Lectue 11 Chapte 8 Centipetal Foce Couse website: http://faculty.uml.edu/andiy_danylov/teaching/physicsi PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
Today we ae going to discuss: Chapte 8: Unifom Cicula Motion: Section 8. Cicula Obits: Section 8.3 easoning about Cicula Motion: Section 8.4 PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
Let s ecall cicula motion (acceleations) (two sevants of a king) v tan a tan esults fom a change in the magnitude of v tan Tangential acceleation a tan is always tangent to the cicle. ; PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics a (centipetal acceleation) esults fom a change in the diection of v tan Finally, any object that is undegoing cicula motion expeiences two acceleations: centipetal and tangential. Let s simplify ou life Centipetal acceleation a always points towad the cente of the cicle. In unifom cicula motion the speed is constant v t =const so the tangential acceleation a t =0 But, the centipetal acceleation is not zeo vt a const a a a tan v tan a
The best coodinate system fo a Unifom Cicula Motion When descibing cicula motion, it is convenient to define a moving t-coodinate system. t The -axis (adial) points fom the paticle towad the cente of the cicle. v tan The t-axis (tangential) is tangent to the cicle, pointing in the ccw diection. a The oigin moves along with a cetain paticle moving in a cicula path. PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
If thee is an acceleation, thee must be a foce The figue shows a paticle in unifom cicula motion. If thee is an centipetal (adial) acceleation, thee must be a adial foce (called centipetal) accoding to N. nd law. v tan t The net foce points in the adial diection, towad the cente of the cicle. F net a F net This centipetal foce is not a new foce. This can be any one of the foces we have aleady encounteed: tension, gavity, nomal foce, fiction, PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
Examples Wall of death N mg Bike going in a cicle: the wall exets an inwad foce (nomal foce) on a bike to make it move in a cicle. f s F ma v a N mv v velocity of the motobike - adius of the cicle Nomal foce povides the centipetal acceleation https://www.youtube.com/watch?v=9h4juptw4vk A hamme going in a cicle: the cod exets an inwad foce (tension) on a hamme to make it move in a cicle. F ma T mv Tension povides the centipetal acceleation f s Ca going in a cicle: the oad exets an inwad foce (fiction) on a ca to make it move in a cicle. F ma mv f s Fiction povides the centipetal acceleation PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
ConcepTest Missing Link A Ping-Pong ball is shot into a cicula tube that is lying flat (hoizontal) on a tabletop. When the Ping-Pong ball leaves the tack, which path will it follow? Once the ball leaves the tube, thee is no longe a foce to keep it going in a cicle. Theefoe, it simply continues in a staight line, as Newton s Fist Law equies! Follow-up: What physical foce povides the centipetal acceleation?
Example Loop the Loop http://phys3p.sl.psu.edu/phys_anim/mech/ PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics End of the class
ConcepTest You e on a Feis wheel moving in a vetical cicle. When the Feis wheel is at est, the nomal foce N exeted by you seat is equal to you weight mg. How does N change at the top of the Feis wheel when you ae in motion? Going in Cicles A) N emains equal to mg B) N is smalle than mg C) N is lage than mg D) none of the above mg N v m v mg m N You ae in cicula motion, so thee has to be a centipetal foce pointing inwad. At the top, the only two foces ae mg (down) and N (up), so N must be smalle than mg. Follow-up: Whee is N lage than mg? N Bottom N mg v m N v mg m
ConcepTest A skie goes ove a small ound hill with adius. Because she is in cicula motion, thee has to be a centipetal foce. At the top of the hill, what is F c of the skie equal to? Going in Cicles A) F c = N + mg B) F c = mg N C) F c = T + N mg D) F c = N E) F c = mg F c points towad the cente of the cicle (i.e., downwad in this case). The weight vecto points down and the nomal foce (exeted by the hill) points up. The magnitude of the net foce, theefoe, is F c = mg N. v N mg Follow-up: What happens when the skie goes into a small dip? F c = N mg
Example Ca on a cicula flat oad PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
ConcepTest You dive you ca too fast aound a cuve and the ca stats to skid. What is the coect desciption of this situation? Aound the Cuve A) ca s engine is not stong enough to keep the ca fom being pushed out B) fiction between ties and oad is not stong enough to keep ca in a cicle C) ca is too heavy to make the tun D) a dee caused you to skid E) none of the above The fiction foce between ties and oad povides the centipetal foce that keeps the ca moving in a cicle. If this foce is too small, the ca continues in a staight line! mv f s Follow-up: What could be done to the oad o ca to pevent skidding?
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Examples. Banked cuve But sometimes, fiction foce is not enough to keep a ca on a cicula oad. Banking the cuve can help to keep cas fom skidding. PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
Banked Cuves (solution) Ncos z F z = Ncos mg = 0 z mg N Nsin F = Nsin = ma a = v / Nsinmv / Ncosmg Take a atio Independent of object mass!!! tanv /g component of nomal foce povides the centipetal acceleation http://phys3p.sl.psu.edu/phys_anim/mech/ca_banked_new.avi PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics
Example: Conical pendulum z F z T z mg 0 (1) a T T T z T F T T Sin mv ma () mg component of tension povides the centipetal acceleation PHYS.1410 Lectue 11 Danylov Depatment of Physics and Applied Physics