Answered: Find the volume of a right circular…

Find the volume of a right circular cylinder of radius a and height h if the density varies as the distance from the base.

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 9.33P: The plane region A is submerged in a ï¬‚uid of weight density . The resultant force of the ï¬‚uid...

See similar textbooks

Related questions

Q: a) Evaluate the surface area of a paraboloid :=4-2-y that lies above the ry-plane.

A: Given that To evaluate the surface area of paraboloid z= 4- x2 - y2 that lies above the XY plane

Q: 1. A vertical triangular surface of height d and horizontal base width b is submerged in a liquid…

Q: an oil tank is in the shape of a right circular cylinder with a radius of r meters and its axis is…

Q: 2. Calculate the density and specific weight of carbon dioxide at a pressure of 300 kN/m² absolute…

A: Dear student, According to the guidelines I am allowed to answer only one…

Q: Find density Mars s= 30% yolume -7c

A: Given data : The value of mass =m=30 g The value of volume=V=7 cm3 Required : Density

Q: Find the dimension and surface area of the shape object according to the pappus-guldinus theorem

A: Pappus theorem is a very simple method exists for calculating the surface area and volume generated…

Q: *Obtain the center of gravity of the surface area of the fixed-thickness plane plate in the given…

Q: A semicircular plate of radius 5ft rests vertically on its diameter at the bottom of a pool filled…

Q: Find the center of mass for a quarter of a uniform sphere in terms of the outside radius of the…

Q: 3. hydrostatic force on each of the four sides. A cuboid tank 8 m long, 4 m wide, and 2 m high is…

Q: Neglecting the atmospheric pressure, compute its center of pressure position X. m. The center of…

Q: A plate with sides in the form of a semicircular area of radius 2 meters is stored in a pool with a…

Q: A piece of irregularly shaped metal weighs 422 N in air. When the metal is completely submerged in…

A: Buoyancy is the force that causes objects to float. It is the force exerted on an object that is…

Q: Find the volumes of the solids generated by revolving the shaded regions The x-axis The y-axis

Q: Find the coordinates of the center of gravity for the plane object shown on the fig. Consider that a…

Q: Approximate the iceberg as a perfect cylinder of uniform density, If the iceberg has a diameter of…

A: Let B be the point on the cube of the centroid of the displaced fluid Just above that let G be the…

Q: Find the controid for the shaded area 120

A: The centroid is the point from the x and y-axis where the total mass of the area supposed to act. It…

Q: A As shown in figure (4), find the pressure at point (A), and the absolute pressure on it.

Q: If the pressure in container A in the given image is 538.55 kPa, compute the pressure in container…

A: Moving upwards negative sign is used moving downwards positive sign is considered with respect to…

Q: 800 N/m B 1m 3 m

Q: A trough is filled with a liquid of density 840 kg/m3 . Theends of the trough are equilateral…

A: Let us draw the trough as shown below. Generally, In an equilateral triangle a perpendicular from a…

Q: Surface AB is a circular arc with a radius of 2 m and a width of 1 m into the paper. The distance EB…

Q: Three smooth cylinders, each weighing 500 N, is placed inside a smooth box as shown in the figure.

Q: nent on the relationship between the depth of the center of pressure and the de mersion. 5

Q: A 10 m long and 3 m deep rectangular vessel floats in water. The vessel is rotated 10° to the left.…

A: Given: The length of the vessel, L = 10 m The height of the vessel, H = 3 m The rotation = 10 degree…

Q: The face of a dam adjacent to the water has the shape of an isosceles trapezoid of altitude 20 m,…

Q: Some coordinates measured on an aluminum plate are seen in the shaded area of the figure given…

Q: 3 m

A: Given that, Density of the plate, ρ=800 kg/m3Length of plank, l=3 m, Drawing the free body diagram…

Q: the stone weight 400N in air and 240 N in water, determine the volume of stone in cubic meter

A: Write the given data in the problem. W=400 NWa=240 N Here, W is the weight of the stone in air,…

Q: Volume obtained by rotating the shaded area shown in the figure about x-axis. y = kx /3 xr

Q: A conical vessel has a height of 24cm and a base diameter of 12 cm. It holds water to a depth of 18…

Q: Determine the total pressure on a circular plate of diameter 1.5m which is placed vertically in…

A: Given: diameter of circular plate is d=1.5 m distance from the free surface to the centre of the…

Q: 11. Find the force exerted on one side of the annular disk shown in Fig. and also locate the center…

A: Given data as per question Distance between free surface of water and center of plate =3m The outer…

Q: The flat square of side length 2 m is submerged vertically in water, 2 m below the surface as…

A: GIVEN DATA - FLAT SQUARE PLATE GIVEN 2m*2m WEIGHT DENSITY OF WATER =9810N/m3 WE HAVE TO FIND FORCE…

Q: Resolve the horizontal 600-lb force in Fig. 2-12a into components acting along the u and v axes and…

A: F = 600 lb find the component of force on u and v

Q: Find the moments of the lamina S of constant density p = 2 g/cm? occupying the region between y = x²…

Q: A body weighs 250 lb at the earth's surface. Determine c. The weight of the body on the moon's…

A: Given weight of the body on the earth's surface = 250 lb…

Q: Two solid spherical bodies have 12 in. and 10 in.diameters and are made of a material that…

A: Given data: Diameter of the spherical body 1, Radius of the spherical body 1, Diameter of the…

Q: Find the hydrostatic force in kN acting in a triangular plate of base 2 m and height 3 m which is…

Q: Two spheres, each 1.20 m in diameter, weighs 4kN and 12kN respectively. They are connected with a…

A: Diameter of sphere, d = 1.2 m Weight of first sphere, W1 = 4kN Weight of second sphere, W2= 12 kN

Q: Find the volume of the solid generated be revolving the shaded region about the given axis.

A: we will use pappus- guldinus theorem to solve the question volume of revolved solid = area * 2 *…

Q: ree smooth cylinders, each weighing 500 N, is placed inside a smooth ox as shown in the figure.

Q: Express the hydrostatic force against one side of the plate as an integral and evaluate it.

A: Given: A hemispherical plate d=10 ft d=1 ft Density = 62.5 lb/ft3 To determine: The hydro-static…

Q: Q3/ Find the resultant force and its direction which is exerted on the hemi-sphere shape of gate as…

A: Given: Density of water (ρ)=1000kg/m3 Width of the gate (w)=1m (assumed)

Q: 3.6 The tube shown is filled with mercury at 20°C. Calculate the force applied to the piston. d = 10…

A: Given data ,D=50 mm=0.05 m Density of Mercury At 20°d=10 mm= 0.01 m ∫m=13,550…

Concept explainers

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.

Question

Find the volume of a right circular cylinder of
radius a and height h if the density varies as the
distance from the base.
Note :- By Triple Integrals |

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

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

Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y of the plane region shown.
Find the elevation h (km) where the weight of an object is one-tenth its weight on the surface of the earth.
The 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.
The center of gravity of the plane wire figure is located at G. Determine the lengths a and b.
The equation of the catenary shown is y = 100 cosh (x/100) where x and y are measured in feet (the catenary is the shape of a cable suspended between two points). Locate the y-coordinate 0f the centroid of the catenary by numerical integration using x=25ft.
A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what distance d will kx for the new region be the same as kx (for the region before the cutout was removed?
Determine Ix for the triangular region shown.
The parametric equations of the plane curve known as a cycloid are x=a(sin) and y=a(1cos). Use integration to find the coordinates of the centroid of the cycloid obtained by varying from 0 to 2 rad.
Determine Ix and Iy for the plane region using integration.
The plane region A is submerged in a ï¬‚uid of weight density . The resultant force of the ï¬‚uid pressure on the region is R acting at the point C (called the pressure center) located at the distance h below the surface of the ï¬‚uid. Show that R=Qa and h=Ia/Qa, where Qa and Ia are the first and second moments of A about the axis a-a.
It can be show that a plane area may he represented by a vector A=A, where A is the area and represents a unit vector normal to the piano: of the area. Show that the area vector of the parallelogram formed by the vectors a and b shown in the figure is A=ab.