05 Uniform Circular Motion

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[ 5 ] v 2vaR1 2vF ma mR1 00Fa vvvv 5-1 5-1 0.300 kg 0.140 m F ma1 224 RaTr1 ( )( )224 0.14022.10.50ar1 1 T = = 0.50 m/s2 ( ) ( )0.300 22.1 6.63 F 5-2 5-2 m L v r v vv x y 0yF xF ma12sinxvF T mru cos 0 T mg u y x2tanvrgu v tan v rg u r = L sin sin tan v Lg u u 5-35-3 0.30 kg 2.0 m 40 40mgT sin T cos T sin tan v Lg u u ( ) ( )( ) ( )2.0 9.8 sin 40 tan 403.25v o om/s 5-45-4 BMW 230 m s = 0.87 2x svF f mR 0yF N mg N mg , max s s sf N mg 2svmg mR sv gR ( ) ( ) ( )0.87 9.8 230 44 v m/s 5-55-5 25 / 230 x y 2sinxvF N mRu cos 0yF N mg u 2tanvgRu ( )( ) ( )225tan 0.2779.8 230u 1tan 0.277 15 u

o = 180o = 0ocos F T mg ma u1 1sin F mg ma u P P2vT m gR| ` . ,2vT m gR| ` + . , 5-65-6 60.0 kg 8.00 10.0 vmgN 2tvF mg N mR1 ( )2 8.0025.0310RvTrr m/s2tvN m gR| ` . ,( )25.0360.0 9.8 3988.00tN| ` . , 2BvF N mg mR1 2BvN m gR| ` + . ,( )25.0360.0 9.8 7788.00BN| ` + . , G G = 6.67259 X 10-11 N.m2/kg2 1 22Gm mFr5-75-7 3.84 X 108 27.3 m M 22v GmMF mR R1 2RvMG( )6hour min s27.3 day 24 60 60 2.36 10 sday hour minT| `| `| ` . ,. ,. ,( )8362 3.84 1021.02 102.36 10RvTrr m/s2RvMG( ) ( ) 28 311243.84 10 1.02 106.67 105.99 10