Ch06: Force and Motion - II

Transcription

1 Ch6: oce and Motion - II Static iction Kinetic iction iction popetie Unifom cicula motion Centipetal acceleation Newton law in Unifom cicula motion 6.: iction ictional foce ae common and impotant in ou dail lie: due to fiction we can wal on eath ca unde dange can top due to fiction when beaing ou can t moe hea cate when puhing it due to fiction ictional foce i due to the inteaction of two adjacent uface at the atomic o molecula leel foce i needed to bea the welding between uface fictional foce due to action eaction iction i alwa paallel to the uface of inteaction and oppoite the diection of motion. 6.: iction ictional oce: motion of a cate with applied foce With no applied foce, Thee i no attempt at liding no fiction 6.: iction ictional oce: motion of a cate with applied foce inall, the applied foce ha oecome the tatic fictional foce Bloc lide and acceleate Kinematic fiction f oce attempt liding but i balanced b the fictional foce No motion. Static fictional foce f oce i now tonge but i till balanced b the fictional foce. No motion. Lage tatic fictional foce f 1

2 6.3: Popetie of iction Popet 1. If the bod doe not moe, then the tatic fictional foce f and the component of that i paallel to the uface balance each othe. The ae equal in magnitude, and i f diected oppoite that component of. Popet. The magnitude of f ha a maimum alue f,ma that i gien b µ i coefficient of tatic fiction Popet 3. If the bod begin to lide along the uface, the magnitude of the fictional foce apidl deceae to a alue f gien b iction i popotional to the nomal foce. iction i independent of aea. µ i geneall lage than µ. µ i coefficient of inetic fiction The coefficient do not depend on weight o peed and geneall ange between.3 and : Popetie of iction: Eample A ca diing with a peed. an emegenc beaing made It to top in a ditance of 9 m a hown. If µ between tie and teet i.6, find it initial peed a f a µ N = µ a a = µ g = = (.6)(9.8) = 5.88m / f N = + a = + a = = a ( 5.88)(9) = 58m / 1 g Bo on uface with fiction. If µ =.5 and µ =.3 find a) how lage hould be to get bo tat moing? b) once it moing, find the acceleation Solution: analze to it component in5 a) Stat moing not moing (a=), f but, f i at it maimum coθ f co 5 µ n...(1) Wecanfindn fom-diection a a 6.3: Popetie of iction: Eample - bo on ough uface n + in 5 (a ) (a ) n g in 5...() (co 5 + µ in 5 ) = µ µ = co 5 + µ in 5.5(1)(9.8) = = 53N co 5 + (.5)in 5 co5 co 5 µ n a =, m co 5 µ µ in 5 n g in 5 (fom - diection) b) When moing we hae acceleation a and inetic fiction f a hown 6.3: Popetie of iction: Eample - bo on ough uface a coθ f a co 5 µ n a co 5 µ ( in 5) a = m 53co 5 (.3)((1)(9.8) 53in 5) a = = 1.6m / ² 1 f in5 co5

3 1 g Bo on incline uface with fiction. If µ =.5 and µ =.3 find a) At what angle the object tat moing b) once it moing, find the acceleation Solution: a) Object not mong f a inθ f (a ) inθ µ n...(1) 6.3: Popetie of iction: Eample - bo on ough incline uface a n coθ n g coθ...() (a ) ub fo in(1) N inθ µ coθ inθ = µ coθ tanθ = µ θ = tan µ = tan.5 = : Popetie of iction: Eample - bo on ough incline uface 1 g Bo on incline uface with fiction. If µ =.5 and µ =.3 find b) once it moing, find the acceleation Static fiction become inetic f<f object acceleate at ame angle in pat (a) a inθ f a inθ µ coθ a a = g inθ µ g coθ a = (9.8)(in 6.6 ) (.3)(9.8)(co6.6 ) a = 1.7m / a Two object of mae m 1 and m ae connected b a lightweight cod oe a lightweight, fictionle pulle a hown. foce of magnitude at an angle θ with the hoizontal i applied to the bloc m 1 which i on a ough uface.the coefficient of inetic fiction between the bloc and uface i µ. Detemine the magnitude of the acceleation of the two object. 6.3: Popetie of iction: Eample two object connected b a cod tem = ( m) a coθ µ n = ( m1 + m) a, but n 1g inθ 6.5: Unifom Cicula Motion Since object i otating in cicula path Centipetal acceleation a c diected towad the cente of the cicle of motion (pependicula to the elocit ). Since we hae acceleation towad the cente we hae net poduce a c net (Σ ) i diected towad the cente The ting i appling the foce to eep the ball otating in cicula path 3

4 When the Sting Bea When the ting bea (meaning no adial foce i applied anmoe), the ball continue to moe at contant elocit, in a taight line along the tangent to cicle at the bea point. Newton econd law in the adial diection نصف قطري) (اتجاه i 6.5: Unifom Cicula Motion: Newton law a a c If i towad the cente +e foce If outwad the cente -e foce The ting i appling the foce to eep the ball otating in cicula path 6.5: Unifom Cicula Motion: Eample A.15 g Object on a ting moe in hoizontal cicle with a peed of e./. If the adiu of the cicle i.6m, find the tenion in the ting ac T To find T we need = e./ = (π ) = 4π (.6) = 7.54m / (7.54)² T.15 = 14. N.6 At the bottom of the loop T towad the cente (up) out of cente (down) 6.5: Unifom Cicula Motion: Eample moing on a etical cicle ac T T g + m T 4

5 6.5: Unifom Cicula Motion: Eample moing on a etical cicle At the top of the loop Both T towad the cente (down) ac T + T to maintain cicula motion T mut be +e m > > g = g T i minimum peed to maintain cicula motion 6.5: Unifom Cicula Motion: Eample moing on a etical cicle ind minimum peed a biccle can go without falling. =.7 m. At the top, thee i a nomal foce n fom tac on the biccle, diected downwad, in addition to the weight a n + c At minimum peed biccle about to fall n = g = 5.1m / E: ca ounding a cue without idding? What i the maimum peed of the ca m = 15 g cue = 1 m µ.5 Ca ounding cue a c foce to the cente It i tatic fiction foce f n f E: ca ounding a cue without idding? net ac Maimum peed i when the ca i about to id (at f,ma ) f µ n = µ = µ g ma = µ g = (.5)(1)(9.8) 4.m / ma = n f 5

6 Baned cue We can educe the poibilit of idding b deigning a baned cue Aume a ca diing at peed on baned cue with no fiction. ind the optimum baning angle without idding out of the tac n in θ = ac m = Baned cue If =33m/ and cue adiu =15m, what i the baning angle o that the ca will not lide tanθ = θ = tan g θ = tan g (33) = 4 (9.8)(15) - diection, ncoθ g n = inθ tanθ = coθ coθ g eiew Static fictional foce equal applied foce (object i not moing) Maimum tatic fictional foce (object about to moe) Kinetic fictional foce (object i moing) Newton law in unifom cicula motion a c 6