EAS208_Exam03_111210_FINAL_Solutions

EAS208_Exam03_111210_FINAL_Solutions - Name: EAS208 Fall...

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EAS208 Fall 2010 – Exam 3 SOLUTIONS Name: Person Number: Problem 1: The crank has a constant clockwise angular velocity of . At the instant shown the angular velocity of rigid rod AB 200 rpm BP is 6.98 rad s , determine: a) The acceleration of the piston P b) The angular acceleration of the rigid rod BP (30 points) Solution: The angular velocity of crank is: AB 2m i n 200 200 20.94 60sec AB rad rpm rpm s rev π ω == = (clockwise) The acceleration of point B relative to point A is: ( ) BAA B B A B A B B AA rr αω =+ × + × × aa r r r ( ) ( ) ( ) ( ) 00 2 2 BA B A B ωω =++− ×− × + ak k i j ( ) ( ) 22 B A B A =− × i B j B ai A B j ( ) ( ) 0 . 9 4 0 . 9 4 B j 876.97 876.97 B = −− j 1
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The acceleration of point relative to point P B is: ( ) PBB P P B P B P P BB rr αω ω =+ × + × × aa r r r () ( ) ( ) ( ) ( )( ) ( ) 876.97 876.97 6 2 6 2 PB P B P B P a = + ×−+ × ×− ii j ki j kk i j ( ) ( ) 876.97 876.97 2 6 2 6 P B P B P a ααω ωω =− + + + × + j i j k i B P B P j 22 876.97 876.97 2 6 6 2 P BP BP BP BP a α αωω + + + j i j i j ( ) 2 6 876.97 6 2 876.97 P B P B P B P a ++ j ( ) 2 1169.29 6 779.53 P B P a αα +− j The and i j components must be equal in the above equation, thus: 2 2 1169.29 2 1169.29 2 1169.29 129.92 0 6 779.53 6 779.53 0 P P P BP BP BP a a a rad s ⎪⎪ ⇒⇒⇒ ⎨⎨ = −= jj 2 2 909.45 129.92 P BP in a s rad s = The acceleration of the piston is P ( ) 2 909.45 P in s ai . The angular acceleration of the
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This document was uploaded on 10/27/2011 for the course EAS 208 at SUNY Buffalo.

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EAS208_Exam03_111210_FINAL_Solutions - Name: EAS208 Fall...

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