{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows page 1. Sign up to view the full content.

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 –
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: I have just assumed f = f i . If the assumption is wrong, I will just find f < 0.) α = ⇒ α = α = = ∑ mr f mr I rf M z 2 (2) For rolling motion, α − = r x c & & (3) Substituting (3) into (2) and (2) into (1): β = ⇒ = β ⇒ = = − β = ∑ sin ) 2 / 1 ( 2 sin sin g x x m mg x m x m mg F c c c c x & & & & & & & & . ( ) ( ) ( ) ( ) β = − = ⇒ β = ⇒ β = ∫ ∫ ∫ = = = = = = 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 & & & & & ( ) β = sin ) 4 / 1 ( 2 gt t x f N m g i j k...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online