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Assignment 1 - Solutions - Assignment 1 Solution 1 A A vA 3...

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Assignment 1 - Solution 1. 3 6 , 4 9 1 ( 4 9 ) 106 72 106 A A A v v 2i j k A 3i j k A e 3i j k A v e 2. Work = 9 ft lb f F r Given: Determine: ( , ), ( , ) Solution: ( ) ( ) ( ) cos sin ( r r r z x x r y y r x r r z r y r v v v v v v v v v v v v v v v v v v v v e e k i v i e i e i k j v j ) ( ) ( ) sin cos r z r v v v v e j e j k 3.
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4. Relations are correct ( ) ( ) ( ) ( ) sin cos cos cos sin sin sin cos sin cos cos sin x r r r r r y r z r v v v v v v v v v v v v v v v v v i v i e e e i e i e i e Assignment 1 Solution (Cont.) 5. 1 (2 3 6 ) ( 5 3 ) 490 1 (10 6 3 9 6 30 ) 490 1 ( 21 7 ), 2 490 4 10 d A B e i j k i j k A B e k j k i j i e i k v i j k e v
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Assignment 1 Solution (Cont.) 6. x z y 1 2 3 A B , 2 ( ) ( 2 ) 2 6 3 1 (2 6 3 ) 7 1 7 2 2 7 ( ) 2 surface surface A Q A A 3i j B 3i k A B 3i j 3i k i j k A B e i j k A B A B v e
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1/2 2 2 2 1/2 1/2 (a) 2( ) 2( ) 2((2 3 ) (2 3 )) 8 6 8 (b) | | ( ) ( ) (64 36 64) =2 41 (c) (2 3 ) (2 3 ) 7 (d) = (2 3 ) (2 3 ) xx xx xx D D D E D A B B A i j k i k i j k D D D A B i k i j k F A B i k i j k 1/2 1/2 9 4 +6 ( ) (e) (2 3 ) ( 2 ) 3 7 2 (9 49 4) (62) 1 ( 3 7 2 ) 62 i j k A C e A C A C i k i j k i j k A C n i j k 7. Assignment 1 Solution (Cont.)
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(f) ( ) 1 ( 9 4 +6 ) 133 1 17 ( 2 ) ( 9 4 +6 ) 133 133 17 ( 2 ) ( 9 4 +6 ) 133 1 ( 20 201 164 ) 133 P C C e e A B e i j k A B C e i j k i j k P i j k i j k P i j k B A P C e 7. Assignment 1 Solution (Cont.) 8. Redundant to Prob. 5 removed 9. See notes for stress definition. ( ) ( ) ( ) ( ) ( ) ( ) 1 1 , 2 2 xx yy xy yx x y x xx y yy x xy y yx x xx y yy x xy y yx A x y p p n n n p n p n n n p n p n n dA n n T ii jj ij ji n i j n T
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