HW19-S07-solution

HW19-S07-solution - Homework 18 Problem#1 Goal the maximum...

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Homework 18 – Problem #1 Goal : the maximum and minimum heights (measured from the floor) if the panel is not to tip Given : dimensions shown in figure, P=200 N, m=50kg, μ =0.15 Assume : panel does not tip, so α =0 Equations : = x G x ma F , , = y G y ma F , , = α G z G I M , Solution : ( ) N m kg s N s m kg mg W 490 1 8 . 9 50 2 2 = = = = = 0 W N F A y N W N A 490 = = N N N F A A 5 . 73 490 15 . 0 = = = μ x G x G A x a g W ma F P F , , = = = ( ) 2 , 2 , 53 . 2 5 . 73 200 490 8 . 9 s m a N N N s m a x G x G + = = ( ) ( ) ( ) = = α G A A z G I P m h F m N m M 6 . 0 6 . 0 25 . 0 , ( )( ) ( )( ) ( )( ) α G I N m h N m N m = 200 6 . 0 5 . 73 6 . 0 490 25 . 0 ( )( ) α G I N h m N = 200 4 . 198 Maximum h occurs when α =0, i.e., just about to tip with α <0 (i.e., clockwise), ( )( ) m N m N h N h m N 992 . 0 200 4 . 198 0 200 4 . 198 max max = = = Also need to check lower limit for h to see if it tips CCW about lower left corner, ( ) ( ) ( ) 0 6 . 0 6 . 0 , = = + = α G A A z G I P m F m N x M ( )( ) ( )( ) ( )( ) 0 200 6 . 0 5 . 75 6 . 0 490 = + N m N m N x m x N m N m N x 152 . 0 490 120 3 . 45 = + = Since x =0.152m < 0.25m, panel won’t tip CCW about lower left corner with P=200N .
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