Sol Cap 02 - Edicion 8

COSMOS: Complete Online Solutions Manual Organization System
Chapter 2, Solution 54.
From Similar Triangles we have:
L
2
( 3 m) ( 8 L) ( 4.95 m)
2 2 2
− = − −
− 9 = 64 −16 L − 24.5025
or
L = 3.0311 m
Then
4.95 m
cos β =
8 m − 3.0311 m
or β = 4.9989°
And
3m
cosα =
3.0311 m
or α = 8.2147°
Free-Body Diagram At B:
(a) Σ F x = 0:
−T cosα − T cosα + T cos β = 0
or
ABC DE ABC
T
DE
cos β − cosα
=
T
cosα
Σ F y =
0:
ABC
( )
T sinα + T sinα + T sin β − 720 N = 0
ABC DE ABC
Substituting for α and β gives
T ABC
T ABC
⎡
⎛cos
β − cosα
⎞ ⎤
⎢sinα + sinα⎜
⎟ + sin β⎥=
720
⎣
⎝ cosα
⎠ ⎦
T ABC
=
( 720)
cos
sin ( α + β )
( 720)
cos8.2147°
( °+ ° )
=
sin 8.2147 4.9989
α
T ABC =
3117.5 N
or
T = 3.12 kN "
ABC
cos 4.9989°− cos8.2147°
3117.5 N
cos8.2147°
(b) =
( )
T DE
T DE =
20.338 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.
or
T = 20.3 N "
DE