181 chapter 5 problems PDF

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9/15/2018

Problems

Chapter 5 Problems Article 5/3 Problems Introductory Problems 5/1 With your pencil, make a dot on the position of your best visual estimate of the centroid of the triangular area. Check the position of your estimate by referring to the results of Sample Problem 5/2 and to Table D/3.

PROBLEM 5/1

Horizontal coordinate = 5.67 Vertical coordinate = 3.67 5/2 With your pencil, make a dot on the position of your best visual estimate of the centroid of the area of the circular sector. Check your estimate by using the results of Sample Problem 5/3.

PROBLEM 5/2

5/3 Specify the x-, y-, and z-coordinates of the mass center of the quarter-cylindrical shell. https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV81XzAueGZvcm0.enc?course=crs119… 1/83

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Problems

PROBLEM 5/3

, 5/4 Specify the x-, y-, and z-coordinates of the mass center of the quadrant of the homogeneous solid cylinder.

PROBLEM 5/4

,

,

5/5 Determine the x-coordinate of the centroid of the shaded area.

PROBLEM 5/5

5/6 Determine the y-coordinate of the centroid of the area under the sine curve shown.

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Problems

PROBLEM 5/6

5/7 The homogeneous slender rod has a uniform cross section and is bent into a circular arc of radius a. Determine the x- and y-coordinates of the mass center of the rod by direct integration.

PROBLEM 5/7

, 5/8 Determine the x- and y-coordinates of the centroid of the trapezoidal area.

PROBLEM 5/8

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Problems

Determine the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown.

PROBLEM 5/9

5/10 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/10

, 5/11 If the shaded area is revolved 360° about the y-axis, determine the y-coordinate of the centroid of the resulting volume.

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Problems

PROBLEM 5/11

5/12 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/12

,

Representative Problems 5/13 Determine the coordinates of the centroid of the shaded area.

PROBLEM 5/13

, 5/14 Determine the y-coordinate of the centroid of the shaded area.

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Problems

PROBLEM 5/14

5/15 Determine the x-coordinate of the centroid of the shaded area.

PROBLEM 5/15

5/16 Determine the y-coordinate of the centroid of the shaded area.

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Problems

PROBLEM 5/16

5/17 Find the distance from the vertex of the right-circular cone to the centroid of its volume.

PROBLEM 5/17

5/18 Determine by direct integration the coordinates of the centroid of the rectangular tetrahedron.

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Problems

PROBLEM 5/18

, 5/19 Locate the centroid of the area shown in the figure by direct integration. (Caution: Carefully observe the proper sign of the radical involved.)

PROBLEM 5/19

, 5/20 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/20

, 5/21 Determine the x- and y-coordinates of the mass center of the homogeneous plate of uniform thickness t.

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Problems

PROBLEM 5/21

, 5/22 If the plate of Prob. 5/21 has a density that varies according to

, determine the x- and y-

coordinates of the mass center. , 5/23 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/23

, 5/24 Locate the centroid of the area shown in the figure by direct integration. (Caution: Carefully observe the proper sign of the radical involved.)

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PROBLEM 5/24

, 5/25 Determine the coordinates of the centroid of the shaded area.

PROBLEM 5/25

, 5/26 Locate the centroid of the shaded area between the two curves.

PROBLEM 5/26

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Problems

5/27 Determine the y-coordinate of the centroid of the shaded area.

PROBLEM 5/27

5/28 Determine the z-coordinate of the centroid of the volume obtained by revolving the shaded area under the parabola about the z-axis through 180°.

PROBLEM 5/28

5/29 Determine the x-coordinate of the centroid of the solid spherical segment. Evaluate your expression for h = R/4 and h = 0.

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PROBLEM 5/29

5/30 Determine the z-coordinate of the centroid of the volume obtained by revolving the shaded triangular area about the z-axis through 360°.

PROBLEM 5/30

5/31 Determine the coordinates of the mass center of the solid homogeneous body formed by revolving the shaded area 90° about the z-axis.

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PROBLEM 5/31

, 5/32 The thickness of the triangular plate varies linearly with y from a value t 0 along its base y = 0 to 2t 0at y = h. Determine the y-coordinate of the mass center of the plate.

PROBLEM 5/32

5/33 Determine the y-coordinate of the mass center of the thin homogeneous parabolic shell. Evaluate your results for h = 200 mm and r = 70 mm.

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PROBLEM 5/33

5/34 Determine the y-coordinate of the centroid of the plane area shown. Set h = 0 in your result and compare with the result

for a full semicircular area (see Sample Problem 5/3 and Table D/3). Also evaluate your result for

the conditions

and

.

PROBLEM 5/34

5/35 Determine the coordinates of the centroid of the volume obtained by revolving the shaded area about the z-axis through the 90° angle.

PROBLEM 5/35 https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV81XzAueGZvcm0.enc?course=crs11… 14/83

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Problems

, 5/36 Determine the x- and y-coordinates of the centroid of the volume generated by rotating the shaded area about the zaxis through 90°.

PROBLEM 5/36

5/37 Determine the x-coordinate of the mass center of the cylindrical shell of small uniform thickness.

PROBLEM 5/37

5/38 Determine the x-coordinate of the mass center of the homogeneous hemisphere with the smaller hemispherical portion removed. https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV81XzAueGZvcm0.enc?course=crs11… 15/83

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Problems

PROBLEM 5/38

Article 5/4 Problems Introductory Problems 5/39 Determine the coordinates of the centroid of the trapezoidal area shown.

PROBLEM 5/39

, 5/40 Determine the distance the centroid.

from the upper surface of the symmetric double-T beam cross section to the location of

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PROBLEM 5/40

5/41 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/41

, 5/42 Determine the height above the base of the centroid of the cross-sectional area of the beam. Neglect the fillets.

PROBLEM 5/42

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Problems

5/43 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/43

, 5/44 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/44

5/45 Calculate the y-coordinate of the centroid of the shaded area.

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PROBLEM 5/45

5/46 Determine the coordinates of the mass center of the body which is constructed of three pieces of uniform thin plate welded together.

PROBLEM 5/46

,

,

5/47 Determine the y-coordinate of the centroid of the shaded area.

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PROBLEM 5/47

5/48 Determine the y-coordinate of the centroid of the shaded area. The triangle is equilateral.

PROBLEM 5/48

Representative Problems 5/49 Determine the coordinates of the centroid of the shaded area.

PROBLEM 5/49

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Problems

5/50 Determine the x- and y-coordinates of the centroid of the shaded area.

PROBLEM 5/50

, 5/51 The uniform wire is bent into the shape shown and held by the frictionless pin at O. Determine the angle θ which will allow the wire to hang in the orientation shown.

PROBLEM 5/51

θ = 40.6° 5/52 Determine the coordinates of the mass center of the welded assembly of uniform slender rods made from the same bar stock.

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PROBLEM 5/52

5/53 The rigidly connected unit consists of a 2-kg circular disk, a 1.5-kg round shaft, and a 1-kg square plate. Determine the z-coordinate of the mass center of the unit.

PROBLEM 5/53

5/54 Determine the x-, y-, and z-coordinates of the mass center of the body constructed of three pieces of uniform thin plate which are welded together.

PROBLEM 5/54

,

,

5/55 https://edugen.wileyplus.com/edugen/courses/crs11916/ebook/p01/bWVyaWFtOTc4MTExOTM5MjYyMHAwMV81XzAueGZvcm0.enc?course=crs11… 22/83

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Problems

Determine the x-, y-, and z-coordinates of the mass center of the homogeneous body shown. The hole in the upper surface is drilled completely through the object.

PROBLEM 5/55

,

,

5/56 The welded assembly is made of a uniform rod weighing 0.370 lb per foot of length and the semicircular plate weighing 8 lb per square foot. Calculate the coordinates of the center of gravity of the assembly.

PROBLEM 5/56

, 5/57 Determine the z-coordinate of the centroid of the rectangular solid with the hemispherical hole. The center of the hemisphere is centered on the upper face of the solid, and z is measured upward from the lower face.

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Problems

PROBLEM 5/57

5/58 Determine the depth h of the square cutout in the uniform hemisphere for which the z-coordinate of the mass center will have the maximum possible value.

PROBLEM 5/58

h = 0.416r 5/59 Determine the x-coordinate of the mass center of the bracket constructed of uniform steel plate.

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PROBLEM 5/59

5/60 Determine the x-, y-, and z-coordinates of the mass center of the sheet-metal bracket whose thickness is small in comparison with the other dimensions.

PROBLEM 5/60

, 5/61 Determine the distance

from the bottom of the base to the mass center of the bracket casting.

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PROBLEM 5/61

5/62 The welded assembly is made of a uniform rod having a mass of 2 kg per meter of length and two thin rectangular plates having a mass of 18 kg per square meter. Calculate the coordinates of the mass center of the assembly.

PROBLEM 5/62

, 5/63 Determine the x-, y-, and z-coordinates of the mass center of the fixture formed from thin metal plate of uniform thickness.

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PROBLEM 5/63

,

,

5/64 An opening is formed in the thin cylindrical shell. Determine the x-, y-, and z-coordinates of the mass center of the homogeneous body.

PROBLEM 5/64

,

,

Article 5/5 Problems Introductory Problems 5/65 Using the methods of this article, determine the surface area A and volume V of the body formed by revolving the rectangular area through 360° about the z-axis.

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PROBLEM 5/65

A = 10 300 mm 2, V = 24 700 mm 3 5/66 The circular arc is rotated through 360° about the y-axis. Determine the outer surface area S of the resulting body, which is a portion of a spherical shell.

PROBLEM 5/66

5/67 The area of the circular sector is rotated through 180° about the y-axis. Determine the volume of the resulting body, which is a portion of a sphere.

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PROBLEM 5/67

5/68 Calculate the volume V of the solid generated by revolving the 60-mm right-triangle area about the z-axis through 180°.

PROBLEM 5/68

V = 2.83(10 5) mm 3 5/69 Determine the volume V generated by revolving the quarter-circular area about the z-axis through an angle of 90°.

PROBLEM 5/69

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5/70 Calculate the volume V of the complete ring of cross section shown.

PROBLEM 5/70

V = 315 in.3 5/71 The body shown in cross section is a half-circular ring formed by revolving one of the cross-hatched areas 180° about the z-axis. Determine the surface area A of the body.

PROBLEM 5/71

A = 90 000 mm 2

Representative Problems 5/72 The water storage tank is a shell of revolution and is to be sprayed with two coats of paint which has a coverage of 500 ft 2 per gallon. The engineer (who remembers mechanics) consults a scale drawing of the tank and determines that the curved line ABC has a length of 34 ft and that its centroid is 8.2 ft from the centerline of the tank. How many gallons of paint will be used for the tank including the vertical cylindrical column?

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PROBLEM 5/72

8.82 gal 5/73 Calculate the volume V of the rubber gasket formed by the complete ring of the semicircular cross section shown. Also compute the surface area A of the outside of the ring.

PROBLEM 5/73

A = 29.3 in.2, V = 10.09 in.3 5/74 The lampshade shown is constructed of 0.6-mm-thick steel and is symmetric about the z-axis. Both the upper and lower ends are open. Determine the mass of the lampshade. Take the radii to be to midthickness.

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PROBLEM 5/74

m = 0.293 kg 5/75 The body shown in cross section is a complete circular ring formed by revolving the cross-hatched area about the z-axis. Determine the surface area A and volume V of the body.

PROBLEM 5/75

A = 166.0b2, V = 102.9b3 5/76 Compute the volume V and total surface area A of the complete circular ring whose cross section is shown.

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PROBLEM 5/76

A = 497(103 ) mm2 , V = 14.92(106 ) mm3 5/77 Determine the surface area of one side of the bell-shaped shell of uniform but negligible thickness.

PROBLEM 5/77

A = πa2(π − 2) 5/78 A thin shell, shown in section, has the form generated by revolving the arc about the z-axis through 360°. Determine the surface area A of one of the two sides of the shell.

PROBLEM 5/78

A = 4πr(Rα − r sin α) 5/79 Calculate the weight W of the aluminum casting shown. The solid is generated by revolving the trapezoidal area shown about the z-axis through 180°.

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PROBLEM 5/79

W =...