1. Galimoto yolemera makilogalamu 5000 imathamanga kuchokera pamalo opumula kufika pa 20 m/s. Dziwani ntchito yonse yomwe yachitika pa galimotoyo.
Zodziwika:
Kulemera (m) = 5000 kg
Liwiro loyambirira (v o ) = 0 m/s ( kupuma kwa galimoto )
Liwiro lomaliza (v t ) = 20 m/s
Akufuna : netiweki
Yankho:
Mfundo yaikulu ya mphamvu ya work-kinetic :
W net = Δ EK
ukonde = ½ m (v t 2 – v o 2 )
W net = ntchito yapaintaneti
Δ EK = kusintha kwa mphamvu ya kinetic
m = kulemera (kg),
v t = liwiro lomaliza (m/s),
v o = liwiro loyambirira (m/s).
Netiweki:
ukonde = ½ m (v t 2 – v o 2 )
W ukonde = ½ (5000) (20 2 – 0 2 )
W net = (2500)(400 - 0)
W net = (2500)(400)
W net = 1000,000 Joule
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2. Chinthu cholemera makilogalamu 10 chomwe chathamanga kuchokera pa 5 m/s kufika pa 10 m/s. Dziwani ntchito yochuluka yomwe yachitika pa chinthucho!
Zodziwika:
Kulemera (m) = 10 kg
Liwiro loyambirira (v o ) = 5 m/s
Liwiro lomaliza (v t ) = 10 m/s
Akufuna : netiweki
Yankho:
Netiweki:
W net = Δ EK
ukonde = ½ m (v t 2 – v o 2 )
W ukonde = ½ (10) (10 2 – 5 2 )
W net = (5)(100 - 25)
W net = (5)(75)
W net = 375 Joule
3. Galimoto yolemera makilogalamu 2000 imatsika liwiro kuchoka pa 10 m/s kufika pa 5 m/s. Kodi ntchito yotani yomwe yachitika pa galimotoyo ndi yotani?
Zodziwika:
Kulemera kwa galimoto (m) = 2000 kg
Liwiro loyambirira (v o ) = 10 m/s
Liwiro lomaliza (v t ) = 5 m/s
Akufuna: netiweki
Yankho:
Netiweki:
W net = Δ EK
ukonde = ½ m (v t 2 – v o 2 )
W ukonde = ½ (2000) (5 2 – 10 2 )
W net = (1000)(25 - 100)
W net = (1000)(-75)
W net = -75,000 Joule
Chizindikiro chochotsera chimasonyeza kuti njira yosunthira zinthu ikusiyana ndi njira ya mphamvu ya ukonde.
4. Mphamvu yosasinthika ya 60-N yomwe imagwiritsidwa ntchito pa chinthu cholemera makilogalamu 10 kwa masekondi 12. Liwiro loyambirira la chinthu ndi 6 m/s ndipo malangizo a chinthucho ndi ofanana ndi malangizo a mphamvuyo.
(1) Ntchito yochitidwa pa chinthucho ndi ma Joules 30,240
(2) Mphamvu yomaliza ya kinetic ndi 30,240 joules
(3) Mphamvu ndi 2,520 Watts
(4) Kuwonjezeka kwa mphamvu ya kinetic ya chinthucho ndi 180 Joules
Mawu olondola ndi akuti…
Zodziwika:
Mphamvu (F) = 60 N
Nthawi yopuma (t) = masekondi 12
Kulemera kwa chinthu (m) = 10 kg
Liwiro loyambirira (v o ) = 6 m/s
Kufunidwa: Mawu olondola
Yankho:
Kufulumizitsa chinthu:
∑F = ma
60 = 10 a
a = 60 / 10 = 6 m/s 2
Liwiro lomaliza:
v t = vo + pa
v t = 6 + (6)(12)
v t = 6 + 72
v t = 78 m/s
Mtunda woyenda mu masekondi 12:
s = vot + 1/2 pa 2
s = (6)(12) + 1/2 (6)(12) 2
s = 72 + (3)(144)
s = 72 + 432
s = mamita 504
(1) Ntchito yochitidwa ndi mphamvu
W = F s = (60)(504) = 30,240 Joules
(2) Mphamvu yomaliza ya kinetic
KE = 1/2 mv t 2 = 1/2 (10) (78) 2 = (5) (6084) = 30,420 Joules
(3) Mphamvu
P = W / t = 30,240 / 12 = 2,520 Joules/sekondi
(4) Kuwonjezeka kwa mphamvu ya kinetic
ΔKE = 1/2 mv t 2 – 1/2 mv o 2 = 1/2 m (v t 2 – v o 2 ) = 1/2 (10) (78 2 – 6 2 ) = 5 (6084 –36) = 5 (6048)
ΔKE = 30,240 Joule
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5. Ntchito yaikulu imachitika ndi nambala ya chinthu…
Yankho:
Ntchito yapaintaneti = kusintha kwa mphamvu ya kinetic
ukonde = ½ m (v t 2 – v o 2 )
Ntchito yaikulu:
W 1 = ½ (8)(4 2 – 2 2 ) = (4)(16 – 4) = (4)(12) = 48 Ma Joules
W 2 = ½ (8)(5 2 –3 2 ) = (4)(25 – 9) = (4)(16) = 64 Joules
W 3 = ½ (10)(6 2 – 5 2 ) = (5)(36 – 25) = (5)(11) = 55 Ma Joules
W 4 = ½ (10)(4 2 – 0 2 ) = (5)(16 – 0) = (5)(16) = 80 Ma Joules
W 5 = ½ (20)(3 2 – 3 2 ) = (10)(9 – 9) = (10)(0) = 0 Ma Joules
6. Galimoto yolemera makilogalamu 4000 imayenda molunjika pa liwiro la 25 m/s. Galimotoyo imachepetsedwa liwiro kotero kuti liwiro lomaliza la galimotoyo ndi 15 m/s. Kodi ntchito yochitidwa pa galimotoyo ndi yotani?
Zodziwika:
Kulemera (m) = 4000 kg
Liwiro loyambirira (v o ) = 25 m/s
Liwiro lomaliza (v t ) = 15 m/s
Kufunidwa : Ntchito yochitidwa pagalimoto
Yankho:
W net = ½ m (v t 2 – vo 2 ) = ½(4000)(15 2 -25 2 ) = (2000)(225-625) = (2000)(-400) = -800,000 Ma Joules = -800 kJ
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7. 0.1-kg yoponyedwa mopingasa pa 6 m/s kuchokera kutalika kwa mamita 5. Ngati kuthamanga kwa mphamvu yokoka kuli 10 m/s 2 , ndiye mphamvu ya kinetic ya mpirawo pamtunda wa mamita 2 ndi yotani?
Zodziwika:
Kulemera (m) = 0.1 kg
Kusintha kwa kutalika (h) = 5 m – 2 m = mamita atatu
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Kufunidwa: Mphamvu ya kinetic pamtunda wa mamita awiri.
Yankho:
Kuyenda kwa projectile kungamvekedwe pofufuza zigawo zopingasa ndi zoyima za kuyendako padera. Kuyenda molunjika kolunjika kumasanthulidwa ngati kuyenda kosinthasintha kwa liwiro ndi kuyenda molunjika kolunjika kumasanthulidwa ngati kuyenda kopanda kugwa kapena kuyenda molunjika.
Mphamvu yoyambirira ya makina = mphamvu yokoka.
PE = mgh = (0.1)(10)(3) = 3 Joules.
Mphamvu yomaliza ya makina = mphamvu ya kinetic.
KE = 3 Joules.
8. Galimoto yolemera makilogalamu 1000 imathamanga kwambiri ikapuma ndipo imayenda pa liwiro la 5 m/s. Kodi galimotoyo imagwira ntchito yotani?
Zodziwika:
Kulemera (m) = 1000 kg
Liwiro loyambirira (v o ) = 0
Liwiro lomaliza (v t ) = 5 m/s
Akufuna: Ntchito (W) yochitidwa ndi galimoto
Yankho:
ukonde = ½ m (v t 2 – v o 2 )
Ntchito yochitidwa ndi galimoto:
W net = ½ (1000)(5 2 – 0 2 ) = (500)(25 – 0) = (500)(25) = 12,500 Joules
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9. Mpira wa magalamu 500 umaponyedwa molunjika mmwamba kuchokera pamwamba pa dziko lapansi ndi liwiro loyambirira la 10 m/s 2. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms -2 . Kodi mphamvu yolemera imachitidwa bwanji pamene mpirawo wafika kutalika kwakukulu?
Zodziwika :
Kulemera kwa mpira (m) = 500 magalamu = 0.5 kg
Liwiro loyambirira (v o ) = 10 m/s 2
Liwiro lomaliza (v t ) = 0 (liwiro pamalo okwera kwambiri)
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Kufunidwa: Ntchito (W) perekani potengera kulemera
Yankho:
Ntchito ya ukonde yochitidwa ndi mphamvu ya ukonde pa chinthu = kusintha kwa mphamvu ya kinetic.
W net = ΔEK = EK t – EK o
Ukonde = ½ mv t 2 – ½ mv o 2 = ½ m (v t 2 – v o 2 )
KE t = mphamvu yomaliza ya kinetic, KE o = mphamvu yoyambirira ya kinetic, m = kulemera kwa chinthu, v t = liwiro lomaliza la chinthu, v o = liwiro loyambirira la chinthu.
Netiweki:
Ukonde = ½ m (v t 2 – v o 2 ) = ½ (0.5) (0 2 – 10 2 )
W net = (0.25)(-100) = -25 Joule
Chizindikiro chochotsera chimasonyeza kuti njira yosunthira mpira ndi yosiyana ndi kulemera kwa mpira. Njira ya mpira ndi yowongoka ndipo njira yolemerera mpira ndi yolunjika.
10. Chinthu cholemera makilogalamu 1 chimagwa popanda kusuntha ndipo kusiyana kwa kutalika = mamita 2.5. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms -2 . Kodi ntchito yotani yomwe yachitika pa chinthucho?
Zodziwika:
Kulemera kwa mpira (m) = 1 kg
Liwiro loyambirira (v o ) = 0 m/s
Kutalika (h) = mamita 2.5
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Kufunidwa: Kugwira ntchito pa intaneti panthawi yosamukira
Yankho:
Liwiro lomaliza la mpira (v t )
Kuwerengedwa pogwiritsa ntchito equation ya kuyenda kwa free fall. Yodziwika: Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2 , Kusintha kwa kutalika kwa mpira (h) = mamita 2.5. Kufunidwa: Liwiro lomaliza.
v t 2 = 2 gh = 2(10)(2.5) = 2(25)
v t = √2(25)
v t = 5√2
Ntchito yapaintaneti = kusintha kwa mphamvu ya kinetic
W ukonde = ΔEK = ½ m (v t 2 – v o 2 ) = ½ (1){(5√2) 2 – 0 2 }
W net = ½ (25)(2) = 25 Joule
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11. Chinthu cholemera makilogalamu awiri chimayenda pa liwiro la 72 km/ola. Pambuyo poyenda mamita 400, liwiro lomaliza la chinthucho ndi 144 km/ola. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms -2 . Pezani ntchito ya netiweki.
Zodziwika:
Kulemera kwa chinthu (m) = 2 kg
Liwiro loyambirira (v o ) = 72 km/ola = 20 m/s
Liwiro lomaliza (v t ) = 144 km/h = 40 m/s
Mtunda (ma) = mamita 400
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s 2
Akufuna: Netiweki
Yankho:
Ntchito ya ukonde = kusintha kwa mphamvu ya kinetic
W ukonde = ΔEK = ½ m (v t 2 – v o 2 ) = ½ (2) (40 2 – 20 2 }
W net = ½ (2)(1600 - 400) = 1200 Joules
12. Chinthu cholemera makilogalamu awiri chimayenda pa 2 ms -1 . Ntchito yochitidwa pa chinthucho ndi ma Joules 21. Kodi liwiro lomaliza la chinthucho ndi liti?
Zodziwika:
Kulemera (m) = 2 kg
Liwiro loyambirira (v o ) = 2 m/s
Ntchito (W) = 21 Joule
Kufunidwa: liwiro lomaliza (v t )
Yankho:
W net = ΔEK
W net = 1/2 mv t 2 -1/2 mv o 2
ukonde = 1/2 m (v t 2 – v o 2 )
21 = 1/2 (2) (v t 2 – 2 2 )
21 = (v t 2 – 2 2 )
21 = v t 2 – 4
v t 2 = 21 + 4 = 25
v t = √25
v t = 5 m/s
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1 3. Mphamvu yosasinthika ya 8 N imagwira ntchito pa chinthu cholemera makilogalamu 16. Ngati chinthucho poyamba chili pamalo opumulira, ndiye kuti dziwani liwiro la chinthucho pambuyo pake mphamvu imagwira ntchito pa chinthucho kwa masekondi anayi.
Zodziwika:
Mphamvu yosalekeza (F) = 8 Newton
Kulemera kwa chinthu (m) = 16 kg
Liwiro loyambirira la chinthu (v o ) = 0 m/s
Mphamvu yogwira ntchito pa chinthu (t) = masekondi 4
Kufunidwa: Liwiro lomaliza (v t )
Yankho:
Ntchito = Kusintha kwa mphamvu ya kinetic
W = KE yomaliza – KE yoyamba
W = ½ mv t 2 – ½ mv o 2
W = ½ mv t 2 - 0
W = ½ mv t 2 —— Equation 1
Ntchito = Mphamvu x Kusamutsidwa
W = F d
W = 8 d
Gwiritsani ntchito equation ya kayendedwe kosagwirizana ka mzere pansipa kuti muwerengere kusuntha (d):
d = vot + ½ pa 2
d = kusamuka, v o = liwiro loyambirira, t = nthawi yopuma, a = kuthamanga
d = 0 + ½ pa 2 = ½ pa 2 —-> a = (v t – vo o ) / t = v t / t
d = ½ (v t / t) t 2
d = ½ (v t ) t
Sinthani kusamuka (d) pa equation ya Ntchito ndi kusamuka (d) mu equation iyi:
W = 8 d
W = 8(1/2)(v t )(t)
W = (4)(v t )(t) —— equation 2
Chiyerekezo 1 = Chiyerekezo 2
W = W
½ mv t 2 = (4)(v t )(t)
½ mv t = (4)(t)
½ (16)(v t ) = 4(4)
8 v t = 16
v t = 16/8
v t = mamita awiri/sekondi
14. Kuti muwonjezere liwiro la chinthu kukhala kawiri kuposa liwiro loyamba, dziwani ntchito yomwe ikufunika mu ndondomekoyi…
Zodziwika:
Kulemera kwa chinthu (m) = 1 kg
Liwiro loyambirira (v o ) = 1 m/s
Liwiro lomaliza (v t ) = 2 x liwiro loyambirira = 2 x 1 = 2 m/s
Akufuna: Ntchito
Yankho:
Mphamvu yoyambirira ya kinetic:
KE chiyambi = ½ mv o 2 = ½ (1) (1) 2 = ½ (1) (1) = ½ (1) = 0.5
Mphamvu yomaliza ya kinetic pamene liwiro la chinthucho limakhala kawiri kuposa liwiro lake loyamba:
KUTI chomaliza = ½ mv t 2 = ½ (1)(2) 2 = ½ (4) = 2
Chiphunzitso cha mphamvu ya ntchito-kinetic:
Ntchito = Kusintha kwa mphamvu ya kinetic
Ntchito = Mphamvu yomaliza ya kinetic - mphamvu yoyambirira ya kinetic
Ntchito = 2 – 0.5
Ntchito = 1.5
Mphamvu yoyambirira ya kinetic = 0.5
Ntchito = 3 x 0.5 = 1.5
Ntchito yofunika kuchitidwa katatu kuposa mphamvu yake yoyamba ya kinetic.
15. Galimoto yolemera makilogalamu 1500 imayenda ndi liwiro la makilomita 36 pa ola limodzi pamsewu wolunjika komanso wosalala. Galimotoyo imathamanga kufika makilomita 72 pa ola limodzi. Dziwani ntchito yofunikira kuti galimotoyo iyende mofulumira.
Zodziwika:
Kulemera kwa galimoto (m) = 1500 kg
Liwiro loyamba la galimoto (v o ) = 36 km/ola = 36,000 metres / 3600 second = 10 metres/second
Liwiro lomaliza la galimoto (v t ) = 72 km/ola = 72,000 metres / 3600 second = 20 metres/second
Kufunidwa: Ntchito ikufunika kuti galimoto iyende mofulumira
Yankho:
Chiphunzitso cha mphamvu ya ntchito-kinetic:
W = EK yomaliza – EK yoyamba
W = ½ mv t 2 – ½ mv o 2 = ½ m (v t 2 –v o 2 )
W = ½ (1500)(20 2 - 10 2 )
W = ½ (1500)(400 - 100)
W = ½ (1500)(300)
W = (1500)(150)
W = 225,000 Joules
16. Chinthu cholemera makilogalamu awiri chimayamba kuyenda pa liwiro la makilomita 72. ola -1 . Pambuyo poyenda mumsewu wowongoka wopingasa mpaka mamita 400, liwiro la chinthucho ndi makilomita 144. ola -1 . Dziwani ntchito yonse pa chinthucho.
Zodziwika:
Kulemera kwa chinthu (m) = 2 kg
Liwiro loyambirira (v o ) = 72 km/ola = 72,000 mamita / masekondi 3600 = 20 m/s
Liwiro lomaliza (v t ) = 144 km/ola = 144,000 metres / masekondi 3600 = 40 m/s
Kusamutsidwa kwa chinthu = mamita 400
Kufunidwa: Ntchito yolumikizidwa pa chinthucho
Yankho:
Chiphunzitso cha mphamvu ya ntchito-kinetic chimati ntchito ya netiweki imagwira ntchito pa chinthu chimodzimodzi ndi kusintha kwa mphamvu ya kinetic ya chinthucho.
W net = KUYAMBIRA komaliza – KUYAMBIRA koyambirira
W net = ½ mv t 2 – ½ mv o 2
ukonde = ½ m (v t 2 – v o 2 )
ukonde = ½ (2) (40 2 – 20 2 )
W net = 1600 – 400
W net = 1200 Joule
Kufotokozera:
W = Ntchito, KE = mphamvu ya kinetic
Kinetic mphamvu
17. Chipolopolo cha magalamu 10 chikuyenda pa liwiro losasintha la 100 m/s. Kodi mphamvu ya kayendedwe ka chipolopolocho ndi yotani?
Zodziwika:
Kulemera kwa chipolopolo (m) = magalamu 10 = 10/1000 kilogalamu = 1/100 kilogalamu = 0.01 kilogalamu
Liwiro la chipolopolo (v) = mamita 100/sekondi
Kufunidwa: Mphamvu ya Kinetic
Yankho:
KE = 1/2 mv 2
KE = 1/2 (0,01 kg)(100 m/s) 2
KE = 1/2 (0,01kg)(10.000 m 2 /s 2 )
KE = (0,01kg)(5000 m 2 /s 2 )
KE = 50 kg m 2 /s 2
KE = 50 Joule
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- Ntchito yochitidwa ndi mphamvu ndi mavuto ndi mayankho
- Mavuto ndi mayankho a mphamvu zogwirira ntchito
- Mavuto ndi mayankho a mfundo za mphamvu za makina ndi ntchito
- Mavuto ndi mayankho a mphamvu yokoka
- Mphamvu zomwe zingatheke pa mavuto a masika otanuka ndi mayankho ake
- Mavuto amagetsi ndi mayankho
- Kugwiritsa ntchito mphamvu yamakina yosungira kuti munthu agwe momasuka
- Kugwiritsa ntchito mphamvu yamakina yosungira kayendedwe ka mmwamba ndi pansi mu kayendedwe ka free fall
- Kugwiritsa ntchito kusunga mphamvu yamakina kuti iyende pamwamba pa curve
- Kugwiritsa ntchito mphamvu yamakina yosungira kuti munthu ayende pa ndege yopendekeka
- Kugwiritsa ntchito mphamvu ya makina yosungira kuti zigwiritsidwe ntchito poyendetsa zinthu
