PHY2048 Exam 1 Formula Sheet Vectors. Motion. v ave (3 dim) ( (1 dim) dt. ( (3 dim) Equations of Motion (Constant Acceleration)


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1 Insrucors: Field/Mche PHYSICS DEPATMENT PHY 48 Em Ferur, 5 Nme prin, ls firs: Signure: On m honor, I he neiher gien nor receied unuhoried id on his eminion. YOU TEST NUMBE IS THE 5DIGIT NUMBE AT THE TOP OF EACH PAGE. Code our es numer on our nswer shee use lines 76 8 on he nswer shee for he 5digi numer. Code our nme on our nswer shee. DAKEN CICES COMPETEY. Code our UFID numer on our nswer shee. Prin our nme on his shee nd sign i lso. 3 Do ll scrch work nwhere on his em h ou like. Circle our nswers on he es form. A he end of he es, his em prinou is o e urned in. No credi will e gien wihou oh nswer shee nd prinou. 4 Blcken he circle of our inended nswer compleel, using # pencil or lue or lck ink. Do no mke n sr mrks or some nswers m e couned s incorrec. 5 The nswers re rounded off. Choose he closes o ec. There is no penl for guessing. If ou eliee h no lised nswer is correc, lee he form lnk. 6 Hnd in he nswer shee seprel. Use g = 9.8 m/s
2 PHY48 Em Formul Shee Vecors k j i k j i ˆ ˆ ˆ ˆ ˆ ˆ Mgniudes: Sclr Produc: Mgniude: cos = ngle eween nd Vecor Produc: k j i ˆ ˆ ˆ Mgniude: sin = smlles ngle eween nd Moion Displcemen: dimension r r r 3 dimensions Aerge Veloci: e dim r r r e 3 dim Aerge Speed: s e = ol disnce/ Insnneous Veloci: d d dim d dr 3 dim elie Veloci: BC AB AC 3 dim Aerge Accelerion: e dim e 3 dim Insnneous Accelerion: d d d d dim d r d d d 3 dim Equions of Moion Consn Accelerion Newon s w nd Weigh m F ne m = mss Weigh ner he surfce of he Erh = W = mg use g = 9.8 m/s Mgniude of he Fricionl Force s = sic coefficien of fricion, k = kineic coefficien of fricion Sic: N s s F f m Kineic: N k k F f F N is he mgniude of he norml force Uniform Circulr Moion dius, Tngenil Speed =, Angulr Veloci Cenripel Accelerion & Force: m m F Period: T Projecile Moion horionl surfce ner Erh, = iniil speed, = iniil ngle wih horionl nge: g sin M Heigh: g H sin Time of fligh: g f sin Qudric Formul If: c Then: c 4
3 . A rin reling long he is is iniill he poin i =. The rin hen rels disnce d E o he Es i.e., righ s shown in he figure. I hen reerses direcion nd rels disnce d W o he Wes i.e., lef o he finl poin f. If he rin s erge speed for his rip ws 5 km/h nd is erge eloci for he rip ws km/h, wh ws he disnce d W? Iniil Posiion = is W i E 5d E 3d E 3 d E 4 d E 5 4d E. A rin reling long he is is iniill he poin i =. The rin hen rels disnce d E o he Es i.e., righ s shown in he figure. I hen reerses direcion nd rels disnce d W o he Wes i.e., lef o he finl poin f. If he rin s erge speed for his rip ws km/h nd is erge eloci for he rip ws km/h, wh ws he disnce d W? Iniil Posiion = is W i E 3d E 5d E 3 d E 4 d E 5 4d E 3. A rin reling long he is is iniill he poin i =. The rin hen rels disnce d E o he Es i.e., righ s shown in he figure. I hen reerses direcion nd rels disnce d W o he Wes i.e., lef o he finl poin f. If he rin s erge speed for his rip ws 3 km/h nd is erge eloci for he rip ws km/h, wh ws he disnce d W? Iniil Posiion = is W i E d E 5d E 3 3d E 4 d E 5 4d E 4. Two uomoiles sr from res on he is s shown in he figure. Cr is = nd cr is = d. A = he wo crs egin o moe owrd ech oher consn ccelerions. If he mgniude of he ccelerion of cr is wice he mgniude of he ccelerion of cr, wh poin long he is will he wo crs collide? = d/3 = d/4 3 = d/5 4 = d/ 5 = d/6 Cr = = d Cr is 5. Two uomoiles sr from res on he is s shown in he figure. Cr is = nd cr is = d. A = he wo crs egin o moe owrd ech oher consn ccelerions. If he mgniude of he ccelerion of cr is hree imes he mgniude of he ccelerion of cr, wh poin long he is will he wo crs collide? = d/4 = d/3 3 = d/5 4 = d/ 5 = d/6 Cr = = d Cr is
4 6. Two uomoiles sr from res on he is s shown in he figure. Cr is = nd cr is = d. A = he wo crs egin o moe owrd ech oher consn ccelerions. If he mgniude of he ccelerion of cr is four imes he mgniude of he ccelerion of cr, wh poin long he is will he wo crs collide? = d/5 = d/3 3 = d/4 4 = d/ 5 = d/6 Cr = = d Cr is 7. A =, ou len oer cliff nd hrow ll UP wih speed m/s, nd simulneousl hrow ll DOWN wih speed m/s. Which of he following gies he disnce eween hem in meers s funcion of ime in seconds? A =, ou len oer cliff nd hrow ll UP wih speed 5 m/s, nd simulneousl hrow ll DOWN wih speed 5 m/s. Which of he following gies he disnce eween hem in meers s funcion of ime in seconds? A =, ou len oer cliff nd hrow ll UP wih speed 3 m/s, nd simulneousl hrow ll DOWN wih speed 3 m/s. Which of he following gies he disnce eween hem in meers s funcion of ime in seconds? An uomoile srs from res on he is s shown in he figure. A = i egins o moelong he is wih eloci h depends on ime ccording o he formul =, where nd reconsns. If = 4 m/s nd = m/s 3, wh ime in s does he cr reurn o is sring poin? Cr = is. An uomoile srs from res on he is s shown in he figure. A = i egins o moelong he is wih eloci h depends on ime ccording o he formul =, where nd reconsns. If = 6 m/s nd = m/s 3, wh ime in s does he cr reurn o is sring poin? Cr = is. An uomoile srs from res on he is s shown in he figure. A = i egins o moelong he is wih eloci h depends on ime ccording o he formul =, where nd reconsns. If = 8 m/s nd = m/s 3, wh ime in s does he cr reurn o is sring poin? Cr = is 3. Ner he surfce of he Erh, srled rmdillo leps ericll upwrd ime =. A ime =.5 s, i is heigh of m oe he ground. Wh mimum heigh in m oe he surfce will he rmdillo rech during he lep?
5 4. Ner he surfce of he Erh, srled rmdillo leps ericll upwrd ime =. A ime =. s, i is heigh of m oe he ground. Wh mimum heigh in m oe he surfce will he rmdillo rech during he lep? Ner he surfce of he Erh, srled rmdillo leps ericll upwrd ime =. A ime =.5 s, i is heigh of m oe he ground. Wh mimum heigh in m oe he surfce will he rmdillo rech during he lep? If he ecor C = A+ B nd he ecor D = A B, nd if he mgniudes of A nd B re A = 3 nd B =, wh is he sclr do produc C D? If he ecor C = A+ B nd he ecor D = A B, nd if he mgniudes of A nd B re A = 4 nd B =, wh is he sclr do produc C D? If he ecor C = A+ B nd he ecor D = A B, nd if he mgniudes of A nd B re A = 5 nd B =, wh is he sclr do produc C D? If he ngle eween he ecor A = 3î 4ĵ nd he ecor B = î+ ĵ is 9, wh is? If he ngle eween he ecor A = 3î 5ĵ nd he ecor B = î+ ĵ is 9, wh is? If he ngle eween he ecor A = 3î 6ĵ nd he ecor B = î+ ĵ is 9, wh is? A o is siling in he ocen consn eloci V o = î+5ĵ wih respec o he shore. The wer curren in he ocen hs eloci V wer = 5î+ĵ lso mesured wih respec o he shore. All eloci componens re in m/s. Wh is he mgniude of he eloci in m/s of he o wih respec o he wer?
6 3. A o is siling in he ocen consn eloci V o = î+4ĵ wih respec o he shore. The wer curren in he ocen hs eloci V wer = 4î+ĵ lso mesured wih respec o he shore. All eloci componens re in m/s. Wh is he mgniude of he eloci in m/s of he o wih respec o he wer? A o is siling in he ocen consn eloci V o = î+ĵ wih respec o he shore. The wer curren in he ocen hs eloci V wer = î+ĵ lso mesured wih respec o he shore. All eloci componens re in m/s. Wh is he mgniude of he eloci in m/s of he o wih respec o he wer? The posiion ecor s funcion of ime,, of running ck on he fooll field is r = 5+3 î+ 3 ĵ, where ime is mesured in seconds nd lengh in meers. Wh is he mgniude of he erge ccelerion in m/s of he pler eween = nd = s? The posiion ecor s funcion of ime,, of running ck on he fooll field is r = 5+3 î+ 3 ĵ, where ime is mesured in seconds nd lengh in meers. Wh is he mgniude of he erge ccelerion in m/s of he pler eween = nd = 3 s? The posiion ecor s funcion of ime,, of running ck on he fooll field is r = 5+3 î+ 3 ĵ, where ime is mesured in seconds nd lengh in meers. Wh is he mgniude of he erge ccelerion in m/s of he pler eween = nd = 4 s? A pricle moes in he plne wih posiion coordines gien = nd = 8, where he ime is mesured in seconds nd disnce in meers. A = s, wh is he mgniude of is eloci in m/s? A pricle moes in he plne wih posiion coordines gien = nd = 8, where he ime is mesured in seconds nd disnce in meers. A = 3 s, wh is he mgniude of is eloci in m/s? A pricle moes in he plne wih posiion coordines gien = nd = 8, where he ime is mesured in seconds nd disnce in meers. A = 4 s, wh is he mgniude of is eloci in m/s?
7 3. Ner he surfce of he Erh, remoe conrolled o cr cceleres from res wih consn ccelerion, = 9.8 m/s, under he power of is own wheels on he horionl roof of squre uilding wih sides of lengh s shown in he figure. If he cr srs from res on he fr edge of he roof, disnce from he end of he uilding, wh is he horionl disnce D from he poin i lef he roof o where he cr lnds on leel ground? D 3 / /3 3. Ner he surfce of he Erh, remoe conrolled o cr cceleres from res wih consn ccelerion, =.45 m/s, under he power of is own wheels on he horionl roof of squre uilding wih sides of lengh s shown in he figure. If he cr srs from res on he fr edge of he roof, disnce from he end of he uilding, wh is he horionl disnce D from he poin i lef he roof o where he cr lnds on leel ground? D 3 / /3 33. Ner he surfce of he Erh, remoe conrolled o cr cceleres from res wih consnccelerion, =.65m/s, under he powerofis ownwheels on he horionl roof of squre uilding wih sides of lengh s shown in he figure. If he cr srs from res on he fr edge of he roof, disnce from he end of he uilding, wh is he horionl disnce D from he poin i lef he roof o where he cr lnds on leel ground? D / /3 34. A ime = projecile is relesed wih n iniil speed n ngle wih he fl horionl surfce of he Erh s shown in he figure. If he mimum heigh oe he surfce reched he projecile is 9.6 m, wh ime in s does i hi he surfce? A ime = projecile is relesed wih n iniil speed n ngle wih he fl horionl surfce of he Erh s shown in he figure. If he mimum heigh oe he surfce reched he projecile is 3.6 m, wh ime in s does i hi he surfce? A ime = projecile is relesed wih n iniil speed n ngle wih he fl horionl surfce of he Erh s shown in he figure. If he mimum heigh oe he surfce reched he projecile is 44. m, wh ime in s does i hi he surfce? On fl horionl soccor field ner he surfce of he Erh he gol keeper kicks he ll wih iniil speed = m/s n ngle = 45 wih he horionl owrds emme h is res disnce d = m w s shown in he figure. A he insn he ll is kicked he emme egins running consn speed V owrd he ll. Wh consn speed V in m/s mus he emme run in order o rech he ll he insn i his he ground? d V
8 38. On fl horionl soccor field ner he surfce of he Erh he gol keeper kicks he ll wih iniil speed = m/s n ngle = 45 wih he horionl owrds emme h is res disnce d = 5 m w s shown in he figure. A he insn he ll is kicked he emme egins running consn speed V owrd he ll. Wh consn speed V in m/s mus he emme run in order o rech he ll he insn i his he ground? d V On fl horionl soccor field ner he surfce of he Erh he gol keeper kicks he ll wih iniil speed = m/s n ngle = 45 wih he horionl owrds emme h is res disnce d = 3 m w s shown in he figure. A he insn he ll is kicked he emme egins running consn speed V owrd he ll. Wh consn speed V in m/s mus he emme run in order o rech he ll he insn i his he ground? d V Ner he surfce of he Erh, wo locks A nd B re res on horionl le. Block A is res on op of lock B nd lock B is res on he le s shown in he figure. An upwrd ericl eernl force F e = 9.8 N cs on lock A. If M A = kg nd M B = kg, wh is he mgniude of he norml force eered he le on lock B in N? A B F e = 9.8 N Ner he surfce of he Erh, wo locks A nd B re res on horionl le. Block A is res on op of lock B nd lock B is res on he le s shown in he figure. An upwrd ericl eernl force F e = 9.8 N cs on lock A. If M A = 3 kg nd M B = kg, wh is he mgniude of he norml force eered he le on lock B in N? A B F e = 9.8 N Ner he surfce of he Erh, wo locks A nd B re res on horionl le. Block A is res on op of lock B nd lock B is res on he le s shown in he figure. An upwrd ericl eernl force F e = 9.8 N cs on lock A. If M A = 4 kg nd M B = kg, wh is he mgniude of he norml force eered he le on lock B in N? A B F e = 9.8 N When res on he ground, In s weigh is mesured o e 65 N. When In is on moing eleor ner he surfce of he Erh, his ppren weigh is 5 N see he figure. If he comined mss of he ssem In nd he eleor is 5 kg, wh is he ension in he eleor cle in N? F T eleor scle 7,95 9,498 3,8 4 6,57 5,
9 44. When res on he ground, In s weigh is mesured o e 65 N. When In is on moing eleor ner he surfce of he Erh, his ppren weigh is 6 N see he figure. If he comined mss of he ssem In nd he eleor is 5 kg, wh is he ension in he eleor cle in N? F T eleor scle 9,498 7,95 3,8 4 6,57 5, 45. When res on he ground, In s weigh is mesured o e 65 N. When In is on moing eleor ner he surfce of he Erh, his ppren weigh is 7 N see he figure. If he comined mss of he ssem In nd he eleor is 5 kg, wh is he ension in he eleor cle in N? F T eleor scle,8 7,95 3 9, ,57 5, 46. Ner he surfce of he Erh mn is siing in oson s chir h dngles from mssless rope, which runs oer mssless, fricionless pulle nd ck down o he mn s hnd s shown in he figure. If he comined mss of he mn nd he chir is 9 kg, wih wh force in N mus he mn pull on he rope if he is o rise consn eloci? ,76 chir rope 47. Ner he surfce of he Erh mn is siing in oson s chir h dngles from mssless rope, which runs oer mssless, fricionless pulle nd ck down o he mn s hnd s shown in he figure. If he comined mss of he mn nd he chir is kg, wih wh force in N mus he mn pull on he rope if he is o rise consn eloci? ,76 chir rope 48. Ner he surfce of he Erh mn is siing in oson s chir h dngles from mssless rope, which runs oer mssless, fricionless pulle nd ck down o he mn s hnd s shown in he figure. If he comined mss of he mn nd he chir is 4 kg, wih wh force in N mus he mn pull on he rope if he is o rise consn eloci? ,76 chir rope
10 49. A lock wih weigh W = 98 N is eing pushed up fricionless rmp wih ngle = 3 relie o he horionl consn speed horionl force s shown in he figure. Wh is he mgniude of he force in N h he rmp eers on he lock? F e W V 5. A lock wih weigh W = 98 N is eing pushed up fricionless rmp wih ngle = 45 relie o he horionl consn speed horionl force s shown in he figure. Wh is he mgniude of he force in N h he rmp eers on he lock? F e W V 5. A lock wih weigh W = 98 N is eing pushed up fricionless rmp wih ngle = 6 relie o he horionl consn speed horionl force s shown in he figure. Wh is he mgniude of he force in N h he rmp eers on he lock? F e W V 5. Ner he surfce of he Erh, ll wih weigh W is ched o hin rope wih negligile mss nd lengh = 4.9 m. The ll nd rope re ched o ericl pole nd he enire pprus, including he pole, roes wih consn ngulr eloci ou he pole s smmer is, s shown in he figure. If he ension in he hin rope is W, how long in seconds does i ke he ll o mke one complee reoluion? is of roion Ner he surfce of he Erh, ll wih weigh W is ched o hin rope wih negligile mss nd lengh = 4.9 m. The ll nd rope re ched o ericl pole nd he enire pprus, including he pole, roes wih consn ngulr eloci ou he pole s smmer is, s shown in he figure. If he ension in he hin rope is 4W, how long in seconds does i ke he ll o mke one complee reoluion? is of roion Ner he surfce of he Erh, ll wih weigh W is ched o hin rope wih negligile mss nd lengh = 4.9 m. The ll nd rope re ched o ericl pole nd he enire pprus, including he pole, roes wih consn ngulr eloci ou he pole s smmer is, s shown in he figure. If he ension in he hin rope is 6W, how long in seconds does i ke he ll o mke one complee reoluion? is of roion
11 55. Ner he surfce of he Erh, cr is reling consn speed round fl circulr rce rck wih rdius of 5 m. If he coefficiens of kineic nd sic fricion eween he cr s ires nd he rod re µ k =., µ s =.4, respeciel, wh is he mimum speed he cr cn rel wihou sliding off he circulr rck? 4 m/s 8 m/s 3 56 m/s 4 m/s 5 7 m/s 56. Ner he surfce of he Erh, cr is reling consn speed round fl circulr rce rck wih rdius of m. If he coefficiens of kineic nd sic fricion eween he cr s ires nd he rod re µ k =., µ s =.4, respeciel, wh is he mimum speed he cr cn rel wihou sliding off he circulr rck? 8 m/s 4 m/s 3 56 m/s 4 m/s 5 7 m/s 57. Ner he surfce of he Erh, cr is reling consn speed round fl circulr rce rck wih rdius of 8 m. If he coefficiens of kineic nd sic fricion eween he cr s ires nd he rod re µ k =., µ s =.4, respeciel, wh is he mimum speed he cr cn rel wihou sliding off he circulr rck? 56 m/s 4 m/s 3 8 m/s 4 m/s 5 7 m/s 58. Ner he surfce of he Erh, kg mss is whirled round consn speed on he end of sring o form he conicl pendulum s shown in he figure. The ericl heigh of he pendulum is h = 3 m nd he rdius of he circle h he mss rels in is = m. Wh is he speed of he mss in m/s s i rels round he circle? h M Ner he surfce of he Erh, kg mss is whirled round consn speed on he end of sring o form he conicl pendulum s shown in he figure. The ericl heigh of he pendulum is h = 4 m nd he rdius of he circle h he mss rels in is = m. Wh is he speed of he mss in m/s s i rels round he circle? h M Ner he surfce of he Erh, kg mss is whirled round consn speed on he end of sring o form he conicl pendulum s shown in he figure. The ericl heigh of he pendulum is h = 5 m nd he rdius of he circle h he mss rels in is = m. Wh is he speed of he mss in m/s s i rels round he circle? h M FOOWING GOUPS OF QUESTIONS WI BE SEECTED AS ONE GOUP FOM EACH TYPE TYPE Q# S Q# S Q# S 3 TYPE Q# S 4 Q# S 5 Q# S 6 TYPE 3
12 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 33 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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