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T1a7s - Assignment 7 solutions(Fall term Physics 102 7.9...

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7.9 Main Rotor: ( ) 2 rad rev 1 min 3.80 m 450 min 1 rev 60 s v r π ω = = = 179 m s m = 179 = s 343 m s sound v v 0.522 sound v Tail Rotor: ( ) 2 rad rev 1 min 0.510 m 4138 min 1 rev 60 s v r π ω = = = 221 m s m = 221 = s 343 m s sound v v 0.644 sound v 7.21 Friction must supply the needed centripetal force. Hence, it is necessary that ( ) c s max F f , or ( ) 2 t s v m m r µ g and the maximum safe speed is ( ) ( )( ) ( ) 2 0.70 20 m 9.80 m s t s max v r g µ = = = 12 m s . 7.23 (a) ( ) ( ) 2 2 2.00 m 3.00 rad s c a r ω = = = 2 18.0 m s (b) ( ) ( ) 2 50.0 kg 18.0 m s c c F m a = = = 900 N (c) We know the centripetal acceleration is produced by the force of friction. Therefore, the needed static friction force is 900 N s f = . Also, the normal force is . Thus, the minimum coefficient of friction required is 490 N n mg = = ( ) 900 N = 490 N s max s f n µ = = 1.84 .
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