Moenu Do our work on a earae hee of aer or noebook. or each roble, draw clearl labeled diagra howing he ae and elociie for each objec before and afer he colliion. Don forge abou direcion oenu, eloci and iule are VETORS.. A.38 kg rojecile i fired wih a eloci of 5 / a an angle of 3 o aboe he horizonal. Deerine he oenu of he rojecile 3 o a) A i aiu heigh A a heigh, = and ==co3=5co3=43.3/ ==(.38)(43.3)= 3 kg / horizonall, o righ b) ju before i land a= o doe no change. ecaue i land a he ae heigh ha i wa launched, i equal and ooie. Therefore iac eed i ae a launch eed, direcion i 3 o below horizonal. = = (.38)(5) = 9 N kg / 3 o below horizonal. A or car of a ha he ae kineic energ a an wih a 3 a each i drien along he ae road. Which ehicle, if eiher, ha he large oenu and wha i he difference in heir oena? Ere our reul a a ercenage. Kcar K 3 car car (3) 3 car car (3)( 3. A bug and he windhield of a oing car collide. Indicae which of he following aeen are TRUE. a. The iac force on he bug and he car are he ae agniude. TRUE (Newon 3 rd Law) b. The iule on he bug and he car are he ae agniude. TRUE (boh he force and he ie of conac are he ae ) c. The change in oenu of he bug and he car are he ae agniude. TRUE (ae iule o ae ) d. The change in eloci of he bug and he car are he ae. ALSE (Since he change in oenu i he ae, he bug wih aller a u hae a greaer change in eloci) car.577 ) 3.577 4. A.5 kg car raeling a 4 / along a horizonal fricionle rack collide wih a car a re. A lo of he force eered on car (he.5 kg car). ie i hown on he righ. =4 / = (N).3.5 () =.5kg -
a. Deerine he aerage force alied o car during he colliion. The iule on car (he.5 kg) i he area under he - cure = -3 N ne ne 3 3/ 3/.5 6N b. Wha i he iule alied o car? ecaue he e of car + car ha no ne eernal force on i, here i alo no ne iule. The inernal colliion force and iule are equal and ooie according o Newon 3 rd Law. Therefore he iule on car i equal and ooie he iule on car ne ne 3N c. If he eloci of car afer he colliion i +4/, wha i he a of car? ne 3N 3 ( ).75kg (4 ) d. Deerine he eloci of car afer he colliion. Iule-Moenu Theore OR oneraion of Moenu ne 3N 3 ( ).5( 4) e. I he colliion elaic or inelaic? Juif our anwer wih aroriae calculaion K K before afer K K K K K K afer K before olliion i inelaic becaue kineic energ i lo 3J.5(4) (.75)(4).5 5. A block of a raeling o he righ a a eloci of.5, hi a aionar concree block of a reing on a fricionle urface. Afer he colliion, he fir block recoil and rael o he lef wih a eloci of. Ere our anwer in er of he gien ariable, and. The e of block i iolaed; in oher word, here are no ne eernal force on he e. Therefore, oenu of he e doe no change. Moenu of he e i conered. (.5)(4 ) 4J (.5)( ) (.75)(4 ) 7J
efore Afer =.5 a. Wha i he oal oenu of he e of he bulle and block? b. How fa and in wha direcion will he concree block be oing afer he fir block hi i? (righ) c. Deerine and coare he kineic energ before and afer he een. Ue hi coarion o deerine he e of colliion (elaic, inelaic, or eloion). K K afer K before (.5 K K ) ().35.5 M K lo, o inelaic d. In anoher cenario, he wo block (one a raeling o he righ a a eloci of.5, oward a aionar concree block of M) ick ogeher afer he colliion. or he erfecl inelaic colliion, deerine he eed and direcion of he block afer he colliion and he kineic energ diiaed in he colliion. (.5 K before K afer K (.5 ) ( ).5.5 5 )..36 ( ()(.5 ) (.36 ). K K before.5 afer ) (.5 (. ).5 ).8
6. Rocio rike a.58 kg golf ball wih a force of 7 N and gie i a eloci of 6. /. a) How long wa Rocio club in conac wih he ball? ne ball ball ball ne ball i = ( f i ) ne ball ne =7.58(6 ) 7 f =6. b) If he golf ball iniial eloci of 6/ i a an angle of 3 o aboe he leel ground, wha i he oenu of he ball a i aiu heigh? Once he ball i airborne, he onl force acing on i i grai and i becoe a rojecile. A he a heigh, he erical coonen of he ball eloci i zero and o he eak eloci i horizonal. Since here i no horizonal acceleraion he eed a he eak i = co3 = 6co3 = 54 / 3.596N..3 7 3 o c) Wha i he oenu of he ball righ before i hi he ground? The final eed i 6 / ince i land a he ae leel. Therefore he iac oenu i f = f =.58(6) = 3.6 kg / 7. A.4 kg olleball aroache Tina wih a eloci of 3.8 /. Tina bu he ball, giing i a eed of.4 / in he ooie direcion. Wha aerage force did he al if he ineracion ie beween her hand and he ball wa.5? i =3.8 =.4 =.5 f =.4 =.4
ne ball ne ball ball ball ( f i ).4(.4 ( 3.8)).488N. ( f i ).4(.4 ( 3.8)).488 59.5N.5.5 8. Sall are ued o ake in adjuen in he eed of aellie. One uch ha a hru of 35 N. If i i fired o change he eloci of a 7, kg acecraf b 63 c/, how long hould i be fired? hru =35 ne ne ( f ) ne i 7 35 7(.63) 4536 35 35 96.6in 9. The grah how he force, in eganewon ( 6 N), eered b a engine on he a a funcion of ie. If he a i 4 kg, a wha eed i he oing when he engine o firing? Aue i goe raigh u aring fro re, and neglec he force of grai, which i uch le han a eganewon. (You will hae o eiae he aerage force or iule oer he ec). Area under he grah i a = Iule of engine on. If grai on he i negleced, hen he iule of he engine i he ne iule which i equal o he change in oenu of he. The area under he cure i aroiael he area under he red riangle which i 6MN = 6 6 N Area = ne 6 6 6 6 65 ( ) 4( )
. A 73-N an and in he iddle of a frozen ond of radiu 5.. He i unable o ge o he oher ide becaue of a lack of fricion beween hi hoe and he ice. To oercoe hi difficul, he hrow hi.-kg hic ebook horizonall oward he norh hore, a a eed of 5. /. How long doe i ake hi o reach he ouh hore? The e of an and book before and iediael afer he hrow hae no ne eernal force acing on i (no fricion, noral balance grai). Therefore, he oenu of he e doe no change i i conered. M M 74.49.(5) M.8 Since he ice i fricionle, he an will lide a a conan eed of.8 /. To reach he hore, he u rael 5. M d / d / M M 5/.8 6.7 r=5. a) A.3-kg bulle i fired ericall a / ino a.5-kg block ha i iniiall a re. How high doe he cobinaion rie afer he colliion, auing he bulle ebed ielf in he block? (Noe: here are wo ar o hee roble: he colliion ar and wha haen afer he colliion. The ar are linked b he eloci afer he colliion) If we neglec air reiance and look a he bulle and block e iediael before he colliion o iediael afer, hen we can conider bulle and block o be an iolaed e (no ne force) in which he equal and ooie colliion force are AR bigger han he force/iule of grai on he bulle. Then we can ue coneraion of oenu o find he eed of he block and bulle iediael afer he colliion. Once he bulle ranfer oenu (and energ) o he block, he block and bulle hae kineic energ ha i ranfored ino graiaional oenial energ a he block rie. The echanical energ of he e of block, bulle and Earh i conered ince here are no eernal force doing work on he e. The onl force acing wihin he e i he coneraie force of grai. (We canno ue coneraion of oenu of he bulle +block while he rie becaue he loe = oenu o he Earh due o he force/iule of grai. To conere e oenu, we would hae o include he Earh in he e) =/ M h h=
Par The colliion- ONSERVATION O MOMENTUM of bulle+block; (-D roble in - direcion) ( ).3().8 33.3 Par Righ afer he colliion - The rie- ONSERVATION O ENERGY of he bulle+block+earh e ( E ) E ( h T ) gh 56.6 g b) Anoher.3-kg bulle i fired horizonall a / ino a.5-kg block ha i iniiall a re. Again, he bulle ebed ielf in he block afer he colliion. How far doe he block/bulle lide if he coefficien of fricion beween he block and urface i.3? There i fricion acing on he block, o block and bulle i NOT an iolaed e ince fricion i a NET eernal force ha change he oenu of he e. Howeer, if we look a he block and bulle e iediael before he colliion and iediael afer (before fricion ha decreaed he oenu), hen we can conider bulle and block o be an iolaed e (no ne force). Then we can ue coneraion of oenu o find he eed of he block and bulle a he inan ha oenu i ranferred o he block and ju begin o lide. =/ efore Afer f k = N g f = Once he bulle ranfer oenu (and energ) o he block, he block and bulle lide along he urface and he ne force of fricion low i down. Righ afer he colliion, we can ue kineaic and Newon Law OR Work-Energ o find he diance i lide.
Par The colliion- ONSERVATION O MOMENTUM of he block and bulle (-D roble in - direcion) ( ) 33.3 Par Righ afer he colliion kineaic and Newon nd Law 33.3 ind he acceleraion a uing Newon nd Law: fk a a a k N kg a a k g.94 Now knowing hree ariable, ue kineaic o find 33.3 89 a (.94)( ). (-D roble) A 345 kg car oing ea a 5.7 / i ruck b a 93 kg car oing norh. The are uck ogeher and oe wih an iniial eloci of 4.5 / a = 63.5. Wa he norh oing car eceeding he. / eed lii? THe e of car i iolaed iediael before o iediael afer he colliion; oenu o he e i conered fro iediael before o iediael afer. =4.5 =5.7 63.5 93 93 -direcion ( ) (345 93) =345 =? 447.36. ( eceedli i) 368 in 63.5 =93
3. (-D roble) A aionar billiard ball, wih a a of.7 kg, i ruck b an idenical ball oing a 4. /. Afer he colliion, he econd ball oe 6 o he lef of i original direcion. The aionar ball oe 3 o he righ of he original ball original direcion. Wha i he eloci of each ball afer he colliion? If he urface ha he ball rael on i fricionle, hen he e of he ball i iolaed ince no ne force ac on he e. Then oenu of he e of he ball i conered. There are unknown. The equaion are coneraion of in -dir and coneraion of in -direcion before -direcion 4 4.5 -direcion before afer co6 afer.866.866 in 6 co3.5 in 3.866.5.866( 3.46 4.5.866.5 ).5 4. A.-kg in can i reing on o of a.7--high fence o. A.-kg bulle i fired horizonall a he can. I rike he can wih a eed of 9 /, ae hrough i, and eerge wih a eed of 7 /. When he can hi he ground, how far i i fro he fence o? Diregard fricion while he can i in conac wih he o. (Noe: here are wo ar o hi roble: he colliion ar and wha haen afer he colliion. The ar are linked b he eloci afer he colliion). =.7.7 EORE ATER Se i he ulle and an ince here i a colliion beween he. The e i iolaed (no ne eernal force) Look a oenu in -direcion: Moenu before colliion equal he oenu afer. Once oe of he bulle oenu i ranferred o he can, i ha oe horizonal oenu and eloci,
and becoe a rojecile once in air. To find ou how far he can goe before hiing he ground, we need i iniial eloci fro he colliion. an i launched ino air wih horizonal eloci of 3.7/ and becoe a rojecile: / 3.7..44.8. (.)(7) (.)(9)? / 3.7 a.7 / 9.8 / a a.93 3.7(.589).589