Explanation Draw the free-body diagram of the shaded area as in Figure (1). Write the equation to find y as follows: y = k x 2 (1) Apply the boundary condition. When x = 2 a ; y = h . Substitute h for y and 2 a for x in Equation (1). h = k ( 2 a ) 2 k = h 4 a 2 Substitute h 4 a 2 for k in Equation (1). y = h 4 a 2 x 2 Consider a small strip as in Figure 1. Find the area of the small strip with respect to x -axis as follows: d A = y d x Substitute h 4 a 2 x 2 for y . d A = h 4 a 2 x 2 d x Integrate the equation and apply the limits. ∫ d A = ∫ a 2 a h 4 a 2 x 2 d x A = h 4 a 2 [ x 3 3 ] a 2 a = h 4 a 2 [ ( 2 a ) 3 3 − a 3 3 ] = h 4 a 2 [ 7 a 3 3 ] = 7 a h 12 Find the change in moment of inertia with respect to x -axis using the relation. d I x = 1 3 y 3 d x Substitute h 4 a 2 x 2 for y . d I x = 1 3 ( h 4 a 2 x 2 ) 3 d x = h 3 x 6 192 a 6 d x Integrate the equation and substitute the limits in x -axis

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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 9.1, Problem 9.16P

To determine

The moment of inertia and radius of gyration of the shaded area with respect to the x axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.1, Problem 9.15P

Chapter 9.1, Problem 9.17P

Students have asked these similar questions

This is an old practice exam. Fce = 110lb and FBCD = 62 lb but why

Quiz/An eccentrically loaded bracket is welded to the support as shown in Figure below. The load is static. The weld size for weld w1 is h1 = 4mm, for w2 h2 = 6mm, and for w3 is h3 =6.5 mm. Determine the safety factor (S.f) for the welds. F=29 kN. Use an AWS Electrode type (E100xx). 163 mm S 133 mm 140 mm Please solve the question above I solved the question but I'm sure the answer is wrong the link : https://drive.google.com/file/d/1w5UD2EPDiaKSx3W33aj Rv0olChuXtrQx/view?usp=sharing

Q2: (15 Marks) A water-LiBr vapor absorption system incorporates a heat exchanger as shown in the figure. The temperatures of the evaporator, the absorber, the condenser, and the generator are 10°C, 25°C, 40°C, and 100°C respectively. The strong liquid leaving the pump is heated to 50°C in the heat exchanger. The refrigerant flow rate through the condenser is 0.12 kg/s. Calculate (i) the heat rejected in the absorber, and (ii) the COP of the cycle. Yo 8 XE-V lo 9 Pc 7 condenser 5 Qgen PG 100 Qabs Pe evaporator PRV 6 PA 10 3 generator heat exchanger 2 pump 185 absorber

Chapter 9 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - Prob. 9.3P Ch. 9.1 - Prob. 9.4P Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.7P Ch. 9.1 - Prob. 9.8P Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P

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.