exam2_solns - TAM 212 Spring, 2003 Exam 2 Solutions 1. ) (...

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Unformatted text preview: TAM 212 Spring, 2003 Exam 2 Solutions 1. ) ( ) ( ) ( ) ( 1 2 1 2 2 1 t m t m t t dt c c t t ext v v L L F − = − = ∫ ∑ ( ) 3 / 2 ) ( ) ( 2 1 v v v m m mv m t m dt f f i i i i i i t t t ext = ⇒ + = ⇒ = ⇒ = ∑ ∑ ∫ ∑ = = v v F 2. ∑ ∑ ∫ ∑ − = = = i i i i i i t t t ext m t m dt ) ( ) ( 2 1 v v F . x-direction ∑ ∑ ∫ ∑ − = ⇒ = = i i x i i i x i t t t ext x v m t v m dt F ) ( ) ( , , , 2 1 Take x-direction parallel to the slope, and consider the system of man and plank together mg mg F ext x 4 30 sin 8 , = = ∑ ) ( ) ( 7 4 4 2 1 − + = = ⇒ ∫ = = t mv t mv mgt mgdt man plank t t t [ ] g L t L x x gt dt t v t v gtdt man plank t t t man plank t t t / 25 . 2 5 . 4 7 2 ) ( ) ( 7 4 2 2 1 2 1 = ⇒ = ∆ + ∆ = ⇒ + = ⇒ ∫ ∫ = = = = 3. For ref. frame F (fixed to the page) take direction I to the right, J, up, and K out of the page. Consider also a second, ref. frame B fixed to bar B , with the same directions: i to the right, j, up, and k out of the page. , with the same directions: i to the right, j, up, and k out of the page....
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This note was uploaded on 04/09/2008 for the course TAM 212 taught by Professor Keane during the Spring '08 term at University of Illinois at Urbana–Champaign.

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