eligheor
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EligheorTRANSCRIPT
Dibujamos el diagrama de cuerpo libre:
Llevamos las medidas de mm a metros:
280 ๐๐ = 0,28 ๐ 180 = 0,18 ๐ 100 = 0,10 ๐
Aplicando las ecuaciones de equilibrio obtenemos:
๐! = 0: โ ๐ด 0,18 + 150 sin 30 0,10 + 150 cos 30 0,28 = 0
0,28!!
0,18!!
0,10!!
30ยฐ
!
!
150!!
!!
!!
!
!
!
!!
COSMOS: Complete Online Solutions Manual Organization System
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 ยฉ 2007 The McGraw-Hill Companies.
Chapter 4, Solution 19.
Free-Body Diagram:
(a) From free-body diagram of lever BCD
( ) ( )0: 50 mm 200 N 75 mm 0C AB
M Tฮฃ = โ =
300AB
Tโด =(b) From free-body diagram of lever BCD
( )0: 200 N 0.6 300 N 0x x
F Cฮฃ = + + =
380 N or 380 Nx x
Cโด = โ =C
( )0: 0.8 300 N 0y y
F Cฮฃ = + =
N 240or N 240 =โ=โดyy
C C
Then ( ) ( )2 22 2380 240 449.44 N
x yC C C= + = + =
and ยฐ=โโ
โโโ
โ
โโ=โโ
โ
โโโโ
โ= โโ
276.32380
240tantan
11
x
y
C
Cฮธ
or 449 N=C 32.3ยฐโน
๐ด = 150 sin 30 0,10 + 150 cos 30 0,28
0,18 = ๐๐๐,๐๐ ๐ต
๐ ๐ด = 244 ๐ โ
๐น! = 0: 243,74+ 150 sin 30+ ๐ท! = 0
๐ท! = โ243,74โ 150 sin 30 = โ๐๐๐,๐๐ ๐ต
๐น! = 0: ๐ท! โ 150 cos 30 = 0
๐ท! = 150 cos 30 = ๐๐๐,๐๐๐ ๐ต
โด ๐ท = ๐ท!! + ๐ท!! = โ318,74 ! + 129,904 ! = ๐๐๐,๐๐ ๐ต
๐ฆ ๐ = tan!!๐ท!๐ท!
= tan!!129,904โ318,74 = โ๐๐,๐๐๐ยฐ
๐ ๐ท = 344 ๐ ๐ = 22,2ยฐ
COSMOS: Complete Online Solutions Manual Organization System
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 ยฉ 2007 The McGraw-Hill Companies.
Chapter 4, Solution 19.
Free-Body Diagram:
(a) From free-body diagram of lever BCD
( ) ( )0: 50 mm 200 N 75 mm 0C AB
M Tฮฃ = โ =
300AB
Tโด =(b) From free-body diagram of lever BCD
( )0: 200 N 0.6 300 N 0x x
F Cฮฃ = + + =
380 N or 380 Nx x
Cโด = โ =C
( )0: 0.8 300 N 0y y
F Cฮฃ = + =
N 240or N 240 =โ=โดyy
C C
Then ( ) ( )2 22 2380 240 449.44 N
x yC C C= + = + =
and ยฐ=โโ
โโโ
โ
โโ=โโ
โ
โโโโ
โ= โโ
276.32380
240tantan
11
x
y
C
Cฮธ
or 449 N=C 32.3ยฐโน
COSMOS: Complete Online Solutions Manual Organization System
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 ยฉ 2007 The McGraw-Hill Companies.
Chapter 4, Solution 19.
Free-Body Diagram:
(a) From free-body diagram of lever BCD
( ) ( )0: 50 mm 200 N 75 mm 0C AB
M Tฮฃ = โ =
300AB
Tโด =(b) From free-body diagram of lever BCD
( )0: 200 N 0.6 300 N 0x x
F Cฮฃ = + + =
380 N or 380 Nx x
Cโด = โ =C
( )0: 0.8 300 N 0y y
F Cฮฃ = + =
N 240or N 240 =โ=โดyy
C C
Then ( ) ( )2 22 2380 240 449.44 N
x yC C C= + = + =
and ยฐ=โโ
โโโ
โ
โโ=โโ
โ
โโโโ
โ= โโ
276.32380
240tantan
11
x
y
C
Cฮธ
or 449 N=C 32.3ยฐโน
COSMOS: Complete Online Solutions Manual Organization System
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 ยฉ 2007 The McGraw-Hill Companies.
Chapter 4, Solution 21.
Free-Body Diagram:
(a)
( ) 0in.9.0cos
in.2.4:0 =โโ
โ
โโโ
โโ=ฮฃ spฮx FAฮฮฑ
or ( )8lb 1.2 in.
cos30sp
F kx k= = =ยฐ
Solving for k:
7.69800 lb/in.k = 7.70 lb/in.k = โน
(b)
( ) 8 lb0: 3 lb sin30 0
cos30x x
F Bโ โฮฃ = ยฐ + + =โ โยฐโ โ
or 10.7376 lbx
B = โ
( )0: 3 lb cos30 0y y
F Bฮฃ = โ ยฐ + =
or 2.5981 lby
B =
( ) ( )2 210.7376 2.5981 11.0475 lb,B = โ + = and
1 2.5981tan 13.6020
10.7376ฮธ โ= = ยฐ
Therefore: 11.05 lb=B 13.60ยฐ โน
Dibujamos el diagrama de cuerpo libre:
Aplicando las ecuaciones de equilibrio obtenemos:
๐! = 0: ๐ 2๐ + ๐ cos๐ โ ๐๐ + ๐๐ = 0
๐ =๐ท
๐+ ๐๐จ๐ฌ๐ฝ (๐)
!! !
2!+ !
cos!
!
! !
!!
!!
!!
!!
!! !!
!!
COSMOS: Complete Online Solutions Manual Organization System
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 ยฉ 2007 The McGraw-Hill Companies.
Chapter 4, Solution 19.
Free-Body Diagram:
(a) From free-body diagram of lever BCD
( ) ( )0: 50 mm 200 N 75 mm 0C AB
M Tฮฃ = โ =
300AB
Tโด =(b) From free-body diagram of lever BCD
( )0: 200 N 0.6 300 N 0x x
F Cฮฃ = + + =
380 N or 380 Nx x
Cโด = โ =C
( )0: 0.8 300 N 0y y
F Cฮฃ = + =
N 240or N 240 =โ=โดyy
C C
Then ( ) ( )2 22 2380 240 449.44 N
x yC C C= + = + =
and ยฐ=โโ
โโโ
โ
โโ=โโ
โ
โโโโ
โ= โโ
276.32380
240tantan
11
x
y
C
Cฮธ
or 449 N=C 32.3ยฐโน
๐น! = 0: ๐ถ! โ ๐ sin๐ = 0
๐ถ! = ๐ป ๐ฌ๐ข๐ง๐ฝ (๐) De la ecuaciรณn (a) en la ecuaciรณn (b) se tiene que:
๐ถ! = ๐ท ๐ฌ๐ข๐ง๐ฝ๐+ ๐๐จ๐ฌ๐ฝ (๐)
๐น! = 0: ๐ถ! + ๐ + ๐ cos๐ โ ๐ = 0
๐ถ! = ๐ทโ ๐ป ๐+ ๐๐จ๐ฌ๐ฝ (๐) De la ecuaciรณn (a) en la ecuaciรณn (d) se tiene que:
๐ถ! = ๐ โ๐ 1+ cos๐1+ cos๐ = 0
๐ถ! = 0 , ๐ถ = ๐ถ!
๐ถ = ๐ท ๐ฌ๐ข๐ง๐ฝ๐+ ๐๐จ๐ฌ๐ฝ (๐)
๐๐๐๐ ๐ = 60ยฐ ๐ ๐ก๐๐๐ฃ๐๐ ๐๐๐ ๐๐๐ข๐๐๐๐๐๐ De la ecuaciรณn (a) se tiene que:
๐ =๐
1+ cos๐ = ๐
1+ cos 60 = ๐
1+ 12=
๐๐ ๐ท
De la ecuaciรณn (e) se tiene que:
๐ถ = ๐ sin๐1+ cos๐ =
๐ sin 601+ cos 60 =
๐ 0,87
1+ 12= ๐,๐๐ ๐ท
COSMOS: Complete Online Solutions Manual Organization System
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 ยฉ 2007 The McGraw-Hill Companies.
Chapter 4, Solution 19.
Free-Body Diagram:
(a) From free-body diagram of lever BCD
( ) ( )0: 50 mm 200 N 75 mm 0C AB
M Tฮฃ = โ =
300AB
Tโด =(b) From free-body diagram of lever BCD
( )0: 200 N 0.6 300 N 0x x
F Cฮฃ = + + =
380 N or 380 Nx x
Cโด = โ =C
( )0: 0.8 300 N 0y y
F Cฮฃ = + =
N 240or N 240 =โ=โดyy
C C
Then ( ) ( )2 22 2380 240 449.44 N
x yC C C= + = + =
and ยฐ=โโ
โโโ
โ
โโ=โโ
โ
โโโโ
โ= โโ
276.32380
240tantan
11
x
y
C
Cฮธ
or 449 N=C 32.3ยฐโน
COSMOS: Complete Online Solutions Manual Organization System
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 ยฉ 2007 The McGraw-Hill Companies.
Chapter 4, Solution 19.
Free-Body Diagram:
(a) From free-body diagram of lever BCD
( ) ( )0: 50 mm 200 N 75 mm 0C AB
M Tฮฃ = โ =
300AB
Tโด =(b) From free-body diagram of lever BCD
( )0: 200 N 0.6 300 N 0x x
F Cฮฃ = + + =
380 N or 380 Nx x
Cโด = โ =C
( )0: 0.8 300 N 0y y
F Cฮฃ = + =
N 240or N 240 =โ=โดyy
C C
Then ( ) ( )2 22 2380 240 449.44 N
x yC C C= + = + =
and ยฐ=โโ
โโโ
โ
โโ=โโ
โ
โโโโ
โ= โโ
276.32380
240tantan
11
x
y
C
Cฮธ
or 449 N=C 32.3ยฐโน