Energy Problems 9/3/2009. W F d mgh m s 196J 200J. Understanding. Understanding. Understanding. W F d. sin 30

Size: px

Start display at page:

Download "Energy Problems 9/3/2009. W F d mgh m s 196J 200J. Understanding. Understanding. Understanding. W F d. sin 30"

Coleen Byrd
5 years ago
Views:

1 9/3/009 nderanding Energy Proble Copare he work done on an objec o a.0 kg a) In liing an objec 0.0 b) Puhing i up a rap inclined a 30 0 o he ae inal heigh 30 0 puhing 0.0 liing nderanding Copare he work done on an objec o a.0 kg a) In liing an objec 0.0 nderanding Copare he work done on an objec o a.0 kg a) In liing an objec 0.0 b) Puhing i up a rap inclined a 30 0 o he ae inal heigh liing puhing 0.0 W F d gh.0kg J 00J 30 0 The diance raelled up he rap 0.0 d 0 in30 pplied Force Fapplied g in Work W F d applied W g in d W.0kg 9.8 in 30 0 W 00J

2 9/3/009 Eaple.00kg block i puhed again a pring wih negligible a and a orce conan k=400 N/, copreing i 0.0. when he block i releaed, i oe along a ricionle horizonal urace and hen up a ricionle incline wih a lope o a) Wha i he peed o he block a i lide along he horizonal urace aer haing le he pring? b) ow ar doe he block rael up he incline beore aring o lide back down? Soluion o Eaple.00kg block i puhed again a pring wih negligible a and a orce conan k=400 N/, copreing i 0.0. when he block i releaed, i oe along a ricionle horizonal urace and hen up a ricionle incline wih a lope o a) Wha i he peed o he block a i lide along he horizonal urace aer haing le he pring? b) ow ar doe he block rael up he incline beore aring o lide back down? Le ind he Spring Poenial Energy ir. S k N J When releaed he Spring Poenial Energy i ranerred ino kineic energy o he lock, where we can ole or EK 9.68J.00kg 9.68J.00kg 3. Soluion o Eaple.00kg block i puhed again a pring wih negligible a and a orce conan k=400 N/, copreing i 0.0. when he block i releaed, i oe along a ricionle horizonal urace and hen up a ricionle incline wih a lope o a) Wha i he peed o he block a i lide along he horizonal urace aer haing le he pring? b) ow ar doe he block rael up he incline beore aring o lide back down? We can ue coneraion o Spring Poenial and Graiaional Poenial Energy Queion ruck oe wih elociy 0 = 0 / on a lick road when he drier applie he brake. The wheel lide and i ake he car 6 econd o op wih a conan deceleraion. a) ow ar doe he ruck rael beore opping? b) Deerine he kineic ricion beween he ruck and he road. G gh k gh 9.68J 9.68J h.00kg ing Trig, we will ranlae he erical diance o a rap diance in 37.0 d d in

3 9/3/009 Soluion o Queion ruck oe wih elociy 0 = 0 / on a lick road when he drier applie he brake. The wheel lide and i ake he car 6 econd o op wih a conan deceleraion. a) ow ar doe he ruck rael beore opping? b) Deerine he kineic ricion beween he ruck and he road. Soluion o Queion ruck oe wih elociy 0 = 0 / on a lick road when he drier applie he brake. The wheel lide and i ake he car 6 econd o op wih a conan deceleraion. a) ow ar doe he ruck rael beore opping? b) Deerine he kineic ricion beween he ruck and he road. d Fir we need he acceleraion he car eperience. a Since he only acceleraion orce eperienced by he car i ricion F F a a uf n a ug a ug a u g Queion 6 You and your bicycle hae a cobined a o 80.0kg. When you reach he bae o an bridge, you are raeling along he road a 5.00 /. a he op o he bridge, you hae clibed a erical diance o 5.0 and hae lowed o.50 /. Ignoring work done by any ricion: a) Wha i he oal work done by you and your bike when you go ro he bae o he op o he bridge? b) ow uch work hae you done wih he orce you apply o he pedal? Soluion o Queion 6 You and your bicycle hae a cobined a o 80.0kg. When you reach he bae o an bridge, you are raeling along he road a 5.00 /. a he op o he bridge, you hae clibed a erical diance o 5.0 and hae lowed o.50 /. Ignoring work done by any ricion: a) Wha i he oal work done by you and your bike when you go ro he bae o he op o he bridge? b) ow uch work hae you done wih he orce you apply o he pedal? W oal E K K K i i i 80.0 kg J Work i negaie becaue you reduced he kineic energy. 3

4 9/3/009 Soluion o Queion 6 You and your bicycle hae a cobined a o 80.0kg. When you reach he bae o an bridge, you are raeling along he road a 5.00 /. a he op o he bridge, you hae clibed a erical diance o 5.0 and hae lowed o.50 /. Ignoring work done by any ricion: a) Wha i he oal work done by you and your bike when you go ro he bae o he op o he bridge? b) ow uch work hae you done wih he orce you apply o he pedal? Coneraion o energy ae ha iniial kineic energy equal inal kineic energy plu work done by graiy le work done by you W E T K K i i W K Ki p i 90 gh 0 90J 80kg J J Queion 7 We hae preiouly ued he ollowing epreion or he aiu heigh h o a projecile launched wih iniial peed 0 a iniial angle θ: h in 0 g Derie hi epreion uing energy conideraion Soluion o Queion 7 We hae preiouly ued he ollowing epreion or he aiu heigh h o a projecile launched wih iniial peed 0 a iniial angle θ: Derie hi epreion uing energy conideraion Soluion o Queion 7 We hae preiouly ued he ollowing epreion or he aiu heigh h o a projecile launched wih iniial peed 0 a iniial angle θ: Derie hi epreion uing energy conideraion Thi iniially appear o be an eay proble: he poenial energy a poin i =gh, o i ay ee ha all we need o do i ole he energyconeraion equaion K + =K + or. oweer, while we know he iniial kineic energy and poenial energie (K =½ =½ 0 and =0), we don know he peed or kineic energy a poin. We will need o break down our known alue ino horizonal and erical coponen and apply our knowledge o kineaic o help. h in 0 g We can epre he kineic energy a each poin in he er o he coponen uing: y K K y y Coneraion o energy hen gie: K Kgh y 0 in gh y 0 y 0 in gh g h g yh gy h gh y u, we recall ha Furherore, u, he -coponen ince projecile y i ju he y- coponen o elociy doe o iniial no ha change, zero erical elociy: elociy a highe y = 0 in(θ) poin, y =0 h in 0 g 4

5 9/3/009 Queion 8 Couin Vinney kaeboard down a playground rap. e (5.0 kg) oe hrough a quarer-circle wih radiu R=3.00. a) Deerine hi peed a he boo o he rap b) Deerine he noral orce ha ac on hi a he boo o he cure. c) Suppoe he rap i no ricionle and ha Vinney peed a he boo i only 6.00 /. wha work wa done by he ricion orce acing on hi? Soluion o Queion 8 Couin Vinney kaeboard down a playground rap. e (5.0 kg) oe hrough a quarercircle wih radiu R=3.00. a) Deerine hi peed a he boo o he rap b) Deerine he noral orce ha ac on hi a he boo o he cure. c) Suppoe he rap i no ricionle and ha Vinney peed a he boo i only 6.00 /. wha work wa done by he ricion orce acing on hi? Fro Coneraion o Energy K K 0 gr 0 gr Soluion o Queion 8 Couin Vinney kaeboard down a playground rap. e (5.0 kg) oe hrough a quarercircle wih radiu R=3.00. a) Deerine hi peed a he boo o he rap b) Deerine he noral orce ha ac on hi a he boo o he cure. c) Suppoe he rap i no ricionle and ha Vinney peed a he boo i only 6.00 /. wha work wa done by he ricion orce acing on hi? Soluion o Queion 8 Couin Vinney kaeboard down a playground rap. e (5.0 kg) oe hrough a quarercircle wih radiu R=3.00. a) Deerine hi peed a he boo o he rap b) Deerine he noral orce ha ac on hi a he boo o he cure. c) Suppoe he rap i no ricionle and ha Vinney peed a he boo i only 6.00 /. wha work wa done by he ricion orce acing on hi? The ree body diagra o he noral i hrough-ou hi journey i: F a y FN FG R gr FN g R g g c 3g gr The noral orce doe no work, bu he ricion orce doe do work. Thereore he non-graiaional work done on Vinney i ju he work done by ricion. K W K F W K K F 0 0 gh 5.0 kg kg J The ree body diagra o he noral i hrough-ou hi journey i: 5

6 9/3/009 Queion kg eleaor wih broken cable i alling a 5 / when i ir conac a cuhioning pring a he boo o he ha. The pring i uppoed o op he eleaor, copreing 3.00 a i doe. During he oion a aey clap applie a conan 7,000 N ricional orce o he eleaor. a) Deerine he orce conan o he pring. Soluion o Queion kg eleaor wih broken cable i alling a 5 / when i ir conac a cuhioning pring a he boo o he ha. The pring i uppoed o op he eleaor, copreing 3.00 a i doe. During he oion a aey clap applie a conan 7,000 N ricional orce o he eleaor. a) Deerine he orce conan o he pring. The eleaor iniial kineic energy i: K 000 kg 5 65,000 J I we ue Poin o be he origin, hen we hae =0 and gra =0, and o =0 Poin, here i boh graiaional and elaic poenial energy, bu no kineic energy gy ky Puing he coneraion o energy o work: K + +W oher =K + Soluion o Queion kg eleaor wih broken cable i alling a 5 / when i ir conac a cuhioning pring a he boo o he ha. The pring i uppoed o op he eleaor, copreing 3.00 a i doe. During he oion a aey clap applie a conan 7,000 N ricional orce o he eleaor. a) Deerine he orce conan o he pring. K 65,000 J I we ue Poin o be he origin, hen we hae =0 and gra =0, and o =0 gy ky K W K oher 65,000J 0J Woher 0J gy ky 65,000J 7,000N kg k N.40 Eaple n objec o a.0 kg raelling a 5.0 / ener a region o ice where he coeicien o kineic ricion i 0.0. e he Work Energy Theore o deerine he diance he objec rael beore coing o a hal..0 kg 6

7 9/3/009 Soluion n objec o a.0 kg raelling a 5.0 / ener a region o ice where he coeicien o kineic ricion i 0.0. e he Work Energy Theore o deerine he diance he objec rael beore coing o a hal. F N Force We can ee ha he objec weigh i balanced by he noral orce eered by he ice. Thereore he only work done i due o he ricion acing on he objec. Le deerine he ricion orce. F u F k N u g k 0.0.0kg N Now apply he work Energy Theore and ole or d W KE F F d i 3 g 0.98N d.0kg 0.0kg 5.0.5J d 0.98N Eaple bo o a i releaed ro re a poin, he op o a long ricionle lide. Poin i a heigh aboe he leel poin and C. lhough he lide i ricionle, he horizonal urace ro poin o C i no. The coeicien o kineic ricion beween he bo and hi urace i, and he horizonal diance beween poin and C i. a) Find he peed o he bo when i heigh aboe he ground i / b) Find he peed o he bo when i reache. c) Deerine he alue o, o ha i coe o a re a C d) Deerine he alue o i C wa a a heigh o h aboe he ground. e) I he lide wa no ricionle, deerine he work done by ricion a he bo oed ro o i he peed a wa ½ o he peed calculaed in b) C Eaple bo o a i releaed ro re a poin, he op o a long ricionle lide. Poin i a heigh aboe he leel poin and C. lhough he lide i ricionle, he horizonal urace ro poin o C i no. The coeicien o kineic ricion beween he bo and hi urace i, and he horizonal diance beween poin and C i. a) Find he peed o he bo when i heigh aboe he ground i / Eaple bo o a i releaed ro re a poin, he op o a long ricionle lide. Poin i a heigh aboe he leel poin and C. lhough he lide i ricionle, he horizonal urace ro poin o C i no. The coeicien o kineic ricion beween he bo and hi urace i, and he horizonal diance beween poin and C i. b) Find he peed o he bo when i reache. E K g 0 g oal G K E G oal g g g g E K g 0 g oal G K E G oal 0 g g g C C 7

8 9/3/009 Eaple bo o a i releaed ro re a poin, he op o a long ricionle lide. Poin i a heigh aboe he leel poin and C. lhough he lide i ricionle, he horizonal urace ro poin o C i no. The coeicien o kineic ricion beween he bo and hi urace i, and he horizonal diance beween poin and C i. c) Deerine he alue o, o ha i coe o a re a C W K W i i Fd i guk i C i uk g g Eaple bo o a i releaed ro re a poin, he op o a long ricionle lide. Poin i a heigh aboe he leel poin and C. lhough he lide i ricionle, he horizonal urace ro poin o C i no. The coeicien o kineic ricion beween he bo and hi urace i, and he horizonal diance beween poin and C i. d) Deerine he alue o i C wa a a heigh o h aboe he ground. K W KC C g 0 F L 0 gh g u g co L gh k u co L h k L C h uk Lco h Eaple bo o a i releaed ro re a poin, he op o a long ricionle lide. Poin i a heigh aboe he leel poin and C. lhough he lide i ricionle, he horizonal urace ro poin o C i no. The coeicien o kineic ricion beween he bo and hi urace i, and he horizonal diance beween poin and C i. e) I he lide wa no ricionle, deerine he work done by ricion a he bo oed ro o i he peed a wa ½ o he peed calculaed in b) K W K K W g 0W g g g W 4 g 3 W g g 4 4 Eaple 3 The acroba wing ro he horizonal. When he acroba wa wung an angle o 30 0, wha i hi elociy a ha poin, i he lengh o he rope i L? ecaue graiy i a coneraie orce (he work done by he rope i angen o he oion o rael), Graiaional Poenial Energy i conered o Kineic Energy. gh glin 30 gl G K E gl 30 L hlin 30 8

9 9/3/009 Eaple 3 block o a 3.00 kg i on a horizonal ricionle urace. I i aached o a pring wih a pring conan o 36.0 N /. The weigh i pulled 0.6 away ro he equilibriu poin and hen releaed. a) uing no daping, wha i he peed o he block, i) a i pae hrough he equilibriu poin? ii) when i ha oed 5.0 c ro i releae poin? b) Find he ie aer releae ha he block ir paed hrough he poiion = 3.0 c (on he oppoie ide o i equilibriu poin). Eaple 3 Soluion block o a 3.00 kg i on a horizonal ricionle urace. I i aached o a pring wih a pring conan o 36.0 N /. The weigh i pulled 0.6 away ro he equilibriu poin and hen releaed. a) uing no daping, wha i he peed o he block, i) a i pae hrough he equilibriu poin? We can ole hi in wo dieren way 0.6 ) ing Energie k k k N kg Eaple 3 Soluion block o a 3.00 kg i on a horizonal ricionle urace. I i aached o a pring wih a pring conan o 36.0 N /. The weigh i pulled 0.6 away ro he equilibriu poin and hen releaed. a) uing no daping, wha i he peed o he block, i) a i pae hrough he equilibriu poin? Eaple 3 block o a 3.00 kg i on a horizonal ricionle urace. I i aached o a pring wih a pring conan o 36.0 N /. The weigh i pulled 0.6 away ro he equilibriu poin and hen releaed. a) uing no daping, wha i he peed o he block, ii) when i ha oed 5.0 c ro i releae poin? We can ole hi in wo dieren way We can ole hi in wo dieren way ) ing Velociy Funcion k k in We need only he ie when he a i a he equilibriu poin (ie =0). We can ge ha by eing he poiion uncion = 0 and oling or ie or by uing one quarer o he period. ¼ o T T k 3 T in ) ing Energie 5c k k 6 c k k k i he poiion ha he pring i reched ro he equilibriu a ha a ha elociy. Thi diance i 6c 5 c= c. N kg

10 9/3/009 Eaple 3 block o a 3.00 kg i on a horizonal ricionle urace. I i aached o a pring wih a pring conan o 36.0 N /. The weigh i pulled 0.6 away ro he equilibriu poin and hen releaed. a) uing no daping, wha i he peed o he block, ii) when i ha oed 5.0 c ro i releae poin? Eaple 3 block o a 3.00 kg i on a horizonal ricionle urace. I i aached o a pring wih a pring conan o 36.0 N /. The weigh i pulled 0.6 away ro he equilibriu poin and hen releaed. b) Find he ie aer releae ha he block ir paed hrough he poiion = 3.0 c (on he oppoie ide o i equilibriu poin). We can ole hi in wo dieren way Thi i a job or he poiion uncion. ) ing Velociy Funcion k k in Seing he poiion uncion o 0. and oling or ie k co 36 5c co 3 6 c 36 co in co k co k 3 c co co 3 co 0.88 co c 0

Elastic and Inelastic Collisions

Elastic and Inelastic Collisions laic and Inelaic Colliion In an LASTIC colliion, energy i conered (Kbefore = Kafer or Ki = Kf. In an INLASTIC colliion, energy i NOT conered. (Ki > Kf. aple: A kg block which i liding a 0 / acro a fricionle