Motion. ( (3 dim) ( (1 dim) dt. Equations of Motion (Constant Acceleration) Newton s Law and Weight. Magnitude of the Frictional Force
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1 Insucos: ield/mche PHYSICS DEPARTMENT PHY 48 Em Sepeme 6, 4 Nme pin, ls fis: Signue: On m hono, I he neihe gien no eceied unuhoied id on his eminion. YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP O EACH PAGE. Code ou es nume on ou nswe shee use lines 76 8 on he nswe shee fo he 5-digi nume. Code ou nme on ou nswe shee. DARKEN CIRCLES COMPLETELY. Code ou UID nume on ou nswe shee. Pin ou nme on his shee nd sign i lso. 3 Do ll scch wok nwhee on his em h ou like. Cicle ou nswes on he es fom. A he end of he es, his em pinou is o e uned in. No cedi will e gien wihou oh nswe shee nd pinou. 4 Blcken he cicle of ou inended nswe compleel, using # pencil o lue o lck ink. Do no mke n s mks o some nswes m e couned s incoec. 5 The nswes e ounded off. Choose he closes o ec. Thee is no penl fo guessing. If ou eliee h no lised nswe is coec, lee he fom lnk. 6 Hnd in he nswe shee sepel. Use g = 9.8 m/s
2 PHY48 ll 4 PHY48 Em omul Shee Vecos k j i k j i Mgniudes: Scl Poduc: Mgniude: cos = ngle eween nd Veco Poduc: k j i Mgniude: sin = smlles ngle eween nd Moion Displcemen: dimension 3 dimensions Aege Veloci: e dim e 3 dim Aege Speed: s e = ol disnce/ Insnneous Veloci: d d dim d d 3 dim Relie Veloci: BC AB AC 3 dim Aege Acceleion: e dim e 3 dim Insnneous Acceleion: d d d d dim d d d d 3 dim Equions of Moion Consn Acceleion Newon s Lw nd Weigh m ne m = mss Weigh ne he sufce of he Eh = W = mg use g = 9.8 m/s Mgniude of he icionl oce s = sic coefficien of ficion, k = kineic coefficien of ficion Sic: N s s f m Kineic: N k k f N is he mgniude of he noml foce Unifom Cicul Moion Rdius R, Tngenil Speed = R, Angul Veloci Cenipel Acceleion & oce: R R mr R m Peiod: R T Pojecile Moion hoionl sufce ne Eh, = iniil speed, = iniil ngle wih hoionl Rnge: g R sin M Heigh: g H sin Time of fligh: g f sin Qudic omul If: c Then: c 4 Pge of
3 . A in eling long he -is is iniill he poin i =. The in hen els km o he Es i.e., igh s shown in he figue. I hen eeses diecion nd els disnce d o he Wes i.e., lef o he finl poin f. If he in s ege speed fo his ip ws 5 km/h, nd is ege eloci fo he ip ws km/h, wh ws he disnce d in km? W Iniil Posiion = i -is E. A in eling long he -is is iniill he poin i =. The in hen els km o he Es i.e., igh s shown in he figue. I hen eeses diecion nd els disnce d o he Wes i.e., lef o he finl poin f. If he in s ege speed fo his ip ws km/h, nd is ege eloci fo he ip ws km/h, wh ws he disnce d in km? W Iniil Posiion = i -is E 3. A in eling long he -is is iniill he poin i =. The in hen els km o he Es i.e., igh s shown in he figue. I hen eeses diecion nd els disnce d o he Wes i.e., lef o he finl poin f. If he in s ege speed fo his ip ws 3 km/h, nd is ege eloci fo he ip ws km/h, wh ws he disnce d in km? W Iniil Posiion = i -is E 4. An ojec is elesed fom es = ne he sufce of n unknown plne no Eh nd flls mees duing he ime inel fom = s o = s. Ignoing mospheic esisnce, how f does i fll in m duing he ime inel fom = s o = 3 s?.5 m 3. m m m 5.9 m 5. An ojec is elesed fom es = ne he sufce of n unknown plne no Eh nd flls mees duing he ime inel fom = s o = s. Ignoing mospheic esisnce, how f does i fll in m duing he ime inel fom = s o = 4 s? 3. m.5 m m m 5.9 m 6. An ojec is elesed fom es = ne he sufce of n unknown plne no Eh nd flls mees duing he ime inel fom = s o = s. Ignoing mospheic esisnce, how f does i fll in m duing he ime inel fom = s o = 5 s? 5.5 m.5 m 3 3. m m 5.9 m 7. A moois dies long sigh od consn speed of 8 m/s. A = she psses pked mooccle police office, nd he office kes off fe he wih cceleion, =, whee is consn nd is he ime i.e., he cceleion ies linel wih ime. If he office minins his e of cceleion, wh is he speed of he police office when he eches he moois in m/s?
4 8. A moois dies long sigh od consn speed of 85 m/s. A = she psses pked mooccle police office, nd he office kes off fe he wih cceleion, =, whee is consn nd is he ime i.e., he cceleion ies linel wih ime. If he office minins his e of cceleion, wh is he speed of he police office when he eches he moois in m/s? A moois dies long sigh od consn speed of 9 m/s. A = she psses pked mooccle police office, nd he office kes off fe he wih cceleion, =, whee is consn nd is he ime i.e., he cceleion ies linel wih ime. If he office minins his e of cceleion, wh is he speed of he police office when he eches he moois in m/s? Ne he sufce of he Eh suspension idge is heigh H oe he leel se of goge. A sone is hown o dopped fom he idge. Ignoe i esisnce. If ou dop he sone fom es, i kes 3 seconds fo i o fll o he se of he goge. If ou how he sme sone sigh down wih speed of m/s, how long in s efoe i his he gound? Ne he sufce of he Eh suspension idge is heigh H oe he leel se of goge. A sone is hown o dopped fom he idge. Ignoe i esisnce. If ou dop he sone fom es, i kes 3 seconds fo i o fll o he se of he goge. If ou how he sme sone sigh down wih speed of 5 m/s, how long in s efoe i his he gound? Ne he sufce of he Eh suspension idge is heigh H oe he leel se of goge. A sone is hown o dopped fom he idge. Ignoe i esisnce. If ou dop he sone fom es, i kes 3 seconds fo i o fll o he se of he goge. If ou how he sme sone sigh down wih speed of m/s, how long in s efoe i his he gound? If he -componen of he eco A shown in he figue is nd he ngle i mkes wih he -is = 5, wh is he -componen? -is A is 4. If he -componen of he eco A shown in he figue is nd he ngle i mkes wih he -is = 6, wh is he -componen? -is A is
5 5. If he -componen of he eco A shown in he figue is nd he ngle i mkes wih he -is = 7, wh is he -componen? -is A is 6. If A+ B = C, A B = C, nd C = î ĵ, hen wh is he lue of he scl poduc A B? If A+ B = C, A B = C, nd C = î 4ĵ, hen wh is he lue of he scl poduc A B? If A+ B = C, A B = C, nd C = î 6ĵ, hen wh is he lue of he scl poduc A B? Two ecos he he sme mgniude. If he mgniude of hei eco poduc is wice he mgniude of hei scl poduc, wh is he ngle eween hem? Two ecos he he sme mgniude. If he mgniude of hei eco poduc is hee imes he mgniude of hei scl poduc, wh is he ngle eween hem? Two ecos he he sme mgniude. If he mgniude of hei eco poduc is one-hlf he mgniude of hei scl poduc, wh is he ngle eween hem? A pojecile is lunched fom he posiion = = n ngle of wih he hoionl is. I eches miumu heigh H nd els mimum hoionl disnce R efoe lnding ck =. If H = R, wh is he ngle? A pojecile is lunched fom he posiion = = n ngle of wih he hoionl is. I eches miumu heigh H nd els mimum hoionl disnce R efoe lnding ck =. If H = R, wh is he ngle? A pojecile is lunched fom he posiion = = n ngle of wih he hoionl is. I eches miumu heigh H nd els mimum hoionl disnce R efoe lnding ck =. If H = R/, wh is he ngle?
6 5. A eng is hown hoionll fom dom oom window. The heigh of he window is h = mees oe he gound s shown in he figue. If he eng s eloci jus efoe impc wih he gound is = 3 elow he hoionl, wh hoionl disnce d in m fom he dom diecl elow he window fom which i ws hown does he enghi he gound? Ignoe i esisnce. Dom h d gound A eng is hown hoionll fom dom oom window. The heigh of he window is h = mees oe he gound s shown in he figue. If he eng s eloci jus efoe impc wih he gound is = 35 elow he hoionl, wh hoionl disnce d in m fom he dom diecl elow he window fom which i ws hown does he enghi he gound? Ignoe i esisnce. Dom h d gound A eng is hown hoionll fom dom oom window. The heigh of he window is h = mees oe he gound s shown in he figue. If he eng s eloci jus efoe impc wih he gound is = 4 elow he hoionl, wh hoionl disnce d in m fom he dom diecl elow he window fom which i ws hown does he enghi he gound? Ignoe i esisnce. Dom h d gound Jck wns o ow diecl coss ie fom he es shoe o poin on he wes shoe, s shown in he figue. The widh of he ie is 5 m nd he cuen flows fom noh o souh.5 m/s. The ip kes Jck 4 minues. A wh speed in m/s wih espec o he sill we is Jck le o ow? We Cuen Jck N W E Shoe Shoe S 9. Jck wns o ow diecl coss ie fom he es shoe o poin on he wes shoe, s shown in he figue. The widh of he ie is 5 m nd he cuen flows fom noh o souh. m/s. The ip kes Jck 4 minues. A wh speed in m/s wih espec o he sill we is Jck le o ow? We Cuen Jck N W E Shoe Shoe S
7 3. Jck wns o ow diecl coss ie fom he es shoe o poin on he wes shoe, s shown in he figue. The widh of he ie is 5 m nd he cuen flows fom noh o souh.5 m/s. The ip kes Jck 4 minues. A wh speed in m/s wih espec o he sill we is Jck le o ow? We Cuen Jck N W E Shoe Shoe S 3. A smll o els fo min 3 km noh nd hen els fo 4 min 4 km es. Wh is he mgniude of he o s ege eloci in km/h fo he one-hou ip? A smll o els fo min 6 km noh nd hen els fo 4 min 8 km es. Wh is he mgniude of he o s ege eloci in km/h fo he one-hou ip? A smll o els fo min 9 km noh nd hen els fo 4 min km es. Wh is he mgniude of he o s ege eloci in km/h fo he one-hou ip? A i is dshing hough he foes. Is posiion s funcion of ime is gien = 3 5î+3 3 ĵ, whee posiion is mesued in mees nd ime in seconds. ind he mgniude of he i s eloci in m/s = s A i is dshing hough he foes. Is posiion s funcion of ime is gien = 3 5î+3 3 ĵ, whee posiion is mesued in mees nd ime in seconds. ind he mgniude of he i s eloci in m/s = s A i is dshing hough he foes. Is posiion s funcion of ime is gien = 3 5î+3 3 ĵ, whee posiion is mesued in mees nd ime in seconds. ind he mgniude of he i s eloci in m/s =.5 s Ne he sufce of he Eh, child pulls sled up snow hill consn speed. Wh is he mss of he sled in kg if he child is pulling wih foce of 9.6 N nd he slope s ngle is 3? Neglec ficion Ne he sufce of he Eh, child pulls sled up snow hill consn speed. Wh is he mss of he sled in kg if he child is pulling wih foce of 9.4 N nd he slope s ngle is 3? Neglec ficion
8 39. Ne he sufce of he Eh, child pulls sled up snow hill consn speed. Wh is he mss of he sled in kg if he child is pulling wih foce of 39. N nd he slope s ngle is 3? Neglec ficion Ne he sufce of he Eh, suden is using simple pulle o lif ce of mss M = 3 kg fom es o heigh H pulling on he ope wih consn foce s shown in he figue. If he eking sengh of he ope is 4 N, wh is he minimum ime in s equied fo he suden o hul he ce o heigh H = m? Assume h he pulle is mssless nd ficionless H ope M ce gound 4. Ne he sufce of he Eh, suden is using simple pulle o lif ce of mss M = 35 kg fom es o heigh H pulling on he ope wih consn foce s shown in he figue. If he eking sengh of he ope is 4 N, wh is he minimum ime in s equied fo he suden o hul he ce o heigh H = m? Assume h he pulle is mssless nd ficionless H ope M ce gound 4. Ne he sufce of he Eh, suden is using simple pulle o lif ce of mss M = 4 kg fom es o heigh H pulling on he ope wih consn foce s shown in he figue. If he eking sengh of he ope is 4 N, wh is he minimum ime in s equied fo he suden o hul he ce o heigh H = m? Assume h he pulle is mssless nd ficionless H ope M ce gound 43. Ne he sufce of he Eh, wo locks A nd B e es on le s shown in he figue. If M A = kg nd he mgniude of he noml foce eeed he le on lock B is 9.4 N, wh is he mss of lock B in kg? A B Ne he sufce of he Eh, wo locks A nd B e es on le s shown in he figue. If M A = kg nd he mgniude of he noml foce eeed he le on lock B is 39. N, wh is he mss of lock B in kg? A B
9 45. Ne he sufce of he Eh, wo locks A nd B e es on le s shown in he figue. If M A = kg nd he mgniude of he noml foce eeed he le on lock B is 49. N, wh is he mss of lock B in kg? A B Conside mss M = kg suspended e ligh sing fom he ceiling of ilwcne he sufceof he Eh. The c hs consn cceleion s shownin he figue, cusing he mss o hng n ngle wih he eicl. If he cceleion of he ilw c is = 5 m/s, wh is he ension in he sing in N? Conside mss M = 3 kg suspended e ligh sing fom he ceiling of ilwcne he sufceof he Eh. The c hs consn cceleion s shownin he figue, cusing he mss o hng n ngle wih he eicl. If he cceleion of he ilw c is = 5 m/s, wh is he ension in he sing in N? Conside mss M = 4 kg suspended e ligh sing fom he ceiling of ilwcne he sufceof he Eh. The c hs consn cceleion s shownin he figue, cusing he mss o hng n ngle wih he eicl. If he cceleion of he ilw c is = 5 m/s, wh is he ension in he sing in N? Ne he sufce of he Eh, lock A, wih mss m A, is iniill es on hoionl floo. Block B, wih mss m B, is iniill es on he hoionl op sufce of A. The sum of he wo msses is m A + m B = kg. Block A is pulled wih hoionl foce s shown in he figue. If he coefficien of sic ficion eween he wo locks is µ s =.8, nd if lock B egins o m B m A slide off lock A when is gee hn 98 N, wh is he kineic coefficien of ficion, µ k, eween lock A nd he floo? Ne he sufce of he Eh, lock A, wih mss m A, is iniill es on hoionl floo. Block B, wih mss m B, is iniill es on he hoionl op sufce of A. The sum of he wo msses is m A + m B = kg. Block A is pulled wih hoionl foce s shown in he figue. If he coefficien of sic ficion eween he wo locks is µ s =.7, nd if lock B egins o m B m A slide off lock A when is gee hn 98 N, wh is he kineic coefficien of ficion, µ k, eween lock A nd he floo? Ne he sufce of he Eh, lock A, wih mss m A, is iniill es on hoionl floo. Block B, wih mss m B, is iniill es on he hoionl op sufce of A. The sum of he wo msses is m A + m B = kg. Block A is pulled wih hoionl foce s shown in he figue. If he coefficien of sic ficion eween he wo locks is µ s =.6, nd if lock B egins o m B m A slide off lock A when is gee hn 98 N, wh is he kineic coefficien of ficion, µ k, eween lock A nd he floo?
10 5. Ne he sufce of he Eh lock of mss M = kg is pushed long he floo consn speed V n eenl foce e = N pplied downwd ngle = 5 elie o he hoionl s shown in he figue. Wh is he coefficien of kineic ficion µ k eween he lock nd he floo? e M V Ne he sufce of he Eh lock of mss M = kg is pushed long he floo consn speed V n eenl foce e = N pplied downwd ngle = 3 elie o he hoionl s shown in he figue. Wh is he coefficien of kineic ficion µ k eween he lock nd he floo? e M V Ne he sufce of he Eh lock of mss M = kg is pushed long he floo consn speed V n eenl foce e = N pplied downwd ngle = 4 elie o he hoionl s shown in he figue. Wh is he coefficien of kineic ficion µ k eween he lock nd he floo? e M V A mn wih weigh of N dies c speed = 4 m/s oe cicul hill nd hen ino cicul lle wih he sme dius, u wih speed, sshown in he figue. A he op ofhe hill, he noml foce on he mn fom he c se is eo. If he mgniude of he noml foce on he mn fom he se when he c psses hough he oom of he lle is 5 N, wh is he speed in m/s? Rdius Rdius A mn wih weigh of N dies c speed = 4 m/s oe cicul hill nd hen ino cicul lle wih he sme dius, u wih speed, sshown in he figue. A he op ofhe hill, he noml foce on he mn fom he c se is eo. If he mgniude of he noml foce on he mn fom he se when he c psses hough he oom of he lle is, N, wh is he speed in m/s? Rdius Rdius A mn wih weigh of N dies c speed = 4 m/s oe cicul hill nd hen ino cicul lle wih he sme dius, u wih speed, sshown in he figue. A he op ofhe hill, he noml foce on he mn fom he c se is eo. If he mgniude of he noml foce on he mn fom he se when he c psses hough he oom of he lle is,7 N, wh is he speed in m/s? Rdius Rdius A cnil ide ne he sufce of he Eh consiss of he ides snding gins he inside wll of clindicl oom wih dius R = 5. m. The oom spins ou he eicl clinde is wih consn speed. Once i is up o speed, he floo of he oom flls w. If he clindicl oom complees 6 eoluions pe minue, wh minimum coefficien of sic ficion eween he ides nd he wll will keep hem fom dopping wih he floo? ω
11 OLLOWING GROUPS O QUESTIONS WILL BE SELECTED AS ONE GROUP ROM EACH TYPE TYPE Q# S Q# S Q# S 3 TYPE Q# S 4 Q# S 5 Q# S 6 TYPE 3 Q# S 7 Q# S 8 Q# S 9 TYPE 4 Q# S Q# S Q# S TYPE 5 Q# S 3 Q# S 4 Q# S 5 TYPE 6 Q# S 6 Q# S 7 Q# S 8 TYPE 7 Q# S 9 Q# S Q# S TYPE 8 Q# S Q# S 3 Q# S 4 TYPE 9 Q# S 5 Q# S 6 Q# S 7 TYPE Q# S 8 Q# S 9 Q# S 3 TYPE Q# S 3 Q# S 3 Q# S A cnil ide ne he sufce of he Eh consiss of he ides snding gins he inside wll of clindicl oom wih dius R = 5. m. The oom spins ou he eicl clinde is wih consn speed. Once i is up o speed, he floo of he oom flls w. If he clindicl oom complees 8 eoluions pe minue, wh minimum coefficien of sic ficion eween he ides nd he wll will keep hem fom dopping wih he floo? ω A cnil ide ne he sufce of he Eh consiss of he ides snding gins he inside wll of clindicl oom wih dius R = 5. m. The oom spins ou he eicl clinde is wih consn speed. Once i is up o speed, he floo of he oom flls w. If he clindicl oom complees eoluions pe minue, wh minimum coefficien of sic ficion eween he ides nd he wll will keep hem fom dopping wih he floo? ω
12 TYPE Q# S 34 Q# S 35 Q# S 36 TYPE 3 Q# S 37 Q# S 38 Q# S 39 TYPE 4 Q# S 4 Q# S 4 Q# S 4 TYPE 5 Q# S 43 Q# S 44 Q# S 45 TYPE 6 Q# S 46 Q# S 47 Q# S 48 TYPE 7 Q# S 49 Q# S 5 Q# S 5 TYPE 8 Q# S 5 Q# S 53 Q# S 54 TYPE 9 Q# S 55 Q# S 56 Q# S 57 TYPE Q# S 58 Q# S 59 Q# S 6
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