Explanation Given: The specific weight of the material, γ = 90 lb / ft 3 . Show the assembly of the material as in Figure 1. From Figure 1, Compute the moment of inertia of the assembly about an axis passing through the center of mass O . I O = I G + m d 2 = I G + m ( a + b ) 2 (I) Here, the mass of the material is m , the diameter is d , and the moment of inertia about G is I G . Compute the moment of inertia of the assembly about an axis passing through the center of mass G . I G = { 1 2 [ γ g π ( a + b ) 2 e ] ( a + b ) 2 − 1 2 [ γ g π b 2 e ] b 2 + 1 2 [ γ g π ( b ) 2 d ] b 2 − 1 2 [ γ g π ( e ) 2 ( d ) ] e 2 } (II) Here, the acceleration due to gravity is g . Compute the mass of the material. m = γ g π ( b 2 − e 2 ) d + γ g π [ ( a + b ) 2 − b 2 ] e (III) Conclusion: Take the value of g as 32 .2 ft / s 2 . Substitute 32 .2 ft / s 2 for g , 0 .5 ft for a , 0 .25 ft for d , 2 ft for b , 1 ft for e , 1 ft for c , and 90 lb / ft 3 for γ in Equation (II). I G = { 1 2 [ 90 32.2 π ( 0.5 + 2 ) 2 ( 1 ) ] ( 0.5 + 2 ) 2 − 1 2 [ 90 32.2 π ( 2 ) 2 ( 1 ) ] ( 2 ) 2 + 1 2 [ 90 32.2 π ( 2 ) 2 ( 0.25 ) ] ( 2 ) 2 − 1 2 [ 90 32.2 π ( 1 ) 2 ( 0.25 ) ] ( 1 ) 2 } = { ( 0

Engineering Mechanics: Statics, Student Value Edition; Modified Mastering Engineering with Pearson eText -- Standalone Access Card -- for Engineering Mechanics: Statics (14th Edition)

14th Edition

ISBN: 9780134246192

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Clutches, Brakes, Couplings, and Flywheels

The clutch is described as a machine element used to connect or disconnect two shafts together to transmit torque or power. The clutch works on the principles of friction. The clutch is commonly used in automobiles to transfer power from the driving shaf…

Videos

Question

Chapter 10.8, Problem 107P

To determine

The moment of inertia of the assembly about an axis that is perpendicular to the page passing through the center of mass O .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.8, Problem 106P

Chapter 10.8, Problem 108P

Students have asked these similar questions

First monthly exam Gas dynamics Third stage Q1/Water at 15° C flow through a 300 mm diameter riveted steel pipe, E-3 mm with a head loss of 6 m in 300 m length. Determine the flow rate in pipe. Use moody chart. Q2/ Assume a car's exhaust system can be approximated as 14 ft long and 0.125 ft-diameter cast-iron pipe ( = 0.00085 ft) with the equivalent of (6) regular 90° flanged elbows (KL = 0.3) and a muffler. The muffler acts as a resistor with a loss coefficient of KL= 8.5. Determine the pressure at the beginning of the exhaust system (pl) if the flowrate is 0.10 cfs, and the exhaust has the same properties as air.(p = 1.74 × 10-3 slug/ft³, u= 4.7 x 10-7 lb.s/ft²) Use moody chart (1) MIDAS Kel=0.3 Q3/Liquid ammonia at -20°C is flowing through a 30 m long section of a 5 mm diameter copper tube(e = 1.5 × 10-6 m) at a rate of 0.15 kg/s. Determine the pressure drop and the head losses. .μ= 2.36 × 10-4 kg/m.s)p = 665.1 kg/m³

2/Y Y+1 2Cp Q1/ Show that Cda Az x P1 mactual Cdf Af R/T₁ 2pf(P1-P2-zxgxpf) Q2/ A simple jet carburetor has to supply 5 Kg of air per minute. The air is at a pressure of 1.013 bar and a temperature of 27 °C. Calculate the throat diameter of the choke for air flow velocity of 90 m/sec. Take velocity coefficient to be 0.8. Assume isentropic flow and the flow to be compressible. Quiz/ Determine the air-fuel ratio supplied at 5000 m altitude by a carburetor which is adjusted to give an air-fuel ratio of 14:1 at sea level where air temperature is 27 °C and pressure is 1.013 bar. The temperature of air decreases with altitude as given by the expression The air pressure decreases with altitude as per relation h = 19200 log10 (1.013), where P is in bar. State any assumptions made. t = ts P 0.0065h

36 2) Use the method of MEMBERS to determine the true magnitude and direction of the forces in members1 and 2 of the frame shown below in Fig 3.2. 300lbs/ft member-1 member-2 30° Fig 3.2. https://brightspace.cuny.edu/d21/le/content/433117/viewContent/29873977/View

Chapter 10 Solutions

Engineering Mechanics: Statics, Student Value Edition; Modified Mastering Engineering with Pearson eText -- Standalone Access Card -- for Engineering Mechanics: Statics (14th Edition)

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 moment of inertia of the assembly about an axis that is perpendicular to the page passing through the center of mass O .

Solution Summary: The author explains the moment of inertia of the assembly about an axis that is perpendicular to the page and passing through the center of mass O.

Concept explainers

Videos

The moment of inertia of the assembly about an axis that is perpendicular to the page passing through the center of mass O .

Want to see the full answer?

Chapter 10 Solutions