SPH3UW/SPH4U Unit 3.2 Forces in Cetripetal Motion Page 1 of 6. Notes Physics Tool Box
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1 SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page 1 o 6 Note Phyic Tool Box Net Foce: acting on an object in uniom cicula motion act towad the cente o the cicle. Magnitude o Net Foce: combine Newton Second Law, F ma, with the equation o m centipetal acceleation aad to poduce F. Fame o Reeence: o an object moing in a cicle i a noninetial ame. Coioli Foce: i a ictitiou oce ued to explain paticle moing in a otating ame o eeence. Ca negotiating cue on a highway poide an example o cicula motion. Recalling that an object taelling at a contant peed in a cicle (o ac) expeience centipetal acceleation towad the cente o the cicle. Accoding the Newton nd Law, centipetal acceleation i the eult o a net oce acting in the diection o the acceleation and pependicula to the intantaneou elocity ecto. m Theeoe F ma and aad combine to gie u F Whee F i the magnitude o the net oce that caue the cicula motion. I you ate gien the peiod, T and equency, then you can ue m 4 m F 4 m T A led with a ma o 0.0 kg et on a hoizontal heet o ictionle ice. It i attached by a 4.00m ope to a pot et in the ice. Once gien a puh, the led eole uniomly in a cicle aound the pot. I the led make 5 complete eolution eey minute, ind the oce F exeted on it by the ope.
2 SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page o 6 Thee i no acceleation in the y-diection, o the net oce in that diection (the um o the nomal and weight0 i zeo. Fo the x-diection, Newton nd law gie along with the gien peiod and ma: 4 m Fx F max T F kg m kg m N Note: i you doubled the elocity, then the Foce, F would be 4 time geate. Caution: in doing poblem with uniom cicula motion, you may be tempted to include an exta m outwad oce o magnitude to keep the body out thee o to keep it in equilibium. Thi outwad oce i called Centiugal oce (leeing om cente). Reit thi temptation, becaue thi appoach i imply wong. In an inetial ame o eeence thee i no uch thing a centiugal oce. A ticky tuntable pin 3.5 time in 4.0 econd. I a 45.0g coin it 10cm om the cente o the tuntable, what oce i equied to keep the coin on the tuntable i the coeicient o iction i 0.5? 3.5time Gien: Hz, m kg, 0.1m, u 0.5, F? 4.0 Now F F F F and F 0 theeoe Fn Fg F net y n g net y mg F Alo F F n mg F m In the x-diection: F F netx ma F m4 mg F m4 F kg N mg kg m Hz m 0.5
3 SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page 3 o 6 I a ca i ounding a lat, unbanked cue with adiu 30m. I the coeicient o iction between the tie and the oad i 0.87, what i the maximum peed max at which the die can take the cue without liding? Fx maad m F n mg 0 y The econd equation how that n=mg. the it equation how that the iction oce needed to keep the ca moing in it cicula path inceae with the ca peed. The maximum oce aailable i n mg. max Theeoe m mg m max The maximum peed i about max g m m m km 158 km 1000m 1h h m
4 SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page 4 o 6 Fo a ca taelling at a cetain peed, it i poible to bank a cue at jut the ight angle o that no iction at all i needed to maintain the ca tuning adiu. Then a ca can ound the cue een on wet ice with Telon tie. I the adiu o the cue i 50 m and the ca elocity i 88 km/h, what angle hould the bank be? F nin ma x ad F nco mg 0 y Fom the econd equation, mg n co Now ubtitute thi into the it equation: Now a ad mg in co tan ma a g ad ad Theeoe tan g km 1000m 1h 88 1 h km 3600 So tan m m 13.7 The ank i then about 14.
5 SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page 5 o 6 A pilot o ma m in a jet aicat execute a loop-the-loop. In thi manoeue, the aicat moe in a etical cicle o adiu 3.50 km at a contant peed o 55 m/. Detemine the oce exeted by the eat on the pilot (A) at the bottom o the loop and (B) at the top o the loop. Expe you anwe in tem o the weight o the pilot mg. Top G F ma F F ma N mg FN m FN mg m mg 1 g mg mg m m 9.8 m G Bottom F ma F F ma N mg FN m FN m mg mg 1 g mg.90mg m m m
6 SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page 6 o 6 Exta Note and Comment
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