Example 1. Centripetal Acceleration. Example 1 - Step 2 (Sum of Vector Components) Example 1 Step 1 (Free Body Diagram) Example
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1 Centipetal Aeleation 13 Exaple with full olution Exaple 1 A 1500 kg a i oing on a flat oad and negotiate a ue whoe adiu i 35. If the oeffiient of tati fition between the tie and the oad i 0.5, deteine the axiu peed the a an hae in ode to uefully ake the tun. 35 Exaple 1 Step 1 (ee Body Diaga) Exaple 1 - Step (Su of Veto Coponent) f Aeleation dietion f hi tati fition i the only hoizontal foe keeping the a oing towad the ente of the a (ele the a will die off the oad). Vetial Coponent g 0 y 0 G 0 g Stati ition Hoizontal Coponent x f a R R g R g R We hae an eleation in x-dietion o Vetial Coponent Exaple 1 - Step 3 (Inet alue) f Exaple A a i taelling at 5/ aound a leel ue of adiu 10. What i the iniu alue of the oeffiient of tati fition between the tie and the oad to peent the a fo kidding? g R k h k 47 h 10 1
2 Exaple Step 1 (ee Body Diaga) Exaple - Step (Su of Veto Coponent) f Aeleation dietion f hi tati fition i the only hoizontal foe keeping the a oing towad the ente of the a (ele the a will die off the oad). Vetial Coponent g 0 y 0 G 0 g o Vetial Coponent Stati ition Hoizontal Coponent x f a R R g R gr We hae an eleation in x-dietion Exaple - Step 3 (Inet alue) f Exaple 3 An enginee ha deign a banked one with a adiu of 00 and an angle of What hould the axiu peed be o that any ehile an anage the one een if thee i no fition? gr gr We equie the iniu alue Exaple 3 Step 1 (ee Body Diaga) Exaple 3 - Step (Su of Veto Coponent) 18 in 18 o 18 Aeleation it the a dietion he noal to the oad 18 in 18 o 18 ow fo gaity Coponent of oal foe otie along that axi we (we enued hae one no axi tati wa along fition eleation foe in thi dietion exaple (quetion did not equie one) Vetial Coponent y 0 y G 0 o18 g 0 g o18 Hoizontal Coponent x x in 18 g in 18 o18 R g tan 18 R Rgtan 18 o Vetial Coponent We hae an eleation in the x-dietion
3 Exaple 3 - Step 3 (Inet alue) Exaple 4 18 in 18 o 18 An enginee ha deign a banked one with a adiu of 30 and the bank ut handle peed of 88 k/h. What bank angle hould the enginee deign to handle the oad if it opletely ie up? Rg tan tan k h k 91 h? 30 Exaple 4 Step 1 (ee Body Diaga) Exaple 4 - Step (Su of Veto Coponent) in o Aeleation it the a dietion he noal to the oad in o ow fo gaity Coponent of oal foe otie along that axi we (we enued hae one no axi tati wa along fition eleation foe in thi dietion exaple (quetion did not equie one) Vetial Coponent y 0 y G 0 o g 0 g o o Vetial Coponent Hoizontal Coponent x x in g in o R g tan R 1 tan Rg We hae an eleation in the x-dietion Exaple 4 - Step 3 (Inet alue) Exaple 5 in o A kg ball i otated in a etial dietion. he ball i atthed to a light ting of length 3 and the ball i kept oing at a ontant peed of 1 /. Deteine the tenion i the ting at the highet and lowet point. Rg 1 tan k h 88 1 h k 3600 tan Don t foget to ple in ete pe eond 3
4 Exaple 5 Step 1 (ee Body Diaga) Exaple 5 - Step (Su of Veto Coponent) ote: any etial otion poble that do not inlude a olid atthent to the ente, do not aintain a ontant peed, and thu (exept at top and botto) hae an eleation that doe not point towad the ente. (it i bette to ue enegy oneation tehnique) op When the ball i at the top of the ue, the ting i pulling down. Botto When the ball i at the botto of the ue, the ting i pulling up. In both ae, gaity i pulling down op a G g a g g y g ote: eleation i down (-) Botto a G g a y g g g Exaple 5 - Step 3 (Inet alue) op Botto Exaple 6 A onial pendulu onit of a a (the pendulu bob) that tael in a ile on the end of a ting ting out a one. If the a of the bob i 1.7 kg, and the length of the ting i 1.5, and the angle the ting ake with the etial i 5 o. Deteine: a) the peed of the bob b) the fequeny of the bob g 1 kg g 1 kg Exaple 6 Step 1 (ee Body Diaga) Exaple 6 - Step (Su of Veto Coponent) o 5 5 in 5 It eaie to ake the x axi poitie to the left Let deopoe ou enion oe into etial and hoizontal oponent x in 5 a Hoizontal in 5 x a o 5 Vetial y 0 5 in 5 y G 0 o5 g 0 g o5 4
5 Exaple 6 - Step 3 (Inet alue fo eloity) Exaple 6 - Step 3 (Inet alue fo fequeny) in 5 g in 5 o 5 g tan 5 g tan 5 o 5 5 in in 5 tan he peed of the bob i about 1.55 / in 5 a in 5 4 f g o 5 g f in tan 5 4 f g tan f f o 5 g tan in tan in Hz 0.468Hz he fequeny of the bob i about 0.468Hz Exaple 7 Exaple 7 Step 1 (ee Body Diaga) A wing at an aueent pak onit of a etial ental haft with a nube of hoizontal a. Eh a uppot a eat upended fo a able 5.00 long. he uppe end of the able i atthed to the a 3.00 fo the ental haft. Deteine the tie fo one eolution of the wing if the able ake an angle of 30 0 with the etial 30 o in 30 Exaple 7 - Step (Su of Veto Coponent) 30 o Exaple 7 - Step (Su of Veto Coponent) 30 o in 30 a 4 in 30 Hoizontal x x a in 30 Vetial y 0 y G 0 o30 g 0 g o30 4 in 30 g 4 in 30 o in g tan 30 4 g tan 30 in in tan he peiod i
6 Exaple 8 A toy a with a a of 1.60 kg oe at a ontant peed of 1.0 / in a etial ile inide a etal ylinde that ha a adiu of What i the agnitude of the noal foe exeted by the wall of the ylinde at A the botto of the ile and at B the top of the ile Exaple 8 Step 1 (ee Body Diaga) ote: any etial otion poble that do not inlude a olid atthent to the ente, do not aintain a ontant peed, and thu (exept at top and botto) hae an eleation that doe not point towad the ente. (it i bette to ue enegy oneation tehnique) op When the a i at the top of the ue, the noal foe i puhing down. Botto When the ball i at the botto of the ue, the noal foe i puhing up. In both ae, gaity i pulling down Exaple 8 - Step (Su of Veto Coponent) Exaple 8 - Step 3 (Inet alue) op a G g a y g g g ote: eleation i down (-) Botto a G g a y g g g op g kg Botto g kg Exaple 9 Exaple 8 Step 1 (ee Body Diaga) A 0.0g fly it 1 fo the ente of a phonogaph eod eoling at p. a) What i the agnitude of the entipetal foe on the fly? b) What i the iniu tati fition between the fly and the eod to peent the fly fo liding off? 6
7 Exaple 9 - Step (Su of Veto Coponent) Exaple 9 - Step (Su of Veto Coponent) a. a 4 f Conet to oet unit 4 1 e 1in.010 kg in b. a 4 f 4 g g kg Exaple 10 Exaple 10 Step 1 (ee Body Diaga) A 4.00 kg a i atthed to a etial od by the ean of two 1.5 ting whih ae.00 apat. he a otate about the etial haft poduing a tenion of 80.0 in the top ting. a) What i the tenion on the lowe ting? b) How any eolution pe inute doe the yte ake? in Exaple 10 - Step (Su of Veto Coponent) 1 Exaple 10 - Step (Su of Veto Coponent) Hoizontal x a 1 1o 53.1 o 53.1 x x x Vetial y G 1in 53.1 in 53.1 g 0 a) 80.0 in 53.1 in kg kg 4.00kg in 53.1 kg in
8 Exaple 10 - Step (Su of Veto Coponent) Exaple 11 he oon obit the Eath in an appoxiately iula path of adiu 3.8 x It take about 7 day to oplete one obit. What i the a of the Eath a obtained by thi data? b) 1o53.1 o53.1 1o53.1 o f f 1o53.1 o f 1o53.1 o o o o kg e e e in e 45 in Exaple 11 Step 1 (ee Body Diaga) Exaple 11 - Step (Su of Veto Coponent) x a GM E a GM E a GM E a a M E G Hoizontal 4 G 3 4 G h d kg 1d 1h kg he a of the Eath i about 6.0x10 4 kg Exaple 1 Caiopia take a ide on hild ei Wheel. hi ide ha no etaining ba, o that he only ide on the eat a the ide oe. a) Deteine the oal oe he would expeiene fo the botto of the eat when he i at the lowet point on the ide. b) Deteine the oal oe he would expeiene fo the botto of the eat when he i at the highet point on the ide. ) Deteine the et oe he would expeiene fo the botto of the eat when he i at the id-point on the ide with he height equal to the axi. Caiopia take a ide on hild ei Wheel. hi ide ha no etaining ba, o that he only ide on the eat a the ide oe. a) Deteine the oal oe he would expeiene fo the botto of the eat when he i at the lowet point on the ide. With thi ide, gaity alway point down, the noal (eat) foe alway point up, and the entipetal eleation i alway towad the ente. a g a a g W a 8
9 Caiopia take a ide on hild ei Wheel. hi ide ha no etaining ba, o that he only ide on the eat a the ide oe. Deteine the oal oe he would expeiene fo the botto of the eat when he i at the highet point on the ide. With thi ide, gaity alway point down, the noal (eat) foe alway point up, and the entipetal eleation i alway towad the ente. Exaple 1 Caiopia take a ide on hild ei Wheel. hi ide ha no etaining ba, o that he only ide on the eat a the ide oe. Deteine the et oe (foe of eat) he would expeiene fo the botto of the eat when he i at the id-point on the ide with he height equal to the axi. a g et a g a a g W a et a g tan g g tan 1 1 Exaple 13 (Had Quetion) Exaple 13 Step 1 (ee Body Diaga) An enginee ha deign a banked one with a adiu of R and an angle of β. What i the equation that deteine the eloity of the a gien that the oeffiient of fition i µ? Aeleation it the a dietion he noal to the oad ition o Coponent of oal foe along axi (we enued one axi wa along eleation dietion in We hae fition going f down by auing a ow fo want to lide up. hi gaity will poide an equation fo the axiu eloity Exaple 13 Step (Coponent) Exaple 13 Step (Coponent) f o in + x f o in + x Vetial Coponent y 0 y f 0 o g f in 0 o g u in 0 o Vetial o in g Hoizontal Coponent x a x fx in f o in o o Vetial Sub into Hoizontal o in in o g o in in o Sole fo g R gr in o o in gr in o o in Miniu eloity (lide down) grin o o in π 9
10 lah 10
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