COSMOS: Complete Online Solutions Manual Organization System
Chapter 4, Solution 78.
Free-Body Diagram: (for hoist AD)
Note that the hoist AD is a three-force body.
E is the intersection between the lines of action of the three forces
acting on the hoist.
From the free-body diagram:
x AE = (48 in.) cos 30° = 41.5692 in.
y AD = (48 in.)sin 30° = 24 in.
yBE = x AD tan 75° = (41.5692 in.)tan75°
= 155.1384 in.
Then:
yBE − 16 in.
−1 139.1384
= tan
x
41.5692
AD
α = tan −1
= 73.36588°
β = 75° − α = 75° − 73.36588° = 1.63412°
θ = 180° − 15° − β = 165° − 1.63412° = 163.366°
From the force triangle and using the law of sines:
260 lb
B
A
=
=
sinβ
sin θ
sin15°
260 lb
B
A
=
=
sin 1.63412° sin 163.366° sin 15°
Solving for A and B:
(a)
(b)
B = 2609.9 lb
or B = 2.61kips
75.0°
or A = 2.36 kips
73.4°
A = 2359.8 lb
COSMOS Chapter 4 Solution 78
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