ⋅ mm ) 1 ( ρ 1 ) 1 2 ( l ) ( b ) h = [ ( 2.70 × 10 − 6 ) 1 2 ( 30 ) ( 60 ) ( 20 ) ] = 0.0486 10 0.486 2 ( ρ 2 ) ( l ) ( b ) h = [ ( 5.70 × 10 − 6 ) ( 40 ) ( 60 ) ( 20 ) ] = 0.2736 10 2.736 3 ( ρ 3 ) ( l ) ( b ) h = [ ( 7.80 × 10 − 6 ) ( 60 ) ( 60 ) ( 20 ) ] = 0

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 9.2, Problem 79P

To determine

The location (x¯,y¯,z¯) of the center of mass of the block.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 78P

Chapter 9.2, Problem 80P

Students have asked these similar questions

please solve this problem for me the best way that you can explained to solve please show me the step how to solve

plese solbe this problem and give the correct answer solve step by step find the forces and line action

please help me to solve this problems first write the line of action and them find the forces {fx=0: fy=0: mz=0: and them draw the shear and bending moment diagram. please explain step by step

Chapter 9 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

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 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P

Knowledge Booster

The location ( x ¯ , y ¯ , z ¯ ) of the center of mass of the block.

The location (x¯,y¯,z¯) of the center of mass of the block.

Want to see the full answer?

Chapter 9 Solutions