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

2019
Views:

177

Pages:

2
Author:

VequeNupdubr6r

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 114. (a) Let ( R, M D ) be the equivalent force-couple system at D. First note... At x = b; y = h For y = k x2 We have h = k b 2 h or k = 2 b  h  2 ∴ y =  2 x b   h  y =  2  x2 For any contact point c alone the surface b  dy h =2 2x dx b  b2  tan −1    2hx  R = F and ΣΜ D : M D = − ( x ) F sin θ + ( h − y ) F cosθ  b2 = −x F   b 4 + 4h 2 x 2  or MD   2h x  +  h − h x 2  F 2 4   b  b + 4h 2 x 2    h 2  2  − xb +  h − 2 x  ( 2hx )  b    = F  4 2 2 b + 4h x  2h 2 x 3  2 2  − xb + 2h x −  b2   = F b 4 + 4h 2 x 2 or M D .  2h 2 x3  2 2  2h − b x −  b2  = F   b 4 + 4h 2 x 2   ( ) COSMOS: Complete Online Solutions Manual Organization System b = 1 ft, h = 2 ft (b) With  7 x − 8 x3  MD =  F 2   1 + 16 x  For M D to be a maximum Then dM D dx   7 − 24 x 2 = 0 = F    ( ) 1 1 + 16 x 2 − 7 x − 8x3   ( 32 x ) 1 + 16 x 2 2 2 1 + 16 x ( ( ) ) ( ) − 1 2       For the non-trivial solution: ( )( ) ( 0 = 7 − 24 x 2 1 + 16 x 2 − 16 x 7 x − 8 x ) 0 = 256 x 4 + 24 x 2 − 7 Solving by the quadratic formula gives for the positive root. x = 0.354 ft .

COSMOS Chapter 3 Solution 114

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