homework7-solutions

Law of sines ac sin90 bc sin90 l sin bc cos l sin cos

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Unformatted text preview: ty: vA cos( sin ) ) vA sin l cos( Velocity of B: vB vB ( BC ) vA cos cos( l cos sin ) 50 , l vA sin l cos( ) Data: (a) vA sin l cos( 20 , 0.6 m, vA 3 m/s ) 3 m/s sin 50 0.6 m cos(50 20 ) 4.42 rad/s (b) vB 4.423 rad/s cos vA cos( ) cos 20 (3 m/s) cos(50 20 ) 3.2552 m/s vB vB 3.26 m/s 50° Chapter 15, Solution 119 Velocity. Gears: Since vE T Tooth of gear D in contact with gear A vT r A (3 in.) A 0, E is instantaneous center of gear D. vT (3 in.) A 2r D D 2(3 in.) D 1 2 r D A vD (3 in.) 1 2 A (1.5 in.) A Spider: vD (1.5 in.) A (6 in.) (6 in.) S S S 1 4 A A 150 rpm 15.708 rad/s D S 1 2 1 4 A 7.854 rad/s 3.927 rad/s A Acceleration. Spider: S 3.927 rad/s aD aD ( AD) 2 S (6 in.)(3.927 rad/s) 2 92.53 in./s 2 Gear D: Plane motion Trans. with D Rotation about D PROBLEM 15.119 (Continued) (a) Tooth T in contact with gear A. aT aD aT/D aD ( DT ) 2 D 92.53 in./s 2 92.53 in./s 2 (3 in.)(7.854 rad/s) 2 185.06 in./s 2 aT 92.53 in./s 2 aT 92.5 in./s 2 (b) Tooth E in contact with gear E. aE aD a E/D aD ( ED) 2 D 92.53 in./s 2 92.53 in./s 2 (3 in.)(7.854 rad/s) 2 185.06 in./s 2 aE 278 in./s 2 aE 277.6 in./s 2...
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