PHY 121 Finals Review FSE Tutoring Centers Spring 2016

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1 11-Ap Apil,016 Vecto Addition PHY 11 Final Reiew FSE Tutoing Cente Sping 016 Vecto Addition: Place the ecto tip to tail. A ecto ma be moed an wa ou pleae poided that ou do not change it length no otate it. The eultant point fom the tail of the fit ecto to the tip of the econd (A+). To add ecto togethe the mut fit be eoled into component. The () component of a ecto i found b pojecting the ecto onto the () ai. Eample: Vecto A ha a length of 5.00 mete and point along the -ai. Vecto ha a length of 3.00 mete and point 10 fom the +-ai. Compute A+ (=C). A A C A 10 A 3 4 1

2 11-Ap-16 Eample continued opp in hp adj co hp in opp tan co adj A in60 in min60.60m co60 co mco m And A = 5.00 m and A = 0.00 m 5 Eample continued C A 5.00m -1.50m 3.50m The component of C: C A 0.00m.60m.60m The length of C i: C C C C C C =.60 m 3.50 m.60 m C = 3.50 m 4.36 m C.60 m The diection of C i: tan C 3.50 m 1 tan Fom the +-ai 6 Eample: At the intant a taffic light tun geen, an automobile tat with a contant acceleation of. m/. At the ame intant a tuc, taeling with a contant peed of 9.5 m/, oetae and pae the automobile. Eample continued (b) How fat will the ca be taeling at that intant? (a) How much time will elape befoe the automobile oetae the tuc? What i the data ou ae gien? U(tuc)=9.5; u(ca)=0; a(ca)=.; The ditance coeed b both ae the ame; Hence in the ame peiod of time (c) Whee do the meet? 7 8

3 11-Ap-16 Eample: A penn i dopped fom the obeation dec of the Empie State uilding 369 m aboe the gound. With what elocit doe it tie the gound? Ignoe ai eitance. Eample: You thow a ball into the ai with peed 15.0 m/, how high doe the ball ie? 0 Gien: 0 = 0 m/; a = 9.8 m/ ; 0 = 0 m; and f= 369 m Gien: 0 = m/; a = 9.8 m/ a a Unnown: f 369 m 9 10 Eample: An aow i hot into the ai with = 60 (fom the hoizontal) and 0 = 0.0 m/. The aow i eleaed fom a height of 1.80 m aboe the gound. (b) What ae the and component of the diplacement of the aow duing the 3.0 ec inteal? (a) What ae and of the aow when t=3 ec? 0 The component of the initial elocit ae: 60 At t = 3 ec: f f 0 0 co 10.0 m/ in 17.3 m/ gt 1.1m/ m/ 0 f t t t

4 11-Ap-16 Eample continued The initial poition of the aow i 0ˆ 1.8 mˆ The final poition of the aow i 0 Eample: How fa doe the aow in the peiou eample land fom whee it i eleaed? 1 The aow land when = 0 0 0t gt 0 t 30.0 m f f 0 0t gt 9.60m The diplacement i 30m 7.8 m ˆ ˆ Detemine the oot with quadatic fomula The ditance taeled i: t 0.10eco 3.64ec 0t 36.4 m Eample: How high doe the aow go? d The aow ie until 0 d The ma height i eached when with d d dt d d dt d 0 0 gt dt 0 t 1.77ec g Relatie motion Eample: You ae taeling in a ca (A) at 60 mile/hou eat on a long taight oad. The ca () net to ou i taeling at 65 mile/hou eat. What i the peed of ca elatie to ca A? The -coodinate of the aow i 1 t 1.77 t gt 17.1 m

5 11-Ap-16 Eample continued: t=0 t>0 + A AG A G A Eample: You ae taeling in a ca (A) at 60 mile/hou eat on a long taight oad. The ca () net to ou i taeling at 65 mile/hou wet. What i the peed of ca elatie to ca A? Fom the pictue: G AG A A G AG Diide b t: A G AG A 65mile/h eat 60mile/h eat 5 mile/houeat Eample continued: t>0 t=0 + t>0 Eample: The cuent in a ie ha a tead peed of 0.5 m/. A tudent wim upteam a ditance of 1 m and then wim bac to the tating point. If the tudent can wim 1. m/ in till wate, how long doe the ound tip in the ie tae? How long would the ame tip tae in till wate? A AG A Fom the pictue: Diide b t: G A A A G G AG AG In till wate: d t 000m m/ O 835 econd pe leg 65mile/h wet 60mile/h eat 15mile/h wet

6 11-Ap-16 Eample continued Upteam 0.7 m/ up d t 1000m m/ Eample: A jet moing initiall with = 300 mph due eat ente a egion whee the wind i blowing at 100 mph at 30 noth of eat. What i the new elocit of the jet? (noth) wind jet Downteam d t 1.7 m/ up 1000m m/ Place the ecto tip-to-tail: (eat) new jet wind The total time i 00 econd! 1 Eample continued new jet wind 300mph ˆ 100mphco30 ˆ 100mphin30 ˆ 387ˆ 50ˆ mph The magnitude and diection of the elocit ae Fee od Diagam Ue idealized model to account fo all foce acting on each ma (bod) inoled in the tem being analzed. new 390mph tan 0.19 The plane tael 390 mph 7.4 noth of eat 3 4 6

7 11-Ap-16 Eample: Find the tenion in each cod of the tem hown in the figue. Eample: A bo lide aco a ough uface. If the coefficient of inetic fiction i 0.3, what i the acceleation of the bo? FD fo bo: F ;b N b w Appl Newton nd Law: F N f b F f F N ;b w ma b ;b ma w Eample continued (1) () f ma N w 0 b ;b N w mg b Eample: In the peiou eample, a bo liding aco a ough uface wa found to hae an acceleation of -.94 m/. If the initial peed of the bo i 10.0 m/, how long doe it tae fo the bo to come to et? Know: a =.94 m/, 0=10.0 m/, = 0.0 m/ Want: t. Fom (1): Soling fo a: f ;b N mg ma a g b m/.94m/ 0 t a a t m/ 3.40ec. 94m/ 7 8 7

8 11-Ap-16 Eample: A 1.00 g ma i at et an on amp that mae an angle of 0 with epect to the hoizontal. Fo thi ituation = What i the magnitude of the tatic fiction foce? FD fo bo f ;b N b Eample continued (1) () F f F N b ;b mg in 0 mg co 0 The magnitude of the tatic fiction foce can be found fom (1) w f mg in 3.35N ; b Appl Newton nd law F N b f ;b w 0 What i the magnitude of the maimum tatic fiction foce? f ; b Nb mg co 3.68N 9 30 Eample continued If the angle of the amp i changed to 40, what i the acceleation of the ma? Tae = Eample: A 3.00 g ma et on a fictionle tabletop. Thi ma i connected to a 5.00 g ma b a light ting a hown. Aume the pulle i male. The FD i unchanged, ecept f ;b i now the inetic fiction foce of the amp on the bo. a. Daw fee bod diagam fo the two mae and the pulle. Appl Newton nd law F N f b ;b w ma (1) () F f F N b ;b mg in ma mg co

9 11-Ap-16 Eample continued b. Appl Newton Second law to the two mae. Dnamic of Cicula Motion t t t a co ˆ in ˆ in ˆ co ˆ co ˆ in ˆ Rotational motion can be elated to tanlational motion b coneting between Cateian and pola coodinate tem The tangential elocit and adial acceleation of a bod (contant peed cae). Eample: The Hubble Space Telecope obit the Eath at an altitude of about 600 m with an obit peiod of about 100 minute, what i Hubble obital peed? (Aume a cicula obit.) a total ditance a 7300m/ total time t T a a a = R e + h = m T =

10 11-Ap-16 Eample continued (b) What i HST angula peed? Eample: What i the magnitude of the adial acceleation of HST? π a t T 3 ad/ec a 7.63m/ 0. 78g Peioul: Conide an object in unifom cicula motion (peed=contant). t t t a co ˆ in ˆ in ˆ co ˆ The magnitude of the (tangential) elocit i co ˆ in ˆ Eample: The oto i an amuement pa ide whee people tand againt the inide of a clinde. Once the clinde i pinning fat enough the floo dop out. (a) What foce eep the people fom falling out the bottom of the clinde? Daw an FD fo a peon with thei bac to the wall: N wp f ;wp The magnitude of the (adial) acceleation i a 39 w ep It i the foce of tatic fiction

11 11-Ap-16 Eample continued (b) If = 0.40 and the clinde ha =.5 m. what i the minimum angula peed of the clinde o that the people don t fall out? Eample: A coin i placed on a ecod that i otating at 33.3 pm. If = 0.1, how fa fom the cente of the ecod can the coin be placed without haing it lip off? Appl Newton nd law: Fom (): f ;wp N wp w ep m F Nwp f;wp wep ma 1 F N ma m wp F f wep 0 ;wp mg g Fom (1) mg 9.8 m/ 3.13ad/ m 41 Daw an FD fo the coin: N c f ;c w ec Appl Newton nd law: F N f c ;c w ma 1 F f ma m ;c adial F N wec 0 c ec 4 Eample continued Fom 1 : f m ;c f N mg m ;c c Fom () Eample: What i the minimum peed fo the ca o that it maintain contact with the loop when it i in the pictued poition? Soling fo : g What i? FD fo the ca at the top of the loop: e ad 1min ad/ min 1e 60ec g m/ 3.50ad/ 0.08m 43 N w ec Appl Newton nd law: F N w ma F N w ma ec ec N wec m 44 11

12 11-Ap-16 Eample continued N mg m The appaent weight at the top of loop i N m g N m g N = 0 when 0 g Thi i the minimum peed needed to mae it aound the loop. 45 Eample continued Conide the ca at the bottom of the loop, how doe the appaent weight compae to the tue weight? FD fo the ca at the bottom of the loop: N w ec Appl Newton nd law: F N w ma F N wec ma m N mg m N m g Hee, ec N mg 46 Eample continued Eample continued Fom () the nomal foce i Nb mg co c. What i the acceleation of the tem? Uing (1): f ;b mg in ma mg N mg in ma b co mg in ma d. What i the tenion in the ope? a g in co 3.67 m/

13 11-Ap-16 Wo and Eneg Eample: The etinction of the dinoau and the majoit of pecie on Eath in the Cetaceou Peiod (65 M ago) i thought to hae been caued b an ateoid tiing the Eath nea the Yucatan Peninula. The eulting ejecta caued widepead global climate change. If the ma of the ateoid wa g (diamete in the ange of 4-9 mile) and had a peed of 30.0 m/ec, what wa the ateoid inetic eneg? 1 1 K m J g3010 m/ 49 Thi i equialent to ~10 9 Megaton of TNT. 50 Eample: What i the net wo done on a bo of ma m that i being puhed along a ough uface a hown? Eample continued The foce and diplacement (in unit ecto notation) ae F An FD fo the bo at left: N b f ;b w F pb N w f b ;b ˆ ˆ mg F in ˆ ˆ mg ˆ ˆ mg F in F F co ˆ F in ˆ pb N w f b ;b ˆ The wo done b the puhing foce i: 51 W pb F pb F co 5 13

14 11-Ap-16 The wo done b the Nomal foce i: W N Nb 0 The nomal foce i pependicula to the diplacement. The net wo done on the bo i: The wo done b gait i: W g w 0 The foce of gait i pependicula to the diplacement. Wnet Wpf WN Wg Wf F co 0 0 mg F in F co mg F in The wo done b inetic fiction i: W f f ;b mg F in Eample: A ball i toed taight up. What i the wo done b the foce of gait on the ball a it ie? Eample: An ideal ping ha = 0.0 N/m. What i the amount of wo done (b an etenal agent) to teh the ping 0.40 m fom it elaed length? FD fo iing ball: w W g w w co180 mg W F d m 0 1 Fd 0.40 m N/m0.40m 1.6 J W < 0 and the KE of the ball deceae