P7a - I have just assumed f = f i . If the assumption is...

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Discussion 7a: Name: solutions TAM212, Spring, 2003 The mass of the object shown (m) is concentrated around the outside edge. The radius is R. It is released from rest when t = 0. If it rolls (no slipping), what is its displacement after t seconds? Find: x as a function of t Solution: We could find x by first finding the acceleration in the x- direction and integrating. For this, we need to first find the forces: Using the coordinate system shown, = + β = c x x m f mg F sin (1) (Note: I have chosen the direction of f arbitrarily. As long as there is no slipping, this is fine –
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Unformatted text preview: I have just assumed f = f i . If the assumption is wrong, I will just find f < 0.) = = = = mr f mr I rf M z 2 (2) For rolling motion, = r x c & & (3) Substituting (3) into (2) and (2) into (1): = = = = = sin ) 2 / 1 ( 2 sin sin g x x m mg x m x m mg F c c c c x & & & & & & & & . ( ) ( ) ( ) ( ) = = = = = = = = = = sin ) 4 / 1 ( sin ) 2 / 1 ( sin ) 2 / 1 ( 2 gt t x dx g t x dt g x d t x x x t t t t x x x & & & & & ( ) = sin ) 4 / 1 ( 2 gt t x f N m g i j k...
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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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