sol ass2

# sol ass2 - PROBLEM 12.16 Block A has a mass of 40 kg and...

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PROBLEM 12.16 Block A has a mass of 4 0 kg , and block B has a mass of 8 kg . The coefficients of friction between all surfaces of contact are 0.20 s s P m k = 0.15. Knowing that P = 50 N o , determine ( a ) the acceleration of block B , ( b ) the tension in the cord. SOLUTION Constraint of cable: + , 2c o n s t a n t . AB A A B xx x .0 . 0, or B A aa a a . 0 Assume that block A moves down and block B moves up. Block B : + 0: cos 0 yA B B FN W T 6 0 x :s i n B xA B B B W Fm a T N W a g PT 0. . Eliminate AB N and . B a +, sin cos B A BB B TW W W g g TP T . 0 Block A : cos sin 0 A B A N W P TT 0 0 . cos sin AA BA NN W P . 0 + , cos sin WW P . 0 i n c o s A A A A B A A W a T W F FP a g 0 0 . sin cos sin cos A A B a W W g TP 0.0 .0 cos sin cos A A a P P W g . . + , + , sin 3 cos sin cos A A B a W W P g 00 . . . . Check the condition of impending motion. 0.20, 25 sA B PP q + , + , + , sin 3 cos sin cos 0 s A B s s W W P P T . . . A P B 25°

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PROBLEM 12.16 CONTINUED + , + , 3c o s s i n sin cos sA B A B s s WW W W P P TT PT T .0 0 . Blocks will move with 5 0 N . P Calculate A a g using 0.15, 25 , and 5 0 N . k P PP q 2 2m /s B a 25 q W 59 . 8N T W = ( . )( )( . )cos ( )( . ) .s i n c o s 0 20 64 9 81 25 32 9 81 020 25 °− °+ ° = –19.04 N < 50 N a g A = ( )sin ( ) cos ( sin cos ) W W P AB k A B k -- + + + + qm q m q q 3 = ( )( . )sin ( . )( )( . )cos ( )( . sin cos () ( .) 32 9 81 25 015 64 9 81 25 50 015 25 25 ) 48 9 81 ° = 0.203449 a A = (0.203449) (9.81) = 1.995 m/s 2 ( a ) a B = –1.995 m/s 2 ( b ) T = W B (sin q + m cos q ) + W B a g A = (8) (9.81) (sin 25° + 0.15 cos 25°) + (8) (9.81) (0.203449)
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## This note was uploaded on 11/15/2011 for the course CIVE 281 taught by Professor Prof.v.h.chu during the Spring '10 term at McGill.

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sol ass2 - PROBLEM 12.16 Block A has a mass of 40 kg and...

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