ASE 365 - Lecture 2 - Work and energy : work of Increment m...

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Unformatted text preview: Work and energy : work of Increment m F dr dr F ⋅ = dW : energy Kinetic dT m d d m dt dt d m dt m dt dt d m m dW = ⋅ = ⋅ = ⋅ = ⋅ = ⋅ = ⋅ = r r r r r r r r r r dr r 2 1 ) ( ) ( ) ( ) energy kinetic in change done work ( . have must we then , and If =- = = ⋅ = ⋅ = ∫ 1 2 12 2 1 T T W dT dW dW dr F dr F r r ) energy) potential in (change done work ( . and energy potential a is there ve, conservati are forces If- =-- = ) ( 1 2 12 V V W V ) conserved is energy total ( energy total where or so Then = + ≡ = + = +- =-- = V T E E E V T V T T T V V W 2 1 2 2 1 1 1 2 1 2 12 ) ( Systems of particles m1 mi mj m N : for law 2nd s Newton' i m N i m N j i i ij i , , 1 1 = = + ∑ = , a f F i N i N i i N j ij N i i m a f F ∑ ∑ ∑ ∑ = = = = = + 1 1 1 1 : system entire For : cancels so , law, 3rd s Newton' By ∑∑ = =- = N i N j ij ji ij 1 1 f f f system. on force resultant is where F a F F i N i i N i i m ∑ ∑ = = = = 1 1 i N i i tot C N i i C N i i i N i i C m m m m m r r r r r ∑ ∑ ∑ ∑ = = = = = = ≡ 1 1 1 1 so : center mass Define . becomes law 2nd s Newton' and Then C tot C tot C N i i i N i i i N i i m m m m m a F a r r a = = = = ∑ ∑ ∑ = = = 1 1 1 O O O M F r f F r r r r r r r H r r H O Σ = × = + × = × = × + × = × = ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = = = = = = i N i i N j ij i N i i i i N i i i i N i i i i N i i i i N i i m m m m 1 1 1 1 1 1 1 so : about momentum Angular center. mass to relative position is where : center mass About C i i i N i i r r r M F...
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This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas at Austin.

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ASE 365 - Lecture 2 - Work and energy : work of Increment m...

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