A2 9th Edition Solution

A2 9th Edition Solution - PROBLEM 12.16 Block A has a mass...

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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 = 40 N o , determine ( a ) the acceleration of block B , ( b ) the tension in the cord. SOLUTION Constraint of cable: + , 2 constant. A B A A B x x x x x . 0 . 0, or A B B A a a a a . 0 Assume that block A moves down and block B moves up. Block B : + 0: cos 0 y AB B F N W T 6 0 + x : sin B x AB B B W F ma T N W a g P T 6 0 . . Eliminate AB N and . B a + , sin cos B A B B B a a T W W W g g T P T 0 . . 0 Block A : + 0: cos sin 0 y A AB A F N N W P T T 6 0 0 . cos sin A AB A N N W P T T . 0 + , cos sin B A W W P T T . 0 : sin cos A x A A A AB A A W F m a T W F F P a g T T 6 0 . 0 0 . + , sin cos sin cos A B B A B a W W W W g T P T T P T 0 . 0 . 0 + , cos sin cos A B A A a W W P P W g P T P T T 0 . . . + , + , + , + , sin 3 cos sin cos A A B A B A B a W W W W P W W g T P T P T T 0 0 . . . . Check the condition of impending motion. 0.20, 0, 25 s A B a a P P T q + , + , + , sin 3 cos sin cos 0 A B s A B s s W W W W P T P T P T T 0 0 . . . A P B 25°
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PROBLEM 12.16 CONTINUED + , + , 3 cos sin sin cos s A B A B s s W W W W P P T T P T T . 0 0 . Blocks will move with 4 0 N . P Calculate A a g using 0.15, 25 , and 4 0 N . k P P P T q W 58.2 . N T W = ( . )( )( . )cos ( )( . ) . sin cos 0 20 64 9 81 25 32 9 81 0 20 25 25 °− ° + ° = –19.04 N < 40 N a g A = ( )sin ( )cos ( sin cos ) W W W W P W W A B k A B k A B - - + + + + q m q m q q 3 = ( ) ( . ) sin ( . ) ( ) ( . ) cos ( ) ( . sin cos ( ) ( . ) 32 9 81 25 015 64 9 81 25 40 015 25 25
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