# Physics 111. Uniform circular motion. Ch 6. v = constant. v constant. Wednesday, 8-9 pm in NSC 128/119 Sunday, 6:30-8 pm in CCLIR 468

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1 ics Announcements dy, embe 28, 2004 Ch 6: Cicul Motion - centipetl cceletion Fiction Tension - the mssless sting Help this week: Wednesdy, 8-9 pm in NSC 128/119 Sundy, 6:30-8 pm in CCLIR 468 Announcements Ch 4: Newton s Lws Note the following: How does you weight chnge while you e Don t foget to ed oe the lb wite-up nd be edy fo the quiz. Ascending? Descending? Deceleting? Acceleting? Applictions of Newton s Lws Now tht we he seen nd pplied Newton s Lws (t lest few times), let s intoduce couple of new foces. I will NOT coe eeything in this chpte Ch 6 = constnt But... constnt Unifom Cicul Motion: the speed of the object does not chnge, but the object is cceleting thoughout the motion. Unifom cicul motion 1

2 Fo n object moing in cicle, the instntneous elocity ectos e lwys tngent to the cicle of motion! Unifom Cicul Motion: the speed of the object does not chnge, but the object is cceleting thoughout the motion. Although ou objects moes in cicle t constnt speed, it still cceletes. WHY? Recll tht cceletion nd elocity e both ecto quntities. Since cceletion is chnge in elocity oe chnge in time, n object with elocity tht chnges diection is cceleting! c = 2 c whee is the dius of the cicle nd the speed of the object. Poof in the book nd in clss notes. Recll ou definition of cceletion: i Δ i f f = lim Δ Δt 0 Δt = f i lim t f t i t f t i Colo Code: elocity; position in yellow; cceletion i f Velocity Vectos Agin, we e using ecto subtction (emembe, subtcting one ecto fom nothe is like dding its negtie). By geomety, this ngle is the sme s tht on the lst slide between the position ectos! i f Δ Now, we e got two simil, isosceles tingles. i Δ f Δ = Δ Now, etuning to ou definition of cceletion i f c = lim Δ = lim Δ Δt 0 Δt Δt 0 (Δt) = 2 Notice tht s Δt 0, the ecto Δ points towds the exct cente of the cicle. Δ 2

3 The peiod of the ottion is simply the time equied fo the object to go ound the cicle exctly one time. Fo n object moing in cicle with constnt speed, we cn define peiod ssocited with the motion. d 2π T = = T = 2π [T ] = [2π] [ ] Tht s good. We knew peiod hd to he units of time. [peiod] [T ] = m m/s = s A bll of mss m on the end of sting is moing in cicle. We know tht the bll is expeiencing n cceletion. T top iew c m Woksheet Poblem #1 Newton s 2nd Lw tells us tht in ode fo n object to expeience n cceletion, net extenl foce must be cting. Centipetl foce CQ1 stick to the wll NOTE! Newton s 2nd Lw tkes on slightly diffeent fom fo poblems inoling cicul motion. In these poblems, Newton s 2nd Lw sys F net m = mc = 2 (inwd) Newton s 2 nd Lw An utomobile with mss 1500-kg moes t constnt speed oe the cest of hill. The die moes in eticl cicle of dius 28.0 m. At the top of the hill, she notices tht the c bely mintins contct with the od. Find the speed of the ehicle. Poblem Soling Woksheet?P1 utomobile Motion Digm 3

4 Wht is fiction? Let s look t couple of demos inoling blocks sliding coss the floo. Agin, use FBD s to help you undestnd the motion. Clss Woksheet #2: Block Pedictions Block coss the floo t constnt speed. Why is it not cceleting? Block coss the floo fte push. Why does it stop? A mcoscopic (mening, obseble to the eye) foce tht opetes t the intefce between two sufces in diection to oppose the slipping of those sufces coss one nothe. As I push on the ed block with some foce, fiction with the sufce of the blue block cts to peent the ed block fom sliding. Wht is fiction? Wht is fiction? Fist, mke pictoil epesenttion nd descibe the foces pesent. N = noml foce of bottom block on top block = fictionl foce of bottom block on top block = the extenl foce pushing the block W = Weight o the gittionl foce of Eth on block Now let s dw the FBD fo the ed block n W The fictionl foce t the boundy is descibed s the foce ottic fiction, s it eltes to the foce obseed on pi of objects tht do not slip eltie to one nothe. The fictionl foce t the boundy is descibed s the foce ottic fiction, s it eltes to the foce obseed on pi of objects tht do not slip eltie to one nothe. We find tht expeimentlly, the mgnitude of the mximum foce ottic fiction is popotionl to the noml foce exeted by the blue block on the ed block. The constnt of popotionlity is known s the coefficient ottic fiction (µ s ) nd is popety of the mteils t the intefce. sttic fiction sttic fiction 4

5 If I push hd enough, the foce ottic fiction will be boken nd slipping will occu t the intefce. The ed block will begin to ccelete eltie to the blue block. If I push hd enough, the foce ottic fiction will be boken nd slipping will occu t the intefce. The ed block will begin to ccelete eltie to the blue block. When the ed block slips, we note tht it still feels fictionl foce. The mgnitude of tht foce, howee, hs chnged. We find expeimentlly tht the the mximum lue of new fictionl foce is still popotionl to the noml foce exeted by the blue block on the ed block. This foce is descibed s the foce oinetic fiction, s it eltes to the foce obseed on two objects tht slip eltie to one nothe. Woksheet Poblem #3 The constnt of popotionlity is known s the coefficient oinetic fiction (µ k ) nd is popety of the mteils t the intefce. Woksheet Poblem #4 Sttic Cse: Object t est µ s n Kinetic Cse: Object in Motion f k = µ k n The fictionl foces e lwys diected so s to oppose the slippge between the two sufces. both fictionl foces CQ4 Fiction: tilting plne 5

6 Does fiction lwys esult in n object slowing down? Let s look t couple of exmples to find out... Does fiction lwys esult in n object slowing down? Let s look t couple of exmples to find out... Wht s going to hppen to the geen object s I push the blue book coss the tble? Wht hppened to the geen object this time s I pushed the blue book coss the tble? Woksheet Poblem #5 Consult with neighbos. Woksheet Poblem #5b Consult with neighbos. 6

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