MidTerm1Solution

# MidTerm1Solution - 1 3 1 2 ML I = − =(10 points(c Again...

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Mid-term Exam I Solutions Problem 1 (10+15+5 points) Chapters 10,11,12,13,14 (a) As the net torque around the pivot is zero: ). 2 / ( 30 sin L Mg mgL L T + = ° (5 points) (5 points) . 29 ) / 8 . 9 )( 0 . 1 0 . 1 2 ( ) 2 ( 2 / ) 2 / ( N kg N kg kg g M m L gL M m T = + = + = + = . 20 ) / 8 . 9 )( 0 . 1 5 . 0 2 ( N kg N kg kg = + = (for A) (for B) (b) As the net force is zero: ° = = + ° = (1) 30 cos 0 30 cos T R R T F x x x ° + = = + ° = ) 2 ( 30 sin ) ( 0 30 sin T g M m R R Mg mg T F y y y (5 points) N 17 N 25 30 cos ) 1 ( = ° = T R x (for A) (for B) N 7 . 4 N 1 . 5 30 sin ) ( ) 2 ( = ° + = T g M m R y (for A) (for B) (c) Using the result from Part (b): ) 165 ( 15 ) 168 ( 12 / tan ° ° ° ° = = θ x y R R (for B) (for A) (5 points) (5 points) (5 points)

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Problem 2(10+10+10 points) (a)Conservation of angular momentum and the definition of angular momentum (10 points): 2 2 2 2 ) 2 / 17 ( ) 2 )( 2 )( 2 / 1 ( , ) 2 / 1 ( ; ; MR R M I I MR I I L I L I L A B A B B B A A = + = = = = = = ω 059 . 0 17 / ) ) 2 / 17 /(( ] ) 2 / 1 [( ) / ( 2 2 = = = = MR MR I I B A B For A 2 2 2 2 2 531 . 0 ) 16 / 17 )( 2 / 1 ( ) 2 / )( 2 / )( 2 / 1 ( , ) 2 / 1 ( MR MR R M I I MR I A B A = = + = = 94 . 0 ] 531 . 0 /[ ] ) 2 / 1 [( ) / ( 2 2 = = = MR MR I I B A B For B
Problem 2 (cont’d) (b) The moment of inertia about the center of mass I can be obtained from that about one of the ends of a rod I’ using the parallel axis theorem. M L I I 2 ) 2 / ( ' + = where . ) 3 / 1 ( ' 2 ML I = . ) 12 / 1 ( )] 4

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Unformatted text preview: / 1 ( ) 3 / 1 [( 2 ML I = − = (10 points) (c) Again from conservation of angular momentum 2 2 2 2 ) 6 / 5 ( ) 2 / 1 ( ) 2 ( ) 12 / 1 ( , ) 2 / 1 ( ; ; MR MR R M I MR I I L I L I L C A C C C A A = + = = = = = = ω . ) 5 / 3 ( ] ) 6 / 5 /[( ] ) 2 / 1 [( ) / ( 2 2 = = = MR MR I I C A C (10 points) Problem 3(10+10+10) (a) Using the given formula with . 375 , / . 15 , ' Hz f s m v v A L s = − = = (b) Using the given formula with , / . 15 , / . 35 s m v s m v L s = = . 371 ' Hz f B = (10 points) (10 points) (c) The beat frequency is the difference between two frequencies, . 4 ' ' Hz f f B A = − (10 points)...
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MidTerm1Solution - 1 3 1 2 ML I = − =(10 points(c Again...

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