COSMOS Chapter 4 Solution 61

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 61. Free-Body Diagram: 1. Three non-concurrent, non-parallel reactions (a) Completely constrained
(b) Determinate
(c) Equilibrium
From free-body diagram of bracket: ΣM A = 0: B (1 m ) − (100 N )( 0.6 m ) = 0 ∴ B = 60.0 N
ΣFx = 0: Ax − 60 N = 0 ∴ A x = 60.0 N ΣFy = 0: Ay − 100 N = 0 ∴ A y = 100 N ( 60.0 )2 + (100 )2 Then A= = 116.619 N and θ = tan −1   = 59.036°  60.0   100  ∴ A = 116.6 N 59.0°
2. Four concurrent reactions through A (a) Improperly constrained
(b) Indeterminate
(c) No equilibrium
3. Two reactions (a) Partially constrained
(b) Determinate
(c) Equilibrium
COSMOS: Complete Online Solutions Manual Organization System From free-body diagram of bracket ΣM A = 0: C (1.2 m ) − (100 N )( 0.6 m ) = 0 ∴ C = 50.0 N
ΣFy = 0: A − 100 N + 50 N = 0 ∴ A = 50.0 N
4. Three non-concurrent, non-parallel reactions (a) Completely constrained
(b) Determinate
(c) Equilibrium
From free-body diagram of bracket  1.0   = 39.8°  1.2  θ = tan −1  BC = (1.2 )2 + (1.0 )2 = 1.56205 m  1.2   ΣM A = 0:   B  (1 m ) − (100 N )( 0.6 m ) = 0  1.56205   ∴ B = 78.1 N 39.8°
ΣFx = 0: C − ( 78.102 N ) cos 39.806° = 0 ∴ C = 60.0 N
ΣFy = 0: A + ( 78.102 N ) sin 39.806° − 100 N = 0 ∴ A = 50.0 N
5. Four non-concurrent, non-parallel reactions (a) Completely constrained
(b) Indeterminate
(c) Equilibrium
From free-body diagram of bracket ΣM C = 0: (100 N )( 0.6 m ) − Ay (1.2 m ) = 0 ∴ Ay = 50 N or A y = 50.0 N
6. Four non-concurrent non-parallel reactions (a) Completely constrained
(b) Indeterminate
(c) Equilibrium
continued COSMOS: Complete Online Solutions Manual Organization System From free-body diagram of bracket ΣM A = 0: − Bx (1 m ) − (100 N )( 0.6 m ) = 0 ∴ Bx = −60.0 N or B x = 60.0 N
ΣFx = 0: − 60 + Ax = 0 ∴ Ax = 60.0 N or A x = 60.0 N
7. Three non-concurrent, non-parallel reactions (a) Completely constrained
(b) Determinate
(c) Equilibrium
From free-body diagram of bracket ΣFx = 0: Ax = 0 ΣM A = 0: C (1.2 m ) − (100 N )( 0.6 m ) = 0 ∴ C = 50.0 N or C = 50.0 N
ΣFy = 0: Ay − 100 N + 50.0 N = 0 ∴ Ay = 50.0 N ∴ A = 50.0 N
8. Three concurrent, non-parallel reactions (a) Improperly constrained
(b) Indeterminate
(c) No equilibrium