COSMOS Chapter 4 Solution 77 | Michigan State University - Edubirdie

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

2023
Views:

242

Pages:

1
Author:

Tyshawn Shaffer

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 77. Free-Body Diagram: Note that the clamp is a three-force body. D is the intersection of the lines of action of the three forces. From the free-body diagram it follows that: y AD = (4.2 in.) tan 78o = 19.7594 in. yBD = y AD − 2.8 in. = (19.7594 − 2.8) in. = 16.9594 in. Then  yBD    7.8 in.  θ = tan −1   16.9594 in.  = tan −1   = 65.3013° , and  7.8 in.  α = 90° − θ − 12° = 90° − 65.3013° − 12° = 12.6987° (a) Using the maximum allowable compressive force on the clamp: ( RB ) y = RB sin θ = 40 lb or RB = 40 lb = 44.028 lb sin 65.301° or R B = 44.0 lb (b) 65.3° Using the law of sines for the force triangle: RB NA T = = sin12° sin α sin(90° + θ ) 44.028 lb NA T = = sin12° sin12.6987° sin155.301° which gives: N A = 46.551 lb (c) T = 88.485 lb or N A = 46.6 lb or T = 88.5 lb

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