PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about thexaxis.
Step 1
From the figure consider the representative rectangle. The radius of the solid of revolution obtained by revolving the rectangle about the xacis is
R(X) -y9-
To find the volume of a solid of revolution with the-Select
mathod, use the horizontal axis of revolution.
Select
disk
shel
Volume-VE
A triangular plate with base 6 m and height 2 m is submerged vertically in water such that the highest vertex of the plate is 6 meters below the surface and the base is horizontal to the surface.
6 m
6 m
2 m
Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.)
Beta = 2
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- Find the elevation h (km) where the weight of an object is one-tenth its weight on the surface of the earth.arrow_forwardUse integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x-axis.arrow_forwardThe hemispherical glass bowl is filled with water. Find the location y of the center of gravity of the filled bowl. Approximate the bowl as a thin shell of radius R=6.15in. Use 1=162lb/ft3 for glass and 2=62.4lb/ft3 for water.arrow_forward
- Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y of the plane region shown.arrow_forwardDetermine the centroidal coordinates of the plane region by numerical integration.arrow_forwardThe concrete dam shown in cross section holds back fresh water (=1000kg/m3). Determine the resultant force R of the water pressure acting on one meter length of the dam. Also, compute the coordinates of a point on the line of action of R.arrow_forward
- Determine the dimensions of constants A and B far which the following equation is dimensionally homogeneous: F=Akx2sinBxk where F is a force, x is a distance, and k represents stiffness (dimensions: [FL1]).arrow_forwardUse numerical integration to find the centroid of the volume generated by revolving the area shown about the x-axis.arrow_forwardIf the intensity of the line loading is w=[(40xx2)/40]lb/in., where x is measured in inches, use integration to find the resultant.arrow_forward
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