(a) Explanation Calculation: Sketch the cross section as shown in Figure 1. Refer to Figure 1. Find the area ( A 1 ) of half circle as shown below. A 1 = π 2 ( a b ) 2 (1) Substitute 54 mm for a and 36 mm for b in Equation (1). A 1 = π 2 ( 54 ) ( 36 ) = 3 , 053.6 mm 2 Find the area ( A 2 ) of semicircle as shown below. A 2 = − π 2 ( r ) 2 (2) Substitute 18 in . for r in Equation (2). A 2 = − π 2 ( 18 ) 2 = − 508.9 mm 2 Find the total area ( A ) using the relation as follows: A = A 1 + A 2 (3) Here, A 1 is area of section ABCD and A 2 is area of section abc . Substitute 3 , 053.6 mm 2 for A 1 , and − 508.9 mm 2 for A 2 in Equation (3). A = 3 , 053.6 − 508.9 = 2 , 544.7 mm 2 Refer to Figure 1. Find the centroid for section 1 about y axis ( y 1 ) as shown below: y 1 = 4 r 3 π (4) Substitute 18 in . for r in Equation (4). y 1 = 4 ( 36 ) 3 π = 144 3 π = 48 π = 15.2789 mm Find the centroid for section 2 about x axis ( y 2 ) as shown below: y 2 = 4 ( 18 ) 3 π = 72 3 π = 24 π = 7 (b) To determine Find the centroid of the area.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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, Problem 9.189RP

(a)

To determine

Find the polar moment of inertia of the area with respect to point O.

(b)

To determine

Find the centroid of the area.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 9.188RP

Chapter 9, Problem 9.190RP

Students have asked these similar questions

(Read image) (Answer given)

Problem (17): water flowing in an open channel of a rectangular cross-section with width (b) transitions from a mild slope to a steep slope (i.e., from subcritical to supercritical flow) with normal water depths of (y₁) and (y2), respectively. Given the values of y₁ [m], y₂ [m], and b [m], calculate the discharge in the channel (Q) in [Lit/s]. Givens: y1 = 4.112 m y2 = 0.387 m b = 0.942 m Answers: ( 1 ) 1880.186 lit/s ( 2 ) 4042.945 lit/s ( 3 ) 2553.11 lit/s ( 4 ) 3130.448 lit/s

Problem (14): A pump is being used to lift water from an underground tank through a pipe of diameter (d) at discharge (Q). The total head loss until the pump entrance can be calculated as (h₁ = K[V²/2g]), h where (V) is the flow velocity in the pipe. The elevation difference between the pump and tank surface is (h). Given the values of h [cm], d [cm], and K [-], calculate the maximum discharge Q [Lit/s] beyond which cavitation would take place at the pump entrance. Assume Turbulent flow conditions. Givens: h = 120.31 cm d = 14.455 cm K = 8.976 Q Answers: (1) 94.917 lit/s (2) 49.048 lit/s ( 3 ) 80.722 lit/s 68.588 lit/s 4

Chapter 9 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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.

Find the polar moment of inertia of the area with respect to point O .

Solution Summary: The author calculates the polar moment of inertia of the area with respect to point O.