![International Edition---engineering Mechanics: Statics, 4th Edition](https://www.bartleby.com/isbn_cover_images/9781305501607/9781305501607_largeCoverImage.gif)
Concept explainers
(a)
Centroid of the volume generated by revolving the area shown about x axis
![Check Mark](/static/check-mark.png)
Answer to Problem 8.73P
The centroid
Explanation of Solution
Given information:
The centroid of the volume is defined as:
Calculation:
Consider a thin shell element generated by rotating the shaded area about x axis.
The differentiate volume
The centroidal coordinate
The volume V of the element
The first moment
Apply Simpson's rule to evaluate above integrals.
x (in) | y (in) | | |
0 | 0 | 0 | 0 |
2 | 4.9 | 24 | 48 |
4 | 6.93 | 48 | 192 |
6 | 8.49 | 72 | 432.5 |
8 | 9.8 | 96 | 768.5 |
10 | 10.95 | 120 | 1199 |
12 | 12 | 144 | 1728 |
The volume V of the element
The first moment
The point of action
Due to symmetry
Conclusion:
The centroid
(b)
Assume curve OB is a parabola and verify the result found on part a
![Check Mark](/static/check-mark.png)
Answer to Problem 8.73P
The results obtained at sub part 'a' is equal to the results in sub part 'b'.
Explanation of Solution
Given information:
According to table 8.3
Paraboloid of revolution:
Calculation:
The volume V
Substitute and solve
The point of action
The results obtained at sub part 'a' is equal to the results in sub part 'b'.
Conclusion:
The results obtained at sub part 'a' is equal to the results in sub part 'b'.
Want to see more full solutions like this?
Chapter 8 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
- The properties of the unequal angle section are Ix=80.9in.4,Iy=38.8in.4, and Iu=21.3in.4. Determine Ixy.arrow_forwardCompute Ix and Iy for the region shown.arrow_forward3 29knd. A cylinder of 50 mm diameter and height 60 mm is resting on base in H.P. A circular hole of 20 mm diameter is drilled , so that the axis of the hole is perpendicular to V.P and bisects the axis of cylinder at right angles . Draw the development of the lateral surface of the cylinder with the slot . Draw neatly with pencil and take correct values must**arrow_forward
- EXERCISE 1.5 The intersecting edges of a nonorthogonal parallelepiped are defined by the position vectors FB/A = -20ī+30 j+5k, Fc/A = 8ī+25j + 10k, FD/A = 4ī - 2j-15k mm. Determine the volume of this object.arrow_forwardThe piston of a reciprocating engine exerts a firce of 180 kN on crosshead when the crank is 35 degree (angle beta) past TDC. If the stroke of the piston is 800 mm and the length of the connecting rod is 1.65 m, find, in kN. a) the guide force FG and , b) the firce on the connecting rod Rc .hint: radius AC is 1/2 of the stroke and Angle "phi" may be solved using sine law. Draw FBDarrow_forwardDetermine resultant of the force system shown in the figure Ex. 1 10 kN 12 kN 5kN 30 30° 40° Fig. Ex. 1 Source: Sharma, V. Engineering Mechanics : Statics. Oxford, U.K. ISBN 9781783323562. (Marrow_forward
- Approximate the second moment of area of the rigid sheet shown below, rotating about the axis y-y. Carry out the approximation by segmenting the piece to 4 pieces of equal length. The piece is 12 cm long and 8 cm high.arrow_forwardVerify if my answers are correct:R=6kNd=1.875 mHence the resultant force will act at 1.875m away from point A.arrow_forwardFind the magnitude and direction of the resultant force for the system of forces shown in the figure. Where F1 =25 N, F2 =35N, F3 =10 N, F4 =50N. The angles 0, =20°, 02 =25° , 03 = 40°, 04 = 50 ° (Enter only the values in the boxes by referring the units given in bracket. Also upload the hand written copy in the link provided) F2 F1 F3 02 03 04 F4arrow_forward
- 16 - 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 homogeneous wire in the x, y and z axes given correctly?A) (23.57 ; 11.43 ; 17.14)B) (23.57 ; 17.14 ; 11.43)C) (28.29 ; 13.71 ; 20.57)D) (20.61 ; 13.03 ; 9.08)E) (28.29 ; 20.57 ; 13.71)arrow_forwardQ6: A right triangle whose hypotenuse is v3 m long is revolved about one of its legs to generate a right circular cone. Find the radius, height, and volume of the cone of greatest volume that can be made this way? V3 rarrow_forwardIf 150 N of farce is applied on a spanner of 10 cm to open a nut then the length of spanner when the force applied on it is 60 N is * O 40 cm 25 cm O 50 cm O 80 cm Moment arm is the O parallel distance O perpendicular distance normal distance O resultant force A copy of yourresponses will be ejphalled to the address that you provided.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305501607/9781305501607_smallCoverImage.gif)