Explanation Given information: The weight per unit length of wire is w . Calculation: Sketch the brass wire as shown in Figure 1. Express the mass of each component as shown below: m = W g = 1 g w L Here, w is a weight per unit length. Find the mass of component 1 as follows: m 1 = W g ( L ) (1) Substitute ( π × 3 2 a ) for L in Equation (1). m 1 = w g ( π × 3 2 a ) = 3 2 π w g a Find the mass of component 2 as follows: m 2 = w g ( L ) (2) Substitute ( 3 a ) for L in Equation (2). m 2 = w g ( 3 a ) = 3 w g a Find the mass of component 3 as follows: m 3 = w g ( L ) (3) Substitute ( π × a ) for L in Equation (3). m 3 = w g ( ( π × a ) ) = π w g a Find the centroid section ( x 1 ) as shown below: ( x 1 ) = − 2 π ( 3 2 a ) Find the centroid section ( y 1 ) as shown below: ( y 1 ) = 2 a Find the centroid section ( z 1 ) as shown below: ( z 1 ) = 1 2 a Find the total section ( m x ¯ y ¯ ) 1 as shown below: ( m x ¯ y ¯ ) 1 = − 2 π ( 3 2 a ) ( 2 a ) ( 1 2 a ) Similarly calculate the remaining values as shown in Table 1. m x ¯ y ¯ z ¯ m x ¯ y ¯ m y ¯ z ¯ m x ¯ z ¯ 1 3 2 π w g a − 2 π ( 3 2 a ) 2 a 1 2 a − 9 w g a 3 3 2 π w g a 3 − 9 4 w g a 3 2 3 w g a 0 1 2 a 2 a 0 3 w g a 3 0 3 π w g a 2 π a a a − 2 w g a 3 π w g a 3 2 w g a 3 ∑ − 11 w g a 3 w g ( π 2 + 3 ) a 3 − 1 4 w g a 3 Find the mass products of inertia I x y of the machine component. I x y = ∑ ( I x ′ y ′ + m x ¯ y ¯ ) = ( ( I x ′ y ′ ) 1 + ( I x ′ y ′ ) 2 + ( I x ′ y ′ ) 3 + ( m x ¯ y ¯ ) ) (4) Substitute 0 for ( ( I x ′ y ′ ) 1 + ( I x ′ y ′ ) 2 + ( I x ′ y ′ ) 3 ) and − 11 w g a 3 for ∑ ( m x ¯ y ¯ ) in Equation (4)

12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Moment of Inertia

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…

Videos

Question

Chapter 9.6, Problem 9.160P

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.6, Problem 9.159P

Chapter 9.6, Problem 9.161P

Students have asked these similar questions

Derive the equation below ah ap ax 12μ ax, +( ah ap ay 12μ ay Where P P (x, y) is the oil film pressure. 1..ah 2 ax

Can you determine the eignevalues by hand?

Monthly exam 13 2021-2022 Power plant Time: 1.5 Hrs Q1. A The gas-turbine cycle shown in Fig. is used as an automotive engine. In the first turbine, the gas expands to pressure Ps, just low enough for this turbine to drive the compressor. The gas is then expanded through the second turbine connected to the drive wheels. The data for the engine are shown in the figure, and assume that all processes are ideal. Determine the intermediate pressure Ps, the net specific work output of the engine, and the mass flow rate through the engine. Find also the air temperature entering the burner T3 and the thermal efficiency of the engine. Exhaust Air intake Φ www Regenerator www Bumer Compressor Turbine Power turbine et 150 kW Wompressor P₁ = 100 kPa T₁ = 300 K PP₁ =60 P-100 kPa T₁ = 1600 K Q2. On the basis of a cold air-standard analysis, show that the thermal efficiency of an ideal regenerative gas turbine can be expressed as 77 = 1- where - () () гp is the compressor pressure ratio, and T₁ and…

Chapter 9 Solutions

VECTOR MECH. FOR EGR: STATS & DYNAM (LL

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.