Chapter 6 Force and Motion II

Transcription

1 hapte 6 Foce and Motion II In thi chapte we will cove the ollowing topic: Decibe the ictional oce between two object. Dieentiate between tatic and kinetic iction, tudy the popetie o iction, and intoduce the coeicient o tatic and kinetic iction. Study the dag oce exeted by a luid on an object moving though the luid and calculate the teminal peed o the object. Reviit uniom cicula motion and uing the concept o centipetal oce apply Newton econd law to decibe the motion. (6-1)

2 Fiction: We can exploe the baic popetie o iction (6-) by analyzing the ollowing expeiment baed on ou evey day expeience. We have a heavy cate eting on the loo. We puh the cate to the let (ame b) but the cate doe not move. We puh hade (ame c) and hade (ame d) and the cate till doe not move. Finally we puh with all ou tength and the cate move (ame e). The ee body diagam o ame a-e how the exitence o a new oce which balance the oce F with which we puh the cate. Thi oce i called the tatic ictional oce. A we inceae F, alo inceae and the cate emain at et. When F eache a cetain limit the cate "beak away" and acceleate to the let. Once the cate tat moving the oce oppoing it motion i called the kinetic ictional oce. <. Thu i we wih the k k cate to move with contant peed we mut deceae F o that it balance (ame ). In ame (g) we plot veu time t k

3 F N F mg Popetie o iction: The ictional oce i acting between two dy unlubicated uace in contact Popety 1. I the two uace do not move with epect to each othe, then the tatic ictional oce balance the applied oce F. Popety. The magnitude o the tatic iction i not contant but vaie om 0 to a maximum value = µ F The contant µ i known a,max N the coeicient o tatic iction. I F exceed,m ax the cate tat to lide Popety 3. Once the cate tat to move the ictional oce i known a kinetic iction. It magnitude i contant and i given by the equation: µ i known a the coeicient o kinetic iction. We note that: k Note 1: The tatic and kinetic iction act paallel to the uece in contact The diection oppoe the diection o motion (o kinetic iction) o o attempted motion (in the cae o tatic iction) k k < = µ F k k N,max Note : The coeicient µ doe not depend on the peed o the liding object k,max = µ FN 0 < µ FN k k N = µ F (6-3)

4 Dag oce and teminal Speed (6-4) When an object move though a luid (ga o liquid) it expeience an oppoing oce known a dag. Unde cetain condition (the moving object mut be blunt and mut move at o a the low o the liquid i tubulent) the magnitude o the dag oce i given by the expeion: 1 D Av = ρ Hee i a contant, A i the eective co ectional aea o the moving object, ρ i the denity o the uounding luid, and v i the object peed. onide an object (a cat o ma m in thi cae) tat moving in ai. Initially D = 0. A the cat acceleate D inceae and at a cetain peed v t D = mg At thi point the net oce and thu the acceleation become zeo and the cat move with contant peed v t known the the teminal peed 1 D= ρ Avt = mg v t = mg ρ A

5 (6-5) Uniom icula Motion, entipetal oce In chapte 4 we aw that an object that move on a cicula path o adiu with contant peed v ha an acceleation a. The diection o the acceleation vecto alway point towad the cente o otation (thu the name centipetal) It magnitude i contant and i given by the equation: v a = I we apply Newton law to analyze uniom cicula motion we conclude that the net oce in the diection that point towad mut have F = mv magnitude: Thi oce i known a centipetal oce The notion o centipetal oce may be conuing ometime. A common mitake i to invent thi oce out o thin ai. entipetal oce i not a new kind o oce. It i imply the net oce that point om the otating body to the otation cente. Depending on the ituation the centipetal oce can be iction, the nomal oce o gavity. We will ty to claiy thi point by analyzing a numbe o example

6 . Recipe o poblem that involve uniom cicula motion o an object o ma m on a cicula obit o adiu with peed v y m v x Daw the oce diagam o the object hooe one o the coodinate axe (the y-axi in thi diagam) to point towad the obit cente Detemine Set F ynet F ynet = mv (6-6)

7 A hockey puck move aound a cicle at contant peed v on a hoizontal ice uace. The puck i tied to a ting looped aound a peg at point. In thi cae the net oce along the y-axi i the tenion T o the ting. Tenion T i the centipetal oce. Thu: F ynet = T = mv y (6-7)

8 Sample poblem 6-9: A ace ca o ma m tavel on a lat cicula ace tack o adiu R with peed v. Becaue o the hape o the ca the paing ai exet a downwad oce F L on the ca x I we daw the ee body diagam o the ca we ee that the net oce along the x-axi i the tatic iction. The ictional oce i the centipetal oce. Thu: F xnet = = mv R (6-8)

9 (6-9) Sample poblem 6-8: The Roto i a lage hollow y cylinde o adiu R that i otated apidly aound it cental axi with a peed v. A ide o ma m tand on the Roto loo with hi/he back againt x the Roto wall. ylinde and ide begin to tun. When the peed v eache ome pedetemined value, the Roto loo abuptly all away. The ide doe not all but intead emain pinned againt the Roto wall. The coeicient o tatic iction µ between the Roto wall and the ide i given. We daw a ee body diagam o the ide uing the axe hown in the igue. The nomal eaction F N i the centipetal oce. mv Fxnet, = FN = ma = (eq.1), R F = mg = 0, = µ F mg = µ F (eq.) y, net N N I we combine eq.1 and eq. we get: mv Rg Rg min R µ µ mg = µ v = v =

10 y Sample poblem 6-7: In a 1901 cicu peomance Allo Diavolo intoduced the tunt o iding a bicycle in a looping-the-loop. The loop i a cicle o adiu R. We ae aked to calculate the minimum peed v that Diavolo hould have at the top o the loop and not all We daw a ee body diagam o Diavolo when he i at the top o the loop. Two oce ae acting along the y-axi: Gavitational oce F g and the nomal eaction F N om the loop. When Diavolo ha the minimum peed v he ha jut lot contact with the loop and thu F N = 0. The only oce acting on Diavolo i F g The gavitational oce F g i the centipetal oce. Thu: mvmin Fynet = mg = vmin = Rg R (6-10)