Ejercicios De Trabajo Virtual

COSMOS: Complete Online Solutions Manual Organization System

Chapter 10, Solution 1.

Link ABC: Assume δθ clockwise Then, for point C

δ xC = (125 mm ) δθ
and for point D

δ xD = δ xC = (125 mm ) δθ
and for point E

δ xE = 
Link DEFG: Thus

 250 mm  2  δ xD = δ xD 3  375 mm 

δ xD = ( 375 mm ) δφ

(125 mm ) δθ = ( 375 mm ) δφ
δφ = δθ
1 3

Then

δ G = 100 2 mm δφ =  3 δ yG = δ G cos 45° = 

(

)

 100

 2 mm  δθ 

 100   100  2 mm  δθ cos 45° =  mm  δθ  3   3 

Virtual Work:

Assume P acts downward at G

δ U = 0:

( 9000 N ⋅ mm ) δθ − (180 N )(δ xE

mm ) + P (δ yG mm ) = 0

2   100  δθ  = 0 9000 δθ − 180  × 125 δθ  + P  3    3 
or

P = 180.0 N

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 10, Solution 2.

Have

FA = 20 lb at A
FD = 30 lb at D

Link ABC:

δ y A = (16 in.) δθ

Link BF:

δ yF = δ yB

δ yB = (10 in.) δθ
Link DEFG: or

δ yF =( 6 in.) δφ = (10 in.) δθ δφ = δθ δ yG = (12 in.) δφ = ( 20 in.) δθ
d ED = 5 3

( 5.5 in.)2 + ( 4.8 in.)2
5

= 7.3 in. 

δ D = ( 7.3 in.) δφ =  × 7.3 in.  δθ 3  δ xD =
Virtual Work: 4.8 4.8  5  δD =  × 7.3 in.  δθ = ( 8 in.) δθ 7.3 7.3  3 

Assume P acts upward at G

δ U = 0:
or or

FAδ y A + FDδ xD + Pδ yG = 0

( 20 lb ) (16 in.) δθ  + ( 30 lb ) (8 in.) δθ  + P( 20 in.) δθ  = 0      
P = − 28.0 lb
P = 28.0 lb

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 10, Solution 3.

Link ABC: Assume δθ clockwiseThen, for point C

δ xC = (125 mm ) δθ
and for point D

δ xD = δ xC = (125 mm ) δθ
and for point E

δ xE = 
Link DEFG: Thus or Virtual Work:

 250 mm  2  δ xD = δ xD 3  375 mm 

δ xD = ( 375 mm ) δφ

(125 mm ) δθ = ( 375 mm ) δφ
δφ = δθ
Assume M acts clockwise on link DEFG

1 3

δ U = 0:

( 9000 N ⋅ mm ) δθ − (180 N )(δ xE

mm ) + M δφ = 0

2  1  9000 δθ − 180 ⋅125 δθ  + M  δθ  = 0 3  3 
or

M = 18000 N ⋅ mm

or

M = 18.00 N ⋅ m

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 10, Solution 4.

HaveFA = 20 lb at A FD = 30 lb

at D

Link ABC:

δ y A = (16 in.) δθ δ yB = (10 in.) δθ δ yF = ( 6 in.) δφ = (10 in.) δθ
or

Link BF:

δ yF = δ yB

Link DEFG:

δφ = δθ

5 3

d ED =

( 5.5 in.)2 + ( 4.8 in.)2
5 3

= 7.3 in.  

δ D = ( 7.3 in.) δφ =  × 7.3 in.  δθ
δ xD =
Virtual Work: 4.8 4.8  5  δD =  × 7.3 in.  δθ = ( 8 in.) δθ 7.3 7.3  3  on DEFG 5  δθ  =0 3  M = 28.0 lb ⋅ ft

Assume M acts

δ U = 0:
or or

FAδ y A + FDδ xD + M δφ = 0

( 20 lb ) (16 in.) δθ  + ( 30 lb ) (8 in.) δθ  + M      
M = − 336.0 lb ⋅ 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 10, Solution 5.

Assume δθ

δ x A = 10 δθ in.

δ yC = 4 δθ in.
δ yD = δ yC = 4 δθ in.

δφ =

δ yD
6

=

2 δθ 3 2   

δ xG = 15 δφ = 15  δθ  = 10 δθ in. 3
Virtual Work: Assume that force P is applied at A.

δ U = 0:

δ U = − Pδ x A + 30 δ yC + 60 δ yD + 240 δφ + 80 δ xG = 0
2  − P...