Umsebenzi kanye namandla e-kinetic - izinkinga nezixazululo

Amandla e-Work-Kinetic :

1. Imoto enesisindo esingama-5000 kg isheshiswe ukusuka ekuphumuleni iye kuma-20 m/s. Nquma umsebenzi ophelele owenziwe emotweni.

Kwaziwa:

Isisindo (m) = 5000 kg

Isivinini sokuqala (v _o ) = 0 m/s ( ukuphumula kwemoto )

Isivinini sokugcina (v _t ) = 20 m/s

Okufunwayo : inethiwekhi

Isixazululo:

Umgomo wamandla okusebenza-kinetic :

I-W _inethi = Δ EK

W _inetha = ½ m (v _t ² – v _o ² )

I-W _inethi = umsebenzi wenethi

Δ EK = ushintsho lwamandla e-kinetic

m = isisindo (kg),

v _t = isivinini sokugcina (m/s),

v _o = isivinini sokuqala (m/s).

Inethiwekhi:

W _inetha = ½ m (v _t ² – v _o ² )

W _inetha = ½ (5000)(20 ² – 0 ² )

I-W _inethi = (2500)(400 - 0)

I-W _inethi = (2500)(400)

I-W _inethi = 1000,000 Joule

2. Into enesisindo esingu-10 kg isheshiswe kusuka ku-5 m/s kuya ku-10 m/s. Nquma umsebenzi wenethi owenziwe entweni!

Kwaziwa:

Isisindo (m) = 10 kg

Isivinini sokuqala (v _o ) = 5 m/s

Isivinini sokugcina (v _t ) = 10 m/s

Okufunwayo : inethiwekhi

Isixazululo:

Inethiwekhi:

I-W _inethi = Δ EK

W _inetha = ½ m (v _t ² – v _o ² )

W _inetha = ½ (10)(10 ² – 5 ² )

I-W _inethi = (5)(100 - 25)

I-W _inethi = (5)(75)

I-W _inethi = 375 Joule

3. Imoto enesisindo esingama-2000 kg yehla ngesivinini kusuka ku-10 m/s kuya ku-5 m/s. Yimuphi umsebenzi owenziwayo emotweni?

Kwaziwa:

Isisindo semoto (m) = 2000 kg

Isivinini sokuqala (v _o ) = 10 m/s

Isivinini sokugcina (v _t ) = 5 m/s

Okufunwayo: inethiwekhi

Isixazululo:

Inethiwekhi:

I-W _inethi = Δ EK

W _inetha = ½ m (v _t ² – v _o ² )

W _inetha = ½ (2000)(5 ² – 10 ² )

I-W _inethi = (1000)(25 - 100)

I-W _inethi = (1000)(-75)

I-W _inetha = -75,000 amaJoule

Uphawu lokususa lubonisa ukuthi indlela yokufuduka iphambene nendlela yamandla e-net.

4. Amandla angaguquki angu-60-N asetshenziswa entweni engu-10-kg imizuzwana eyi-12. Ijubane lokuqala lento lingu-6 m/s futhi isiqondiso sento sifana nesiqondiso samandla.

(1) Umsebenzi owenziwe kule nto ungama-Joules angu-30,240

(2) Amandla okugcina e-kinetic angama-30,240 joules

(3) Amandla angama-2,520 Watt

(4) Ukwanda kwamandla e-kinetic ento kungama-Joules ayi-180

Izitatimende eziqondile zithi…

Kwaziwa:

Amandla (F) = 60 N

Isikhawu sesikhathi (t) = imizuzwana eyi-12

Isisindo sento (m) = 10 kg

Ijubane lokuqala (v _o ) = 6 m/s

Okufunwayo: Izitatimende ezifanele

Isixazululo:

Ukusheshisa kwento:

∑F = ma

60 = 10 a

a = 60 / 10 = 6 m/s ²

Ijubane lokugcina:

v _t = vo _o + at

v _t = 6 + (6)(12)

v _t = 6 + 72

v _t = 78 m/s

Ibanga elihanjiwe ngemizuzwana eyi-12 :

s = vot ₊ 1/2 ku- ²

s = (6)(12) + 1/2 (6)(12) ²

s = 72 + (3)(144)

s = 72 + 432

s = amamitha ayi-504

(1) Umsebenzi owenziwe ngenkani

W = F s = (60)(504) = 30,240 amaJoules

(2) Amandla okugcina e-kinetic

KE = 1/2 mv _t ² = 1/2 (10) (78) ² = (5) (6084) = 30,420 Joules

(3) Amandla

P = W / t = 30,240 / 12 = 2,520 amaJoules/isekhondi

(4) Ukwanda kwamandla e-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)

I-ΔKE = 30,240 amaJoule

5. Umsebenzi omkhulu wenziwa ngenombolo yento…

Isixazululo:

Umsebenzi we-Net = ushintsho lwamandla e-kinetic

W _inetha = ½ m (v _t ² – v _o ² )

Umsebenzi omkhulu:

W ₁ = ½ (8)(4 ² – 2 ² ) = (4)(16 – 4) = (4)(12) = 48 Ama-Joules

W ₂ = ½ (8)(5 ² –3 ² ) = (4)(25 – 9) = (4)(16) = 64 Ama-Joules

W ₃ = ½ (10)(6 ² – 5 ² ) = (5)(36 – 25) = (5)(11) = 55 Ama-Joules

W ₄ = ½ (10)(4 ² – 0 ² ) = (5)(16 – 0) = (5)(16) = 80 Ama-Joules

W ₅ = ½ (20)(3 ² – 3 ² ) = (10)(9 – 9) = (10)(0) = 0 Ama-Joules

6. Imoto enesisindo esingamakhilogremu angu-4000 ihamba ngomugqa oqondile ngesivinini esingama-25 m/s. Imoto yehliswa ukuze ijubane lokugcina lemoto libe ngu-15 m/s. Uyini umsebenzi owenziwe emotweni?

Kwaziwa:

Isisindo (m) = 4000 kg

Ijubane lokuqala (v _o ) = 25 m/s

Ijubane lokugcina (v _t ) = 15 m/s

Okufunwayo : Umsebenzi owenziwe emotweni

Isixazululo:

I-W _inethi = ½ m (v _t ² – vo ₂ ⁾ = ½(4000)(15 ² -25 ² ) = (2000)(225-625) = (2000)(-400) = -800,000 Ama-Joules = -800 kJ

7. I-0.1-kg ephonswe ngokuvundlile ku-6 m/s ukusuka ekuphakameni kwamamitha ama-5. Uma ukusheshisa kwamandla adonsela phansi kungu-10 m/s ² , khona-ke iyini amandla e-kinetic ebhola ekuphakameni kwamamitha ama-2.

Kwaziwa:

Isisindo (m) = 0.1 kg

Ushintsho lokuphakama (h) = 5 m – 2 m = 3 amamitha

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Okufunwayo: Amandla e-kinetic ekuphakameni kwamamitha amabili.

Isixazululo:

Ukunyakaza okubonakalayo kungaqondwa ngokuhlaziya izingxenye ezivundlile neziqondile zokunyakaza ngokwehlukana. Ukunyakaza okuvundlile kuhlaziywe njengokunyakaza kwejubane okungaguquki kanye nokunyakaza okuvundlile kuhlaziywe njengokunyakaza kokuwa kwamahhala noma ukunyakaza okuvundlile.

Amandla okuqala omshini = amandla adonsela phansi anamandla adonsela phansi.

I-PE = mgh = (0.1)(10)(3) = 3 amaJoules.

Amandla okugcina omshini = amandla e-kinetic.

KE = 3 amaJoules.

8. Imoto enesisindo esingamakhilogremu ayi-1000 ishesha kakhulu uma iphumula futhi ihamba ngesivinini esingama-5 m/s. Uyini umsebenzi owenziwa yimoto?

Kwaziwa:

Isisindo (m) = 1000 kg

Ijubane lokuqala (v _o ) = 0

Ijubane lokugcina (v _t ) = 5 m/s

Okufunwayo: Umsebenzi (W) owenziwa ngemoto

Isixazululo:

W _inetha = ½ m (v _t ² – v _o ² )

Umsebenzi owenziwe ngemoto:

I-W _inethi = ½ (1000)(5 ² – 0 ² ) = (500)(25 – 0) = (500)(25) = 12,500 amaJoules

9. Ibhola elingamagremu angu-500 liphonswa phezulu phezulu lisuka ebusweni bomhlaba ngesivinini sokuqala esingu-10 m/s ² . Ukusheshisa ngenxa yamandla adonsela phansi kungu-10 ms ^-2 . Uyini umsebenzi owenziwa amandla esisindo lapho ibhola lifinyelela ukuphakama okuphezulu.

Kwaziwa :

Isisindo sebhola (m) = amagremu angu-500 = 0.5 kg

Ijubane lokuqala (v _o ) = 10 m/s ²

Ijubane lokugcina (v _t ) = 0 (ijubane endaweni ephezulu kakhulu)

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Okufunwayo: Umsebenzi (W) don ngesisindo

Isixazululo:

Umsebenzi we-net owenziwe ngamandla e-net entweni = ushintsho kumandla e-kinetic.

I-W _inethi = ΔEK = EK _t – EK _o

I-Wnet = ½ mv _t ² – ½ mv _o ² = ½ m (v _t ² – v _o ² )

I-KE _t = amandla okugcina e-kinetic, i-KE _o = amandla okuqala e-kinetic, m = isisindo sento, v _t = ijubane lokugcina lento, v _o = ijubane lokuqala lento.

Inethiwekhi:

W _inetha = ½ m (v _t ² – v _o ² ) = ½ (0.5)(0 ² – 10 ² )

I-W _inethi = (0.25)(-100) = -25 Ama-Joule

Uphawu lokususa lubonisa ukuthi indlela yokugudluka iphambene nesisindo sebhola. Indlela ibhola elibheke ngayo iqondile kanti indlela yesisindo iqondile.

10. Into enesisindo esingu-1 kg iyawa ngomehluko wokuphakama = amamitha angu-2.5. Ukusheshisa ngenxa yamandla adonsela phansi kungu-10 ms ^-2 . Uyini umsebenzi owenziwayo entweni?

Kwaziwa:

Isisindo sebhola (m) = 1 kg

Ijubane lokuqala (v _o ) = 0 m/s

Ukuphakama (h) = amamitha angu-2.5

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Okufunwayo: Umsebenzi we-inthanethi ngesikhathi sokufuduka

Isixazululo:

Ijubane lokugcina lebhola (v _t )

Kubalwa kusetshenziswa i-equation yokunyakaza kokuwa okukhululekile. Okuyaziwayo: Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ² , Ushintsho ekuphakameni kwebhola (h) = amamitha angu-2.5. Okufunwayo: Ijubane lokugcina.

v _t ² = 2 gh = 2(10)(2.5) = 2(25)

v _t = √2(25)

v _t = 5√2

Umsebenzi we-Net = ushintsho lwamandla e-kinetic

W _inetha = ΔEK = ½ m (v _t ² – v _o ² ) = ½ (1){(5√2) ² – 0 ² }

I-W _inethi = ½ (25)(2) = 25 amaJoule

11. Into engamakhilogremu angu-2 ihamba ngesivinini esingamakhilomitha angu-72 ngehora. Ngemva kokuhamba amamitha angu-400, ijubane lokugcina lento lingu-144 km ngehora. Ukusheshisa ngenxa yamandla adonsela phansi kungu-10 ms ^-2 . Thola umsebenzi wenethi.

Kwaziwa:

Isisindo sento (m) = 2 kg

Ijubane lokuqala (v _o ) = 72 km/ihora = 20 m/s

Ijubane lokugcina (v _t ) = 144 km/h = 40 m/s

Ibanga (ama) = amamitha angu-400

Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s ²

Okufunwayo: Inethiwekhi

Isixazululo:

Umsebenzi we-net = izinguquko zamandla e-kinetic

W _inetha = ΔEK = ½ m (v _t ² – v _o ² ) = ½ (2)(40 ² – 20 ² }

I-W _inetha = ½ (2)(1600 - 400) = 1200 amaJoules

12. Into engamakhilogremu angu-2 ihamba ngesivinini esingu-2 ms ^–1 . Umsebenzi owenziwe entweni ungama-Joules angu-21. Iyini ijubane lokugcina lento.

Kwaziwa:

Isisindo (m) = 2 kg

Ijubane lokuqala (v _o ) = 2 m/s

Umsebenzi (W) = 21 Joule

Okufunwayo: ijubane lokugcina (v _t )

Isixazululo:

I-W _inethi = ΔEK

I-W _inethi = 1/2 mv _t ² -1/2 mv _o ²

I-W _inetha = 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

1 3. Amandla angaguquki angu-8 N asebenza entweni enesisindo esingu-16 kg. Uma into iqale iphumule, khona-ke nquma ijubane lento ngemva kokuba amandla esebenza entweni imizuzwana emi-4.

Kwaziwa:

Amandla angaguquki (F) = 8 Newton

Isisindo sento (m) = 16 kg

Isivinini sokuqala sento (v _o ) = 0 m/s

Isikhawu sesikhathi amandla asebenza entweni (t) = imizuzwana emi-4

Okufunwayo: Isivinini sokugcina (v _t )

Isixazululo:

Umsebenzi = Ushintsho emandleni e-kinetic

W = KE final – KE initial

W = ½ mv _t ² – ½ mv _o ²

W = ½ mv _t ² – 0

W = ½ mv _t ² —— Isibalo 1

Umsebenzi = Amandla x Ukufuduka

W = F d

W = 8 d

Sebenzisa i-equation yokunyakaza okuqondile okungalingani ngezansi ukuze ubale ukufuduka (d):

d = vot ₊ ½ ku- ²

d = ukufuduka, v _o = ijubane lokuqala, t = isikhawu sesikhathi, a = ukusheshisa

d = 0 + ½ ku- ² = ½ ku- ² —-> a = (v _t – vo _o ) / t = v _t / t

d = ½ (v _t / t) t ²

^d = ½ (v _t ) t

Shintsha ukufuduka (d) ku-equation ethi Umsebenzi ngokufuduka (d) kulesi sibalo:

W = 8 d

W = 8(1/2)(v _t )(t)

W = (4)(v _t )(t) —— isibalo 2

Isibalo 1 = Isibalo 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 = 2 amamitha/umzuzwana

14. Ukuze wandise ijubane lento ibe izikhathi ezimbili zejubane lokuqala, nquma umsebenzi odingekayo enkambisweni…

Kwaziwa:

Isisindo sento (m) = 1 kg

Isivinini sokuqala (v _o ) = 1 m/s

Isivinini sokugcina (v _t ) = 2 x isivinini sokuqala = 2 x 1 = 2 m/s

Okufunwayo: Umsebenzi

Isixazululo:

Amandla okuqala e-kinetic:

KE isiqalo = ½ mv _o ² = ½ (1)(1) ² = ½ (1)(1) = ½ (1) = 0.5

Amandla okugcina e-kinetic lapho ijubane lento liba kabili kunejubane layo lokuqala:

KUYA kokugcina = ½ mv _t ² = ½ (1)(2) ² = ½ (4) = 2

Ithiyori yamandla okusebenza-kinetic:

Umsebenzi = Ushintsho lwamandla e-kinetic

Umsebenzi = Amandla okugcina e-kinetic – amandla okuqala e-kinetic

Umsebenzi = 2 – 0.5

Umsebenzi = 1.5

Amandla okuqala e-kinetic = 0.5

Umsebenzi = 3 x 0.5 = 1.5

Umsebenzi odingekayo izikhathi ezintathu zamandla ayo okuqala e-kinetic.

15. Imoto enesisindo esingu-1500 kg ihamba ngesivinini esingu-36 km/ihora emgwaqweni oqondile nobushelelezi ovundlile. Imoto isheshise yafika ku-72 km/ihora. Thola umsebenzi odingekayo ukuze imoto isheshise.

Kwaziwa:

Isisindo semoto (m) = 1500 kg

Isivinini sokuqala semoto (v _o ) = 36 km/ihora = 36,000 amamitha / 3600 isekhondi = 10 amamitha/isekhondi

Isivinini sokugcina semoto (v _t ) = 72 km/ihora = 72,000 amamitha / 3600 imizuzwana = 20 amamitha/isekhondi

Kufunwa: Kudingeka umsebenzi ukuze kusheshiswe imoto

Isixazululo:

Ithiyori yamandla okusebenza-kinetic:

W = EK final – isiqalo se-EK

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 = amaJoules angu-225,000

16. Into enesisindo esingu-2 kg iqala ukuhamba ngesivinini esingu-72 km. ihora ^-1 . Ngemva kokuhamba emgwaqweni oqondile ovundlile kuze kufike ku-400 m, ijubane lento lingu-144 km . ihora ^-1 . Thola umsebenzi ophelele entweni.

Kwaziwa:

Isisindo sento (m) = 2 kg

Isivinini sokuqala (v _o ) = 72 km/ihora = 72,000 amamitha / 3600 imizuzwana = 20 m/s

Isivinini sokugcina (v _t ) = 144 km/ihora = 144,000 amamitha / 3600 imizuzwana = 40 m/s

Ukufuduka kwento = amamitha angu-400

Okufunwayo: Umsebenzi we-inthanethi entweni

Isixazululo:

Ithiyori yamandla okusebenza-kinetic ithi umsebenzi wenethi usebenza entweni ngendlela efanayo nokushintsha kwamandla okusebenza kwento.

I-W inethi = IYA kokugcina – IYA kokuqala

I-W inethi = ½ mv _t ² – ½ mv _o ²

W inetha = ½ m (v _t ² – v _o ² )

W inetha = ½ (2)(40 ² – 20 ² )

I-W inethi = 1600 – 400

I-W inethi = 1200 Joule

incazelo:

W = Umsebenzi, KE = amandla e-kinetic

Amandla weKinetic

17. Inhlamvu engamagremu ayi-10 ehamba ngesivinini esingaguquki esingu-100 m/s. Iyini amandla e-kinetic enhlamvu.

Kwaziwa:

Isisindo senhlamvu (m) = amagremu ayi-10 = 10/1000 amakhilogremu = 1/100 amakhilogremu = 0.01 amakhilogremu

Isivinini senhlamvu (v) = amamitha ayi-100/umzuzwana

Okufunwayo: Amandla e-Kinetic

Isixazululo:

I-KE = 1/2 mv ²

I-KE = 1/2 (0,01 kg)(100 m/s) ²

KE = 1/2 (0,01 kg)(10.000 m ² /s ² )

KE = (0,01 kg)(5000 m ² /s ² )

KE = 50 kg m ² /s ²

KE = 50 amaJoule

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1. Umsebenzi owenziwa ngezinkinga zamandla nezixazululo
2. Izinkinga zamandla e-kinetic kanye nezixazululo zomsebenzi
3. Izinkinga nezixazululo zesimiso samandla okusebenza-okusebenza ngomshini
4. Izinkinga zamandla adonsela phansi kanye nezixazululo ezingaba khona
5. Amandla angaba khona ezinkinga zentwasahlobo ezinwebekayo nezixazululo
6. Izinkinga zikagesi nezixazululo
7. Ukusetshenziswa kokulondolozwa kwamandla omshini ukuze kuqhutshekwe nokuwa kwamahhala
8. Ukusetshenziswa kokulondolozwa kwamandla omshini wokunyakaza okuphezulu nokwehla ekunyakazeni kokuwa kwamahhala
9. Ukusetshenziswa kokulondolozwa kwamandla okusebenza ukuze kushukunyiswe ebusweni obugobile
10. Ukusetshenziswa kokulondolozwa kwamandla omshini ukuze kushukunyiswe endizeni ethambekele
11. Ukusetshenziswa kokulondolozwa kwamandla okusebenza ngomshini wokunyakaza okubonakalayo