Concept explainers
PROBLEM 5.132
The sides and the base of a punch bowl are of uniform thickness t. If t << R and R = 250 mm, determine the location of the center of gravity of (a) the bowl, (b) the bunch.
(a)
The location of the centre of gravity of the bowl.
Answer to Problem 5.132P
The location of the centre of gravity of the bowl is
Explanation of Solution
Refer Fig. P5.132 and Fig. 1.
For the coordinate axis given below, using the symmetry of the diagram, determine the x and z coordinates of the centre of gravity.
The bowl can be assumed as a shell, where the centre of gravity coincides with the centroid of the shell.
The element of area is obtained by rotating the arc ds about the y-axis for the walls of the bowl.
Write the expression for the area of the element.
Here,
Write the expression for y coordinate of the centroid of the element.
Here,
Write the expression for
Write the expression for y coordinate of the centre of gravity.
Here,
Conclusion:
Calculate the area using equation (I).
Substitute (I) and (II) in (III).
From figure 1, find the area of the base and distance of the centroid of the base to the y axis.
Substitute equations (V), (VI) and (VII) in equation (IV).
Substitute
Therefore, the location of the centre of gravity of the bowl is
(b)
The location of the centre of gravity of the punch.
Answer to Problem 5.132P
The location of the centre of gravity of the bowl is
Explanation of Solution
Refer Fig. P5.132 and Fig. 2.
For the coordinate axis given below, using the symmetry of the diagram, determine the x and z coordinates of the centre of gravity.
The punch can be assumed as homogenous, where the centre of gravity coincides with the centroid of the volume.
The element of volume of the disk has radius x and thickness dy.
Find the expression for
Write the expression for the volume of the element.
Here,
Write the expression for y coordinate of the centre of gravity.
Conclusion:
Calculate the volume using equation (IX).
Find
Substitute equations (XI), and (XII) in equation (X).
Substitute
Therefore, the location of the centre of gravity of the bowl is
Want to see more full solutions like this?
Chapter 5 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics
- A scratch awl has a plastic handle and a steel blade and shank.Knowing that the density of plastic is 1030 kg/m3 and of steel is 7860 kg/m3, locate the center of gravity of the awl.arrow_forwardA- Locate the centroid (X only) of the shaded area _>| w B Fig.1.A 'arrow_forwardA homogeneous wire is bent into the shape shown. Determine by direct integration the x coordinate of its centroid.arrow_forward
- The aluminum shade for the small high-intensity lamp shown has a uniform thickness of 1 mm. Knowing that the density of aluminium is 2800 kg/m3, , determine the mass of the shade.arrow_forwardThe aluminum shade for the small high-intensity lamp shown has a uniform thickness of 1 mm. Knowing that the density of aluminum is 2800 kg/m3, determine the mass of the shade.arrow_forwardProblem #7: A slender homogeneous wire of uniform cross-section is bent into the shape as shown. Determine the coordinates of its center of gravity with respect to the reference X and Y axes.arrow_forward
- Q1: Determine the area A, the centroid y of the parabolic area (Fig 1).arrow_forwardA wastebasket, designed to fit in the corner of a room, is 16 in. high and has a base in the shape of a quarter circle with a radius of 10 in. Locate the center of gravity of the wastebasket, knowing that it is made of sheet metal with a uniform thickness.arrow_forwardA vertical trapezoidal gate that is used as an automatic valve is held shut by two springs attached to hinges located along edge AB . Knowing that each spring exerts a couple of magnitude 1470 N.m determine the depth d of water for which the gate will open.arrow_forward
- An 8-in.-diameter cylindrical duct and a 4x 8-in. rectangular duct are to be joined as indicated. Knowing that the ducts were fabricated from the same sheet metal, which is of uniform thickness, locate the center of gravity of the assembly.arrow_forwardShow that for a regular pyramid of height h and n sides (n = 3, 4, . . .) the centroid of the volume of the pyramid is located at a distance h /4 above the base.arrow_forwardA bronze bushing is mounted inside a steel sleeve. Knowing that the specific weight of bronze is 0.318 lb/in3 and of steel is 0.284 lb/in3 , determine the location of the center of gravity of the assembly.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY