Assignment 1 - Solutions

Assignment 1 - Solutions - Assignment 1 - Solution 1. A A...

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Unformatted text preview: Assignment 1 - Solution 1. A A vA 3. 2i 3j 6k , eA 2. v v eA A 3i 4 j 9k 1 ( 3i 4 j 9k ) 106 72 106 Work = F r Given: v Determine: 9 ft lb f vr e r vx v er vz k v x ( vr , v ), v y v y ( vr , v ) Solution: vx iv vr cos vy jv vr sin vr ( i e r ) v ( i e ) v z ( i k ) v sin vr ( j e r ) v ( j e ) v z (j k ) v cos Assignment 1 Solution (Cont.) 4. Relations are correct vx iv i ( vr e r ve ve ) vr ( i e r ) v ( i e ) v ( i e ) vr sin cos v cos cos v sin vy vr sin sin v cos sin v cos vz vr cos v sin 5. e e e d AB AB 1 (2i 3j 6k ) ( i 5 j 3k ) 490 1 (10k 6 j 3k 9i 6 j 30i ) 490 1 ( 21i 7k ), v i 2 j k 490 4 ev 10 Assignment 1 Solution (Cont.) z 6. A 3i j, B 3i 2k A B ( 3i j) ( 3i 2k ) 2i 6 j 3k e AB AB Asurface B 1 1 (2i 6 j 3k ) 7 1 AB 2 Q ( v e ) Asurface 7 2 7 2 2 3 x A y Assignment 1 Solution (Cont.) 7. (a) D 2( A B) 2( B A ) 2((2i 3j k ) (2i 3k )) 8i 6 j 8k (b) | D | ( D D)1/2 2 ( D xx 2 Dxx 2 Dxx )1/2 (64 36 64)1/2 =2 41 (c) E A B (2i 3k ) (2i 3j k ) 7 (d) F A B = (2i 3k ) (2i 3 j k ) 9i 4 j+6k (e) e ( A C) AC A C (2i 3k ) ( i j 2k ) 3i 7 j 2k AC n (9 49 4)1/2 1 ( 3i 7 j 2k ) 62 (62)1/2 Assignment 1 Solution (Cont.) 7. (f) P C (C e )e e AB AB C 1 ( 9i 4 j+6k ) 133 B e 1 ( i j 2k ) ( 9i 4 j+6k ) 133 17 P ( i j 2k ) ( 9i 4 j+6k ) 133 1 P ( 20i 201j 164k ) 133 17 133 Ce P A 8. Redundant to Prob. 5 – removed 9. See notes for stress definition. T (p n xx )ii ( p yy ) jj xy ij yx ji nx i n y j nT nx ( p xx )i n y ( p yy ) j nx xy j ny yx F nx ( p xx )i n y ( p yy ) j nx xy j ny yx A nx 1 , 2 ny 1 2 i i dA Assignment 1 Solution (Cont.) 10. T Txx ii Txy ij Tyy jj Tyx ji r er T e Txx cos sin Tyy sin cos Tyx sin 2 3 3 3 1 Txx Txy Tyy Tyx 4 4 4 4 15 3 15 10 3 10 25 (1 4 4 4 4 4 4.58 Pa r r r 11. Txy cos2 3) Rectangular Coordinates: A i x Ax x j y Ay y k Az z z ( Ax i Ay j Az k ) Assignment 1 Solution (Cont.) 11. Cylindrical Coordinates: A er = A r e 1 r k z ( Ar e r Ae Az k ) A e Ar 1 Ar e e e r Ar r eA rr Ar 1 1A 1 Ar (e e ) A (e ( e r )) rr r r Ar 1 1A Az Ar rr r z 1 1A Az ( rAr ) rr r z Az z Az z ...
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This note was uploaded on 10/09/2011 for the course ENGINEERIN 3133 taught by Professor Sarkozi during the Spring '11 term at Texas A&M.

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Assignment 1 - Solutions - Assignment 1 - Solution 1. A A...

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