University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2024
Views:

320

Pages:

1
Author:

Dixie Summers

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