Solucionario
Chapter 5, Solution 1.
\
A, mm 2
1 2
x , mm
−100 200
y , mm
250 150
xA, mm3 − 30 000000 24 000 000 21000 000
yA, mm3 6 750 000 18000000 24 750000
200 × 150 = 30000 400 × 300 = 120000 150 000
Σ
Then
X =
Y =
ΣxA 21 000000 = mm ΣA 150000
ΣyA 24 750000 = mm ΣA 150 000
or X = 140.0 mm
or Y = 165.0mm
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.
COSMOS: Complete Online Solutions Manual Organization System
Chapter 5, Solution 2.
A,in 2
1 2
10 × 8 = 80
x ,in.
5
13
y ,in.
4
xA,in 3
400
702
yA,in3
320
216
1 × 9 × 12 = 54 2
134
4
Σ
1102
536
Then and
X = Y =
ΣxA 1102 = ΣA 134
ΣyA 1102 = ΣA 134
or
X = 8.22 in.
or Y = 4.00 in.
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.
COSMOS:Complete Online Solutions Manual Organization System
Chapter 5, Solution 3.
A, mm 2
1
x , mm
xA, mm3 729 000 2 460 375 3 189 375
1 × 90 × 270 = 12 150 2 1 × 135 × 270 = 18 225 2
2 ( 90 ) = 60 3 90 + 1 (135) = 135 3
2
Σ
30375
ΣxA 3189375 mm = ΣA 30375
Then
X =
or X = 105.0 mm
For the whole triangular area by observation:
Y =
1 ( 270 mm ) 3
or Y = 90.0mm
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.
COSMOS: Complete Online Solutions Manual Organization System
Chapter 5, Solution 4.
A,in 2
1
x ,in.
2 ( 21) = 14 3 21 + 1 (13) = 27.5 2 40 −
y ,in.
1 ( 24 ) = 323
xA,in 3
3528
yA,in 3
8064
1 ( 21)( 24 ) = 252 2
2
(13)( 40 ) = 520
772
20
14 300
10 400
Σ
17 828
18 464
Then
X = Y =
ΣxA 17828 = in. ΣA 772 ΣyA 18464 = in. ΣA 772
or
X = 23.1 in.
or Y = 23.9 in.
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen,David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.
COSMOS: Complete Online Solutions Manual Organization System
Chapter 5, Solution 5.
A, mm 2
x , mm
y , mm
xA, mm3
− 3 796 900
yA, mm3 3 796 900
1
π ( 225 )
4
2
= 39 761
−
4 ( 225 ) 3π
= − 95.493
95.493
2
1 ( 375)( 225) = 42 188 2
125
75
5 273 500
3 164 100
Σ81 949
1 476 600
6 961 000
Then
X = Y =
ΣxA 1476600 mm = ΣA 81 949 ΣyA 6961 000 mm = ΣA 81 949
or X = 18.02 mm
or Y = 84.9 mm
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.
COSMOS: Complete Online SolutionsManual Organization System
Chapter 5, Solution 6.
A,in 2
1 2
17 × 9 = 153
x ,in.
8.5
y ,in.
4.5
xA,in 3
1300.5
yA,in 3
688.5
−
π
4
−
× ( 4.5 ) = −15.9043 8 −
2
4 × 4.5 4 × 4.5 = 6.0901 9 − = 7.0901 − 96.857 3π 3π
10.5465 6.4535
−112.761 −182.466
393.27
3
π
4
( 6 )2 = − 28.274
108.822
− 298.19
905.45
Σ
Then and
X =
ΣxA 905.45 =ΣA 108.822
or
X = 8.32 in.
Y =
ΣyA 393.27 = ΣA 108.22
or Y = 3.61 in.
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.
COSMOS: Complete Online Solutions Manual Organization System
Chapter 5, Solution 7....
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