Mecanica vectorial
Chapter 3, Solution 1.
Resolve 90 N force into vector components P and Q where Q = ( 90 N ) sin 40° = 57.851 N Then M B = − rA/BQ
= − (0.225 m )(57.851 N ) = −13.0165 N ⋅ m
M B = 13.02 N ⋅ m
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, WilliamE. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.
COSMOS: Complete Online Solutions Manual Organization System
Chapter 3, Solution 2.
Fx = ( 90 N ) cos 25°
= 81.568 N
Fy = ( 90 N ) sin 25° = 38.036 N x = ( 0.225 m ) cos 65° = 0.095089 m
y = (0.225 m ) sin 65°
= 0.20392 m
M B = xFy − yFx
= ( 0.095089 m )( 38.036 N ) − ( 0.20392 m )( 81.568 N ) =−13.0165 N ⋅ m
M B = 13.02 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 3, Solution 3.
Px = ( 3 lb ) sin 30°
= 1.5 lb
Py = ( 3 lb ) cos 30°= 2.5981 lb
M A = xB/ A Py + yB/ A Px
= ( 3.4 in.)( 2.5981 lb ) + ( 4.8 in.)(1.5 lb ) = 16.0335 lb ⋅ in.
M A = 16.03 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 ManualOrganization System
Chapter 3, Solution 4.
For P to be a minimum, it must be perpendicular to the line joining points A and B with rAB =
( 3.4 in.)2 + ( 4.8 in.)2
= 5.8822 in.
α = θ = tan −1 x
4.8 in. = tan −1 3.4 in.
y
= 54.689°
Then or
M A = rAB Pmin Pmin = M A 19.5 lb ⋅ in. = rAB 5.8822 in.
= 3.3151 lb ∴ Pmin = 3.32 lb
54.7°
or
Pmin = 3.32lb
35.3°
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 3, Solution 5.
By definition where and
M A = rB/ A P sin θ
θ = φ + ( 90° − α ) φ =tan −1
4.8 in. 3.4 in.
= 54.689° Also
rB/ A =
( 3.4 in.)2 + ( 4.8 in.)2
= 5.8822 in.
Then or or
(17 lb ⋅ in.) = ( 5.8822 in.)( 2.9 lb ) sin ( 54.689° + 90° − α )
sin (144.689° − α ) = 0.99658 144.689° − α = 85.260°; 94.740° ∴ α = 49.9°, 59.4°
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 3, Solution 6.
(a)
(a) M A = rB/ A × TBF
M A = xTBFy + yTBFx
= ( 2 m )( 200 N ) sin 60° + ( 0.4 m )( 200 N ) cos 60° = 386.41 N ⋅ m or M A = 386 N ⋅ m (b) (b) For FC to be a minimum, it must be perpendicular to the linejoining A and C.
∴ M A = d ( FC )min
with
d =
( 2 m )2 + (1.35 m )2
= 2.4130 m
Then 386.41 N ⋅ m = ( 2.4130 m ) ( FC )min
( FC )min
and
= 160.137 N 1.35 m = 34.019° 2m
φ = tan −1
θ = 90 − φ = 90° − 34.019° = 55.981°
∴ ( FC )min = 160.1 N
56.0°
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 3, Solution 7.
(a)
M A = xTBFy + yTBFx
= ( 2 m )( 200 N ) sin 60° + ( 0.4 m )( 200 N ) cos 60° = 386.41 N ⋅ m
or M A = 386 N ⋅ m
(b)
Have or
M A = xFC
FC =
MA 386.41 N ⋅ m = 2m x
∴ FC = 193.2 N...
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