# ( ) ( ) Physics 111. Lecture 13 (Walker: Ch ) Connected Objects Circular Motion Centripetal Acceleration Centripetal Force Sept.

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1 Physics Lectue 3 (Wlke: Ch ) Connected Objects Cicul Motion Centipetl Acceletion Centipetl Foce Sept. 30, 009 Exmple: Connected Blocks Block of mss m slides on fictionless tbletop. It is connected by sting nd pulley to hnging mss m. Find the cceletion nd sting tension T. Midtem Exm on Mon. Octobe 5 (Chptes -6; Lectues -3) Lectue 3 /8 Lectue 3 /8 Exmple: Atwood s Mchine F T m T m, x, x ( ) F m g T m T m g ( ) m m g mg ( m+ m) m mm g nd T g m + m m + m Lectue 3 3/8 Atwood s Mchine consists of two msses connected by sting nd pulley. Find the cceletion. Lectue 3 4/8

2 Question 3 F, x T m g m, x T m g m m g T m ( m m ) g ( m + m) F mg T m m m g m + m Lectue 3 5/8. T >T b. T T c. T <T Lectue 3 6/8 Exmple: Stgecft () 00 kg set S is stoed in loft boe stge. Rope holding set psses up nd oe pulley, then is tied bckstge. Diecto tells 00 kg stgehnd to lowe the set. He unties nd holds on to ope nd is hoisted into loft. Wht is his cceletion? (Assume mssless ope & mssless, fictionless pulley.) Lectue 3 7/8 Stgehnd: Set: F T w T m g m ( on M ) y S on M M S on M M M My F T w T m g m m ( on S) y M on S S M on S S S Sy S My TM on S TS on M T T m g m M M My T m g m S M My g( m m ) ( m + m ) S M My S M ( ms mm) (00 kg) My g (9.8 m/s ) 3.7 m/s ( m + m ) (300 kg) S M Lectue 3 8/8

3 Unifom Cicul Motion Pticle in Unifom Cicul Motion T peiod the time equied fo one complete ottion. cicumfeence π peiod T Position: Rdius: Speed: constnt constnt Fo pticle in unifom cicul motion, elocity ecto is constnt in mgnitude, but continuously chnges diection. Pticle hs cceletion Thee must be net foce on pticle Lectue 3 9/8 Lectue 3 0/8 Exmple: A Rotting Cnkshft A 4.0 cm dimete cnkshft tuns t 400 pm. Wht is speed of point on sufce of the cnkshft? 400 e minute 40 e/s minute 60 s T 0.05 s (pe eolution) 40 e/s π π (0.00 m) 5.03 m/s T 0.05 s Acceletion in Unifom Cicul Motion Object moing t constnt speed in cicle of dius hs centipetl (towd cente) cceletion cp Diection of this cceletion cp is towds the cente of the cicle. Size of the cceletion is cp / Lectue 3 /8 Lectue 3 /8

4 Centipetl Foce Since object in unifom cicul motion hs centipetl cceletion cp, foce is needed to poide this cceletion. Foce must be poided by ope, fiction, gity, etc. Mgnitude of foce f cp equied to keep n object of mss m moing t speed in cicle of dius, clled centipetl foce becuse it points towd cente of cicle, is gien by: fcp mcp m (6-6) Lectue 3 3/8 Souces of Centipetl Foce This centipetl foce my be poided by the tension in sting, the noml foce, o fiction, mong othe souces. Lectue 3 4/8 Exmple: Rounding Cone Bnked Cues A c ounds cone of dius. If coefficient of fiction between ties nd od is µ s, wht is mximum speed c cn he without skidding? Fx fs µ sn mx m 0 y µ smg m µ sg Question: Did we need to know mss of c? F N W N mg (0.8)(45.0 m)(9.8 m/s ) 9.0 m/s Lectue 3 5/8 Lectue 3 6/8

5 If od is bnked t the pope ngle θ, c cn ound cue without the ssistnce of fiction between the ties nd the od nd without skidding. Wht bnk ngle θ is needed fo c of mss m teling t speed ound cue of dius? Lectue 3 7/8 F 0 Ncosθ W Ncosθ mg y N cosθ mg Fx N sinθ mx mcp m / N sin θ / tnθ m N cosθ mg g θ ctn g Notice tht thee is only one speed t which gity exctly poides the needed centipetl foce. Lectue 3 8/8 Centifuge A centifuge is lbotoy deice used in chemisty, biology, nd medicine fo septing out solids suspended in liquid by spinning tubes of the liquid t high speed. The liquid noml foce cnnot poide the needed centipetl foce on the solids, so the solids collect t the bottom of the tubes. Lectue 3 9/8 Tngentil & Totl Acceletion An object my be chnging its speed (speeding up o slowing down) s it moes in cicul pth. In tht cse, thee is tngentil cceletion s well s centipetl cceletion. The totl cceletion totl is the ecto sum of the centipetl cceletion cp, which points towd the cente of ottion, nd the tngentil cceletion t, which points in the diection of speed incese. Lectue 3 0/8

6 Centipetl Acceletion Question Which motion hs the lgest centipetl cceletion? cp (centipetl cceletion) t π T (tngentil elocity) Lectue 3 /8 Lectue 3 /8 Exmple: Spinning in Cicle Fthe plces 0 kg child in 5.0 kg ct to which is ttched.0 m long ope. He holds the end of the ope nd spins the ct nd child in cicle, keeping the ope pllel to gound. If tension in ope is 00 N, how mny eolutions pe minute does ct mke? Lectue 3 3/8 m ( Fnet ) F T ; T (.0 m)(00 N) t.83 m/s; m (5 kg) t (.83 m/s).4 d/s 3.5 pm (.0 m) Lectue 3 4/8

7 Exmple: Stellite s Motion Stellite moes t constnt speed in cicul obit bout cente of Eth nd ne sufce of Eth. If mgnitude of its cceletion is g 9.8 m/s nd Eth s dius is 6,370 km, find its speed nd time T equied fo one complete eolution. cp g g 3 3 (6,370 0 m)(9.8 m/s ) m/s 7,700 mi/h T 3 3 π/ π(6,370 0 m)/(7.9 0 m/s) 5,060 s 84.3 min End of Lectue 3 Befoe Fidy, ed Wlke Section 7. Homewok Assignment #6c should be submitted using WebAssign by :00 PM on Study, Oct. 3. (HW #6b due tonight.) MIDTERM I on Mondy Octobe 5. (Chptes -6; Lectues -3.) Lectue 3 5/8 Lectue 3 6/8

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