For the planar area symmetrical with respect to the x-axis in the figure, the cross-section dimensions are a = 1 cm and c = 3 cm, the radius of the semicircle is c. a) Find the center of gravity of this area. b) Find the volume of the object formed by rotating this area 180° around the x-axis.

For the planar area symmetrical with respect to the x-axis in the figure, the cross-section dimensions are a = 1 cm and c = 3 cm, the radius of the semicircle is c. a) Find the center of gravity of this area. b) Find the volume of the object formed by rotating this area 180° around the x-axis.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.13P: Figure (a) shows the cross section of a column that uses a structural shape known as W867...

See similar textbooks

Related questions

Q: 3. What will be the variation in BMD for the diagram? [Assume I = 2m]. 10 KN в А a) Rectangular b)…

Q: 1. Consider a right pyramid whose base is an equilateral triangle of side 4cm each, each slant edge…

Q: 13. For the parabolic seawall shown in Fig. 3-34, what moment about A per ft of wall is created by…

Q: b) Figure Q2b shows a solid and homogeneous section, where (31.25 mm, 41.54 mm) are its centroid…

Q: Q3/A For the figure below, the resultant is.: 20 Ν 75 N

A: Given:

Q: 1. A 80mm long line AB has the end A at a distance of 20mm above HP and 40mm in front of V.P. The…

A: The front view, top view and side view of the specified question has been shown in the figure below.…

Q: The second moment of area for the following figure is 4. MM 3omm 5 3. m 30 mm

A: The given figure converted into three simple figures: 1. rectangle of 80 mm length & 60 mm…

Q: The opposite figure is composed of a rectangle (b=12.2 , h=6.1 m , density 4 kg/m² ) and a triangle…

A: givenrectangle b=12.2mh=6.1mdensity ρ1=4kg/m2triangle b=12.2ma=3.05mdensity ρ2=8kg/m2

Q: 5 - Find the center of gravity M (x,y,z) of the three-dimensional homogeneous ABCD wire in the…

Q: 2 m 1 m For the figure below, the center of :gravity is y₁ 2 m 3 m X'= 2.65 AND Y'= 1.217 O X'=1.217…

Q: 2 m 1 m For the figure below, the center of :gravity is 2 m 3 m X'= 2.65 AND Y'= 1.217 O X'=1.217…

Q: Figure Q2b shows a solid and homogeneous section, where (31.25 mm, 41.54 mm) are its centroid…

Q: The curved surface BC in the figure has an arc of 60 ° and is perpendicular to the bottom at point…

A: given data, ⇒curved panel has an arc of 60°. width of panel =5m resulting force…

Q: Q7: In Figure below the triangular gate hinged at it base as shown, find P. Take a = 5 ft Triangular…

Q: oss section of a beam is as shown in Figure Q1(a),determine; (i) center of gravity with respect to…

Q: a D a A! y

A: Given data: The dimension a = 24 cm. The dimension b = 36 cm.

Q: 4. In the figure below, find T1 and T2 5m 3 m 4 m 500 N

A: Given-Data:- Length of sides as = 5m,4m, and 3m Load=500N To-Find:- T1 and T2

Q: system you choose) at the instance shown in the figure. Dimension: 0₂049 cm, O₂A = 6 cm, AB = 11 cm,…

Q: For the shaded area shown in the figure, a = 3 m, b = 1.5 m, c = 0.75 m.

A: As per bartleby policy only one question can be answered at a time. Please post second question…

Q: 12 - A homogeneous, planar plate of constant thickness in the figure the coordinates of the…

Q: For the figure below find total area * Y 3 2 3

A: It is required to determine total area of given section

Q: Find the resultant force f center of pressure for one Side of submerged area shown in figure below.…

Q: A three-eighths circle is the curved gate as shown in fig. 3, 3 m wide into paper, hinged ta D, and…

A: Consider FD is acting at point D and Fy and Fx are acting at point C. Thus draw the free-body…

Q: B2/for the figure below find. 1- Total shaded area 2- X-Bar 3-Y-Bar

Q: The opposite figure is composed of a rectangle (b=16.8 , h=8.4 m , density 8 kg/m² ) and a triangle…

A: Given: Dimensions of triangle are: b = 16.8 m a = 4.2 m Density of triangle is 16 kg/m2. Dimensions…

Q: Figure Q2b shows a solid and homogeneous section, where (31.25 mm, 41.54 mm) are its centroid…

A: find the centroid of the section and moment of inertia about centroidal x- axis.

Q: Consider the U-beam section shown in the figure below. The beam section splits into 3 segments…

A: due to symmetricity total vertical length = (180 + 30 + 30 ) cm = 240 cm

Q: a. find the area and vertical distances from the bottom edge of the cross-section to the centoid of…

Q: Constant thickness homogeneous planar plate in the figure coordinates of the center of gravity M…

A: Given data, a = 9 t = 3 Find Centre of Gravity.

Q: Find the center of mass of a thin, bent wire in a semicircle, as shown in the figure dl = a de 2=a…

A: Solution: Consider an elemental section 'dl' on the wire and dl is given by,…

Q: The curved surface represented by AB in the figure is the surface of cylinder, hinged at A and…

Q: Piston A Prassure Piston B In the figure if the weight of the car is 20.000 N, the diameter of…

A: According to Pascal's law the fluid at rest transmit equal pressure in all the direction. So it is…

Q: What is the use of parallel plane theorem?

A: Consider the diagram shown below for a body in space.

Q: Q1/ AB is a straight line , the coordinates of its ends are : A(2,0.5) B( 2,3.5)left of A Distance…

Q: find the center of the figure area shown in the image; you must do it with the integral equations…

Q: Balancing masses from the axis of rotation to the distance of ei and Li mm in the rotor R and L…

Q: 29 - Find the center of gravity M (x,y,z) of the three-dimensional homogeneous ABCD wire in the…

A: Given data :-: a = 36 cm b = 12 cm Find :- Coordinates of AB part

Q: Passing an exploratory section through the body and exposing the internal forces acting on the…

A: Given data To explain the given statement.

Q: Consider the rectangular cardboard shown in the figure. If you cut a hole in the material, the…

Q: Find the center of mass of the structure given in the figure below. Assume a uniform thickness of 20…

A: Consider the diagram shown below for the given body.

Q: An electric winch lifts a weight on the end of a 5-m jib pole. Determine angle 0 for the position…

Q: y 2a 2a katka

Q: 3-8. Determine the coordinates of the centroid of the shaded area of Fig. P3-8. The equation of the…

A: Consider a small part of length dy, the area of the shaded part can be written as…

Q: In both cases below, find the projection of FB in the direction of F.. Also, find the angle between…

Q: Q4/ For the figure below, all dimensions in inch. A/The total Area: y 3 1.5 2.5 2.5 2.5 2.5 Q4/C/…

A: Given cross-section

Q: Cross section of a beam is as shown in Figure Q1(a),determine; (1i) center of gravity with respect…

A: Solution:

Q: Consider the rectangular cardboard shown in the figure. If you cut a hole in the material and…

A: Correct answer: (A) increases

Q: Q3: A' am with cross section shown in the following image, find out the principle аxes. 100mm L.…

A: Let's divide the given cross section into two parts Part (1): A rectangle of length 100 mm and…

Concept explainers

Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

Question

For the planar area symmetrical with respect to the x-axis in the figure, the cross-section dimensions
are a = 1 cm and c = 3 cm, the radius of the semicircle is c.
a) Find the center of gravity of this area.
b) Find the volume of the object formed by rotating this area 180° around the x-axis.
4a k C - C →
2a
a
→ X
不

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

It is common to hang objects on doorknobs and over-the-door hooks. There is a limit to the amount of weight that a door can hold because of the forces exerted on the hinges. A door of height h = 2.5 m and width h/2 has a mass of M = 36 kg. The mass is distributed uniformly, so the center of mass is located at the geometric center of the door. One hinge is located a distance h/4 from the top of the door. The second hinge is a distance h/4 from the bottom of the door. Refer to (a) in the figure. The door’s weight is supported entirely by the two hinges and each hinge supports half of the weight. In other words, the vertical force exerted by each hinge is exactly one half of the total weight, including any additional load. For this problem, take the positive y-direction to be directly upward and the positive x-direction pointing from the hinge side of the door to the knob side. 1.) calculate the force, with its sign in Newtons that the upper hinge exerts on the door in the x axis.…
6 - Find the center of gravity M of the three-dimensional homogeneous wire ABCD in the figure using the (x, y, z) coordinate set. The dimensions of the wire are a = 24 cm, b = 36 cm. Which of the following is the correct coordinates of the BC part of the homogeneous wire in the x, y and z axes?A) (36; 12; 24)B) (18; 12; 0)C) (36; 24; 12)D) (36; 12; 0)E) (36; 24; 0)
b)A simply supported beam has a symmetrical rectangular cross-section. If the second moment of area (I) of a beam with a rectangular cross-section is 11.50 x 106 mm4 about its centroidal x-axis and the depth dimension (d) of the rectangular section is 180 mm, determine the breadth dimension (b) for this beam section. Give your answer in millimetres (mm) and to 2 decimal places. Assume the beam section material is homogeneous c) The same rectangular cross-section beam in Q2b is subjected to a maximum bending moment of 25,000 Nm and experiences sagging. Assuming that the centroidal axis passes through the beam section at (d/2), calculate the maximum bending stress (?max) the beam will experience. Give your answer in N/mm2 and to 2 decimal places.
1) A cylindrical rod of constant shear modulus, G is of length L and located between z=0 and z=L. It has a polar moment of inertia given by J=(Jo)/(1-Z/L) and t=-sin(πZ/2L)where Jo is a constant.The boundary conditions are dΦ(o)/dz =0 AND Φ(L)=0 Find Φ(z) and graph (1/GJo)Φ(Z), and (1/GJo)(dΦ(Z)/dz) ?
Consider the image below: A horizontal beam of length 8 m is pinned at its left end so that it is free to rotate about that end. It has a nonuniform linear mass density given by λ(x) = 78 x (kg/m). Its right end is secured by a rope, the angle shown being 45 degrees. Calculate the magnitude of the tension in the rope, in N. (Please answer to the fourth decimal place - i.e 14.3225)
AB, BC, CD, DE are each 2m long and the plane distance from A-D is 4m. Members are at right angles to each other. a) determine the vertical displacement at E b) determine the rotation at E E=200KN/mm^2 G= 80KN/mm^2 Iabce = constant = 25 x 10^-6 m^4 Jabce = constant = 50 x 10^-6 m^4
The parabolic arch is often used in construction because of its great strength. The equation of the bridge arch in Fig. 538 is y=( 36/724)x^2-6.0x+181. Determine the dimensions (ft) B, C,D,and E if A=128.0 ft
10 - Find the center of gravity M (x,y,z) of the three-dimensional homogeneous ABCD wire in the figure by using the coordinate set. The dimensions of the wire are a= 24 cm, b= 36 cm. In which of the following options are the coordinates of the CD part of the homogeneous wire in the x, y and z axes correctly given?A) (18 ; 24 ; 0)B) (18 ; 12 ; 24)C) (18 ; 12 ; 0)D) (18 ; 24 ; 24)E) (18 ; 24 ; 12)
Find the center of mass of the structure given in the figure below. Assume a uniform thickness of 20 cm, and a uniform density of 1 g/cm3.
A cylindrical container of radius r=5.00 cm and height h=40.0 cm is filled with mercury to the top (density of mercury=13.69x10^3kg.m^3). a. Find the mass of mercury inside the container. b. Find the gauge pressure and the absolute pressure on the bottom of the container (the container is open at the top and the atmospheric pressure is 1.013x10^5 Pa) c. Find the net force on the inner surface of the bottom of the container.
1. A non-uniform is 4.5m long and weighs 640N. It is balance when a 270N weight is hung 0.800m from the light end of the bar and the bar is pivoted at its center. Where is the center of gravity of the bar? 2.Two workers carry a non-uniform beam weighing 730N. The beam is 2.6m long and its center of gravity is 1.1 m from one end. If the workers hold the beam at its end, how much does each worker lift?
A loading condition is shown below. Using Castigliano's theorem and by applying a fictitious force Q with a magnitude of 0 at point C, determine: a) The horizontal displacement of point C. a) The vertical displacement of point C.