86 Chapter 7 Energy 7-11 POWER. Answers to the Conceptual Questions

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1 86 Chater 7 Energy nented to make eerythng alrght. We eel t s mortant to show that the nenton o other orms o energy s not whmscal or a arce. A newly nented orm o energy would be alse the new orm was not consstent wth the conseraton law and the other orms o energy. Teachng Ts Ths secton resents a subtle ont that may be sked t doesn't match your course goals. It s an attemt to address a common atttude o students that rules are made wthout rhyme or reason. 7- POWER Goals Introduce the concet o ower as the rate o conertng energy rom one orm to another er unt tme. Dene a watt and a horseower. (Comutng) Calculate the ower requred to kee a car mong at constant seed. (Comutng) Calculate the electrcal energy conerted by a motor. (Problem Solng) Calculate the ower or a common eent. Content Power s the measure o the energy transormed dded by the tme elased. Two common unts o ower are the horseower and the watt. A horseower s about 750 watts. Teachng Ts Ths s a short secton that can be sked the materal s not germane to your goals. I you are nto alcatons, ths s a good secton to use as a srngboard or talkng about local ower needs. Comutng Power We calculate the ower needed to oercome rctonal eects and kee a car mong at a constant seed. We also calculate the electrcal energy used by a motor durng a erod o tme. We show that kwh 3.6 mllon joules. A queston asks or the energy used by a lght bulb n 8 hours. Problem Solng 7.6 We calculate the ower requrements o an acceleratng automoble. Comuter Anmatons Acte Fgure Anmatons are aalable on the Multmeda Manager Instructor s Resource CD. They are organzed by textbook chater, and each anmaton comes wthn a shell that rodes normaton on how to use the anmaton, exloraton acttes, and a short quz. Answers to the Concetual Questons. Momentum s a ector. The ntal momentum o the system s zero.. Energy comes n many laors o whch knetc s only one. 3. Momentum s always consered n a collson whereas knetc energy s rarely consered. 4. Momentum and energy are entrely derent quanttes so t makes no sense to say one s bgger than the other. Ths would be smlar to sayng that a erson s taller than hs weght. 5. Yes. I the knetc energy s zero all objects n the system must be at rest. 6. No. Two dentcal cars aroachng each other at the same seed hae zero total momentum but they do not hae zero knetc energy. 7. The motorboat and water sker because the suertanker s not mong and has zero knetc energy. 8. The Chey has our tmes the knetc energy because the knetc energy s roortonal to the square o the seed. 9. The mnan has the larger knetc energy because the knetc energy s roortonal to the mass. 0. The sorts car now has the larger knetc energy because the knetc energy s roortonal to the square

2 Chater 7 Energy 87 o the seed and only the rst ower o the mass.. Ther knetc energes are the same because ther seeds are the same.. Knetc energy does not deend on drecton and s thereore constant. The length o the momentum ector s constant but, as the jet s drecton changes, so does the drecton o ts momentum ector. 3. Two balls wll leae the other sde wth the same seed as the ncomng balls. Ths conseres both momentum and knetc energy. 4. They wll rebound wth the same seeds, conserng knetc energy and momentum. 5. Because work s the orce n the drecton o moton tmes the dstance moed, we must know how hgh she lted the ball. 6. As Sally carres the bags to the truck, the orce she ales s erendcular to the dslacement and thereore does no work. She does the same work as Bll. 7. The knetc energy decreases because the orce and the dslacement are n ooste drectons. 8. The orce, and thereore the resultng acceleraton, s erendcular to the elocty and so only the drecton o the elocty changes. The knetc energy s constant but the drecton o the momentum changes. 9. The change n knetc energy has to be the same because the same work s done n both cases. The lghter sled wll not be ushed or as many seconds, so the mulse s less on the lghter sled. The lghter sled wll hae less nal momentum. 0. The change n momentum has to be the same because the same mulse s marted n both cases. The lghter sled wll be ushed arther and so more work s done on t than on the heaer sled. The lghter sled wll hae more nal knetc energy.. Although the tractor does oste work on the traler, the rctonal orces and ar resstance do an equal amount o negate work so the knetc energy (and seed) thereore reman constant.. At onts A and B the gratatonal orce s dong oste work and the satellte s knetc energy s ncreasng. At ont C the gratatonal orce s dong negate work and the satellte s knetc energy s decreasng. 3. Force A does less work because the comonent o the orce n the drecton o the dslacement s smaller. 4. Both orces do the same work because the comonent o the orce n the drecton o the dslacement s the same n each case. 5. The change n knetc energy s equal to the work. Thereore, the same work must be erormed on each car to sto the car. Because the orces are equal, the dstances must be equal. 6. The car wth the larger mass wll hae the smaller knetc energy and wll thereore sto n the shorter dstance. 7. No, the knetc energy lost by one object durng a collson could be conerted to many derent orms o energy, ncludng deormaton, sound, thermal energy, etc. 8. I you change an object's drecton, you change ts momentum, but t stll has the same seed, ts knetc energy s unchanged. It s not ossble to change ts knetc energy wthout also changng the magntude o ts momentum N 3 m 9 J and 4 N m 8 J. Thereore, the rst does the most work N 3 m 5 J and 4 N 4 m 6 J. Thereore, the second does the most work. 3. Only derences n otental energy are mortant. The choce or the zero o otental energy s arbtrary and could thereore be chosen as meters aboe the loor. 3. It must be conerted nto thermal energy. 33. What s ganed by the knetc energy s lost by the gratatonal otental energy, mantanng the mechancal energy at a constant alue.

3 88 Chater 7 Energy 34. I the ball s consdered to be the system, only the mechancal energy s consered. I Earth s added to the system, momentum s also consered. 35. The otental energy s a maxmum at ether end where the endulum bob reaches ts greatest heght. The knetc energy s a maxmum at the mdont where the endulum bob reaches ts lowest heght and, consequently, ts lowest otental energy. 36. The orce o the strng s always actng erendcular to the elocty and does no work. 37. The rcton causes the mechancal energy o the endulum to decrease. Thereore the gratatonal otental energy s less at the end o each swng and the heght decreases. 38. The loss n mechancal energy must be due to the work done by a orce such as rcton. 39. As the satellte moes closer to Earth, ts gratatonal otental energy decreases and ts knetc energy ncreases. The reerse haens as the satellte moes arther rom Earth. 40. The catault's otental energy n ts "loaded" oston s transormed nto knetc energy o the sacesh and catault arm. Some o the sh's knetc energy s conerted nto gratatonal otental energy as t leaes Earth and then back nto knetc energy as t aroaches the Moon. Fnally, ths knetc energy s turned nto heat and energy o dstorton as the sacesh hts the Moon. 4. When the ball s at ts maxmum heght, the basketball layer ushes downward on t, dong work on t. Ths work lus the ball's gratatonal otental energy reresents the total mechancal energy o the ball. As the ball alls, t loses otental energy and gans knetc energy. When t strkes the loor, t dstorts and ts knetc energy s transormed nto elastc otental energy n ts dstorton (and that o the loor to a lesser extent). When the ball and loor "srng" back, much o that elastc otental energy returns to knetc energy o the ball. The mssng knetc energy shows u as thermal energy n the ball and loor (to be dscussed n Chater 3). 4. d) They all ht the ground wth the same seed. 43. When the ucks aroach each other, the magnetc reulsons do work on the ucks, slowng one down and seedng the other u. Durng ths transormaton, knetc energy s transormed nto magnetc otental energy, whch s then returned to the ucks as knetc energy. The total mechancal energy o the system remans constant. 44. When the uck stretches the srng, t does work on t. Ths transorms the uck's knetc energy nto elastc otental energy stored n the srng. Ths elastc otental energy s then transormed back nto knetc energy. At all tmes, the total mechancal energy o the uck and srng stays constant we gnore the small amount that shows u as thermal energy n the srng. When the uck s susended rom the celng, the mechancal energy stays the same but we must nclude gratatonal otental energy. 45. The work done n lowng through the drt or sand reduces the knetc energy (and hence the seed) o the truck. 46. The sot sand absorbs the knetc energy o the leg and does not return t lke a srngy track would. 47. The chemcal otental energy s conerted to electrcal energy n the battery. Ths energy s conerted to thermal energy n the socks. 48. The brake shoes do work on the brake drums conertng the car's knetc energy to thermal energy. 49. We cannot comletely recoer the energy transormed due to rctonal eects. (Ths s dscussed more ully n Chater 4.) 50. The book loses 0 joules o energy due to the work done by rcton as the book goes u the ram. It wll lose another 0 joules n sldng down to end u wth 60 joules o knetc energy. 5. The ratng tells you how much work can be done n one second, not the total amount that can be done. I the wnch wll run or more than second, t can do more than 600 joules o work. 5. I the battery s truly twce as owerul, t wll be able to deler twce as much energy n each second makng the bulb burn brghter. Snce ower only deals wth rate o energy delery, we hae no way o

4 Chater 7 Energy 89 knowng how long t wll last wthout knowng the ntal chemcal energy stored n the battery. 53. Klowatt-hour s an energy unt because klowatt s a ower unt and multlyng ower by a tme ges energy J 0 s 0 watts, 5000 J 50 s 00 watts. Valere s more owerul. 55. Klowatt-hour s an energy unt because klowatt s a ower unt and multlyng ower by a tme ges energy. 56. Watt s a unt o ower. The rest are energy unts. Answers to the Exercses. m ( )( ) 800 kg 0 m s J 5. m ( )( ) 3. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 84 kg 0 m s 400 J 4kg 6ms kg 6ms 8kg ms 4kg 3m s + kg m s 4kg m s momentum s not consered 4kg 6m s + kg 6m s 90J 4 kg 3 m s + kg m s 90 J knetc energy s consered Momentum s always consered n a collson. Ths collson could not hae taken lace. 4. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 4kg 6ms kg 6ms 8kg ms 4 kg m s + kg 0 m s 8 kg m s momentum s consered 4kg 6m s + kg 6m s 90J 4 kg m s + kg 0 m s 58 J knetc energy s not consered Momentum s always consered n a collson. Ths collson could hae taken lace. m + 0 4kg 5m s 50J 5. ( )( ) ( ) ( )( ) m + m 5kg 4m s 40J 0J 6. m m + 3kg 6m s + kg 4m s 70J ( ) ( )( ) m + m 5kg m s 0J 60J 7. Fd ( )( ) 8. W 40 N ( 0.5 m) 0 J 9. by hand N 3 m. J F x 0; F 0 F net net J 7 J 5 J N x m 0. W ( ) ( ) net + J 0.8 N 4 m 8.8 J. The angle between the net orce ector and the dslacement ector s greater than 90 or eery small

5 90 Chater 7 Energy oer the next sx months. The work done durng ths tme s negate. 0 oer a year's tme. (Seed o Earth s the same each Jan 4th.) Work done durng ths tme s zero.. No work s erormed because the gratatonal orce s erendcular to the crcular ath. 3. W mg h ( )( ) ( ) 55 kg 0 m s 70 m 396 kj 4. GPE mg h ( ) ( ) ( ) 65 kg 0 m s 3 m 950 J 5. a) mg h ( )( ) ( ) 0.45 kg 0 m s 6 m 8.7 J b) + Work 8.7J 8.7J 0 c) 0 6. GPE mgh Wh ( ) ( ) 50 N.5 m 75 J assumng that the alue or the gratatonal otental energy s chosen to be zero at the loor. 7. mg h ( ) ( ) ( ) 0.5 kg 0 m s 6 m 30 J 8. a) GPE can be chosen to be zero; same GPE mgh kg 0m/s 4m 80J;same b) ( ) ( ) ( ) 80J c) 8.94 m/s; same m kg d) m ( kg)( ) 8.94 m/s 7.9 kg m/s; The two blocks hae eloctes n derent drectons, so the momenta must be derent. 9. mg h ( ) ( ) ( ) 00 kg 0 m s m 44 kj 0. a) GPE mgh ( ) ( ) ( ).. 0. kg 0 m s 5 m 5 J b) zero c) GPE + 5 J + 6 J J d) s ndeendent o drecton. The answer to art c) would not change. E W h ( 300 lb) ( 4 t) h P ( 500 t lb s).73 h 0.8 s 550 t lb s ( )( ) E P 330 W 3s m 80 kg 0 m s 3. E P t ( ) ( ) 5 W 8 h 0 Wh 0. kwh h 0.8 kw 3 mn 0.04 kwh 60 mn 4. E P t ( )( ) Answers to the Problems n Problem Solng. m ( )( ) 50 kg 4 m s 400 J. m ( )( ) 7 30,000 kg 35 m s.84 0 J

6 Chater 7 Energy ,000 J 8.3 m s m 000 kg 00J 3.87 m s m 80 kg 5. m m ( ) ( ) ( ) ( ) m m ( ) ( ) ( ) ( ) + kg 8ms + kg 4ms 0 + kg 6m s + kg 3m s 0 m + m kg 8ms + kg 4ms 48J m + m kg 6m s + kg 3m s 7J Thereore, momentum s consered, whle knetc energy s not consered. 6. m + m ( kg) ( 6ms) + 0 6kg ms m m ( ) ( ) ( ) ( ) + kg ms + kg 4ms 6kg ms ( )( ) m + m kg 6m s + 0 8J m + m kg m s + kg 4m s 8J Thereore, both momentum and knetc energy are consered. 7. mo o m m + mo 4 ( 3 ) m ( ) o o 4 3 m o 4 m 8. o ( ) m mo 4 4 o 3o mo m + 4 m + mo mo m o o 3 36 o o ( 4 ) ( 0.4) m + m m + m mo 9. ( ) ( ) m + m kg 6m s + 0 6kg m s 6kg m s m s m + m kg+ kg ( ) ( )( ) m + m kg+ kg m s 6J 0. ( ) ( ) 0.0 kg 900 m s 9 kg m s o

7 9 Chater 7 Energy.. 9kg ms 4.48 m s m.0 kg ( )( ) ( )( ) 0.0 kg 900 m s 4050 J.0 kg 4.48 m s 0. J racton lost F ( )( ) m 0.5 kg 40 m s 000 N d d 0.0 m where the mnus sgn ndcates that the orce s ooste the moton. ( )( ) m 80 kg 9 m s F 34 N d d 0 m 3. Fd ( ) ( ) 4. Fd ( ) ( ) J N 0. m 0.48 J + 0. J + 0. N 0.5 m 0.3 J 5. Usng the data or 70 mh, we hae 03 t 0 t dtot dreact + 4 dbrake + 07 t 4 6. Usng the data or 90 mh, we hae 3 t 363 t dtot dreact + 4 dbrake + 57 t 4 W Fd 00 N 3 m 300 J 7. ( ) ( ) 8. W Fd ( )( ) 0 N. m 44 J 9. In the second collson, block B wll hae hal the seed, and hence one-ourth the knetc energy, ater the collson. Ths knetc energy s transormed nto otental energy as block B moes u the ram. Block B (and block A) moes only 0 cm u the ram. 0. PE mg h ( )( ) ( ) 0 kg 9.8 m s 0.8 m 78.4 J ( ) ( ) + Fd 78.4J 5N m 8.4J ( ) m.38 m s. GPE mg h ( ) ( ) ( ) 80 kg 9.8 m s 0 m 7840 J. a) GPEcounter Wh ( ) ( ) Wh ( ) ( ) GPEshel N m J N m 4J b) J c) The answers to art a) are J lower; the answer n b) does not change. m m m kg ; work N m kg m; GPE kg m s s s 3. [ ] [ ] [ ]

8 Chater 7 Energy m m m m 5. GPE mg h ( )( ) ( ) 0 30 kg 9.8 m s m 588 J 6. GPE mg h ( )( ) ( ) 85 kg 9.8 m s 0 m 8330 J GPE 9.8 m s 9.8 m 3.9 m s m m 7. g h ( )( ) J 6.6 m s m 30 kg GPE 9.8 m s 0.5 m 3.3 m s m m 30. At the lowest ont: 3.3 m s rom rob 9 9. g h ( )( ) 3. a bob c ( 3.3 m s) ( ) bob R 3m T mg ma c ( )( ) 3.7 m s u T kg 3.7 m s m s 6. N ( 40 m s) m m h 8.6 m W mg g 9.8m s 3. a) W Fnetd ( )( ) W ( N) ( 80m s) N N 8 m 38 J b) m 37 J g 9.8m s c) The change n knetc energy should equal the work done by the net orce. (The small derence s due to round o.) 37 J d) h 37 m mg N ( )( ) m 80 kg 9 m s P 60 W s ( )( ) m 000 kg 30 m s P.5 0 W 4s 35. The work s conerted to gratatonal otental energy as the bucket s rased. 36. The work s transormed nto heat by the rctonal orce. m J 37. N s s P,300 W 38. F 549 N.4 m s