Ukunyakaza okujikelezayo - izinkinga nezixazululo

Ukunyakaza okujikelezayo - izinkinga nezixazululo

I-Torque

1. Ugongolo oluyi-140 cm ubude. Kunezenzo ezintathu zamandla kugongolo, F ₁ = 20 N, F ₂ = 10 N, kanye F ₃ = 40 N ngesiqondiso nendawo njengoba kuboniswe esithombeni esingezansi. Iyini i- torque ebangela ukuthi ugongolo lujikeleze phakathi nendawo yobunzima bogongolo?

Kwaziwa:

Isikhungo sesisindo sitholakala enkabeni ye-beam.

Ubude bomsebe (l) = 140 cm = 1.4 amamitha

I-Force 1 (F ₁ ) = 20 N, ingalo ye-lever 1 (l ₁ ) = 70 cm = 0.7 amamitha

Amandla 2 (F ₂ ) = 10 N, ingalo yesibambo 2 (l ₂ ) = 100 cm – 70 cm = 30 cm = 0.3 amamitha

I-Force 3 (F ₃ ) = 40 N, ingalo ye-lever 3 (l ₃ ) = 70 cm = 0.7 amamitha

Okufunwayo: Ubukhulu be-torque

Isixazululo:

I-torque 1 ijikeleza umsebe ngokwewashi, ngakho-ke i-torque 1 inikezwa uphawu olubi.

τ ₁ = F ₁ l ₁ = (20 N)(0.7 m) = -14 N m

I-torque 2 ijikeleza umsebe ngokuphikisana newashi, ngakho-ke inika i-torque 2 uphawu oluhle.

τ ₂ = F ₂ l ₂ = (10 N)(0.3 m) = 3 N m

I-torque 3 ijikeleza ngomsebe ngokwewashi, ngakho-ke i-torque 3 inikezwa uphawu oluhle.

τ ₃ = F ₃ l3 = (40 N)(0.7 m) = -28 N m

I-torque ephelele:

Στ = -14 Nm + 3 Nm – 28 Nm = – 42 Nm + 3 Nm = -39 Nm

Ubukhulu be-torque bungu-39 N m. Isiqondiso sokujikeleza kogongolo ngokwewashi, ngakho-ke sinikezwe uphawu olubi.

2. Iyini i-torque enetha esebenza ku-beam I-axis yokujikeleza endaweni D. (sin 53 ^o = 0.8)

Kwaziwa:

I-axis yokujikeleza endaweni D

F ₁ = 10 N kanye no-l ₁ = r ₁ isono θ = (40 cm)(isono 53 ^o ) = (0.4 m)(0.8) = 0.32 amamitha

F ₂ = 10√2 N kanye no-l ₂ = r ₂ isono θ = (20 cm)(isono 45 ^o ) = (0.2 m)(0.5√2) = 0.1√2 amamitha

F ₃ = 20 N kanye no-l ₃ = r ₁ isono θ = (10 cm)(isono 90 ^o ) = (0.1 m)(1) = 0.1 amamitha

Okufunwayo: I-torque ephelele

Isixazululo:

τ ₁ = F ₁ l ₁ = (10 N)(0.32 m) = 3.2 Nm

(I-torque 1 ijikeleza umsebe ngokuphambene newashi ngakho-ke sibeka uphawu oluhle ku-torque 1)

τ ₂ = F ₂ l ₂ = (10√2 N)( 0.1√2 m) = -2 Nm

(I-torque 2 ijikeleza ngomsebe ngokwewashi ngakho-ke sibeka uphawu olubi ku-torque 2)

τ ₃ = F ₂ l ₂ = (20 N)(0.1 m) = 2 Nm

(I-torque 3 ijikeleza umsebe ngokuphambene newashi ngakho-ke sibeka uphawu oluhle ku-torque 3)

I-torque ephelele:

Στ = τ ₁ – τ ₁ + τ ₃

Στ = 3.2 Nm – 2 Nm + 2 Nm

Στ = 3.2 Nm

3. Iyini i-torque enetha uma i-axis yokujikeleza endaweni D. (sin 53 ^o = 0.8)

Kwaziwa:

I-axis yokujikeleza endaweni D.

Ibanga eliphakathi kuka-F ₁ kanye ne-axis yokujikeleza (r _AD ) = 40 cm = 0.4 m

Ibanga phakathi kuka-F ₂ kanye ne-axis yokujikeleza (r _BD ) = 20 cm = 0.2 m

Ibanga eliphakathi kuka-F ₃ kanye ne-axis yokujikeleza (r _CD ) = 10 cm = 0.1 m

F ₁ = 10 Newton

F ₂ = 10√2 Newton

F ₃ = 20 Newton

Isono 53 ^o = 0.8

Okufunwayo: I-torque ephelele

Isixazululo:

Isikhathi samandla 1

Στ ₁ = (F ₁ )(r _AD isono 53 ^o ) = (10 N)(0.4 m)(0.8) = 3.2 Nm

(I-torque 1 ijikeleza umsebe ngokuphambene newashi ngakho-ke sibeka uphawu oluhle ku-torque 1)

Isikhathi samandla 2

Στ ₂ = (F ₂ )(r _BD isono 45 ^o ) = (10√2 N)(0.2 m)(0.5√2) = -2 Nm

(I-torque 2 ijikeleza ngomsebe ngokwewashi ngakho-ke sibeka uphawu olubi ku-torque 2)

Isikhathi samandla 3

Στ ₃ = (F ₃ )(r _CD isono 90 ^o ) = (20 N)(0.1 m)(1) = 2 Nm

(I-torque 2 ijikeleza umsebe ngokuphambene newashi ngakho-ke sibeka uphawu oluhle ku-torque 3)

I-torque ephelele:

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = 3.2 – 2 + 2

Στ = 3.2 amamitha e-Newton

Isikhathi sokungakhathali

4. Ubude bentambo = 12 m, l ₁ = 4 m. Unganaki isisindo sentambo. Iyini isikhathi sokungahlali kahle kwesistimu.

Kwaziwa:

Isisindo se -A (m _A ) = 0.2 kg

Isisindo se-B (m _B ) = 0.6 kg

Ibanga eliphakathi kuka-A kanye ne-axis yokujikeleza (r _A ) = amamitha angu-4

Ibanga phakathi kuka-B kanye ne-axis yokujikeleza (r _B ) = 12 – 4 = 8 amamitha

Okufunwayo: Isikhathi sokungakhathali kwesistimu

Isixazululo:

Isikhathi sokungakhathali kwe-A

I _A = (m _A )(r _A ² ) = (0.2)(4) ² = (0.2)(16) = 3.2 kg m ²

Isikhathi sokungakhathali kwe-B

I _B = (m _B )(r _B ² ) = (0.6)(8) ² = (0.6)(64) = 38.4 kg m ²

Isikhathi sokungabi namandla kwesistimu:

Mina = I _A + I _B = 3.2 + 38.4 = 41.6 kg m ²

Amandla okujikeleza

5. Amandla angu-6-N asetshenziswa entanjeni eboshwe nge-pulley enobunzima obungu-M = 5 kg kanye ne-radius R = 20 cm. Iyini i-angular acceleration ye-pulley. I-pulley iyisilinda eqinile efanayo.

Kwaziwa:

Amandla (F) = 6 Newton

Isisindo (M) = 5 kg

Irediyasi (R) = 20 cm = 20/100 m = 0.2 m

Okufunwayo: Ukusheshisa kwe-Angular (α)

Isixazululo:

Isikhathi samandla:

τ = FR = (6 Newton)(0.2 amamitha) = 1.2 N m

Isikhathi sokungakhathali kwesilinda esiqinile:

I = 1/2 MR ²

I = 1/2 (5 kg)(0.2 m) ²

I = 1/2 (5 kg)(0.04 ^m2 )

I = 1/2 (0.2)

I = 0.1 kg m ².

Ukusheshisa kwe-angular:

τ = ngi α

α = τ / I = 1.2 / 0.1 = 12 rad s ^-2

6. Ibhulokhi yobunzima = 4 kg elenga entanjeni egoqwe nge-pulley yobunzima = 8 kg kanye ne-radius R = 10 cm. Ukusheshisa ngenxa yamandla adonsela phansi kungu-10 ms ^-2 . Kuyini ukusheshisa okuqondile kwebhulokhi? I-pulley iyisilinda eqinile efanayo.

Kwaziwa:

Isisindo se-pulley (m) = 8 kg

Irediyasi ye-pulley (r) = 10 cm = 0.1 m

Isisindo sebhulokhi (m) = 4 kg

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

Isisindo (w) = mg = (4 kg)(10 m/s ² ) = 40 kg m/s ² = 40 amaNewton

Okufunwayo: Ukusheshisa kokuwa kwamahhala kwebhulokhi

Isixazululo:

Isikhathi sokungabi namandla kwesilinda esiqinile:

I = 1/2 MR ² = 1/2 (8 kg)(0.1 m) ² = (4 kg)(0.01 m ² ) = 0.04 kg m ²

Isikhathi samandla:

τ = F r = (40 N)(0.1 m) = 4 Nm

Ukusheshisa kwe-angular:

Στ = I α

4 = 0.04 α

α = 4 / 0.04 = 100

Ukusheshisa okuqondile:

a = r α = (0.1)(100) = 10 m/s ²

7. Ibhlokhi elinesisindo esingu-m esilenga entanjeni egoqwe nge-pulley. Uma ukusheshisa kokuwa kwamahhala kwebhlokhi kungu-am/s ² , yisiphi isikhathi sokungakhathali kwe-pulley.

Kwaziwa:

isisindo = w = mg

Ingalo yesilevu = R

Ukusheshisa kwe-angular = α

Ukusheshisa kokuwa kwamahhala kwebhulokhi = a ms ^-2

Okufunwayo: Isikhathi sokungahlali kahle kwe-pulley (I)

Isixazululo:

Ukuxhumana phakathi kokusheshisa okuqondile kanye nokusheshisa kwe-angular:

a = R α

α = a/R

Isikhathi sokungakhathali:

τ = ngi α

I = τ : α = τ : a / R = τ (R / a) = τ R a ^-1

Umfutho we-angular

8. Inhlayiya engu-0.2-gram ihamba ngendilinga ngesivinini esingaguquki esingu-10 m/s. Irediyasi yendilinga ingu-3 cm. Iyini i-angular momentum yenhlayiya?

Kwaziwa:

Isisindo sezinhlayiya (m) = 0.2 gram = 2 x 10 ^-4 kg

Isivinini se-angular (ω) = 10 rad s ^-1

Irediyasi (r) = 3 cm = 3 x 10 ^-2 amamitha

Okufunwayo: Umfutho we-angular we-particle

Isixazululo:

Isibalo somfutho we-angular:

L = I ω

I = umfutho we-angular, I = umzuzu we-inertia, ω = isivinini se-angular

Isikhathi sokungahlali kahle (sezinhlayiya):

I = mr ² = (2 x 10 ^-4 )(3 x 10 ^-2 ) ² = (2 x 10 ^-4 )(9 x 10 ^-4 ) = 18 x 10 ^-8

Umfutho we-angular:

L = I ω = (18 x 10 ^-8 )(10 rad s ^-1 ) = 18 x 10 ^-7 kg m ² s ^-1

1. Kuyini ukunyakaza kokujikeleza?
   • Impendulo: Ukunyakaza kokujikeleza kubhekisela ekuhambeni kwento ezungeze i-axis eqondile. Luhlobo lokunyakaza lapho iphuzu ngalinye lento lihamba khona lijikeleza i-axis.
2. Ijubane eliqondile lihlobana kanjani nejubane eliyindilinga ekuhambeni okujikelezayo?
   • Impendulo: Ijubane eliqondile ($v$) yephuzu entweni ejikelezayo ilingana ngqo nebanga layo ($r$) kusukela ku-axis yokujikeleza kanye nejubane le-angular ($\omega$) lento. Ubudlelwano bunikezwa ngu $v=r\cdot \omega$.
3. Iyini isikhathi se-inertia, futhi sihlobene kanjani nokunyakaza kokujikeleza?
   • Impendulo: I-Moment of inertia iyi-analogue yokujikeleza kwesisindo ekuhambeni okuqondile. Ilinganisa ukumelana kwento nezinguquko esimweni sayo sokujikeleza. I-Moment of inertia incike kokubili kusisindo sento kanye nokusatshalaliswa kwayo maqondana ne-axis yokujikeleza.
4. Umthetho wokuqala kaNewton wokunyakaza usebenza kanjani ekunyakazeni okujikelezayo?
   • Impendulo: Njengoba nje into ehamba ngomugqa ihlala inyakaza ngaphandle kokuba iqhutshwa amandla angaphandle, into ehamba ngokujikeleza izohlala kuleso simo ngaphandle kokuba iqhutshwa yi-torque yangaphandle.
5. Iyini ukubaluleka kwe-radius ye-gyration?
   • Impendulo: Irediyasi ye-gyration inikeza isilinganiso sokusatshalaliswa kwesisindo sento kude ne-axis yayo yokujikeleza. Ngokuyisisekelo ichaza ukuthi kude kangakanani ne-axis yonke isisindo sento kungadingeka sigxile ukuze sibe nesikhathi esifanayo se-inertia njengokusabalalisa kokuqala.
6. Kuyini i-angular momentum futhi ilondolozwa kanjani?
   • Impendulo: Umfutho we-angular ulingana nomfutho oqondile. Ungumkhiqizo womzuzu we-inertia wento kanye nejubane layo le-angular. Ohlelweni oluvaliwe, umfutho we-angular ophelele uhlala ungaguquki ngaphandle kokuthi usetshenziswe yi-torque yangaphandle, okugqamisa ukulondolozwa komfutho we-angular.
7. I-torque ithinta kanjani ukunyakaza kokujikeleza?
   • Impendulo: I-Torque ilingana namandla ajikelezayo. Ibangela izinguquko ekuhambeni kokujikeleza kwento. Ubudlelwano bunikezwa ngumthetho wesibili kaNewton wokujikeleza: $\tau =I\cdot \alpha$, lapho $\tau$ i-torque, $I$ yisikhathi sokungakhathali, futhi $\alpha$ ukusheshisa kwe-angular.
8. Isikhungo sobunzima sihluke kanjani esikhungweni sokujikeleza?
   • Impendulo: Nakuba zingahambisana, isikhungo sobuningi yindawo lapho yonke inqwaba yento ingacatshangwa ukuthi igxile khona ngenhloso yokubala ngokunyakaza okuqondile, kanti isikhungo sokujikeleza siyiphuzu (noma i-axis) into ejikeleza ngalo.
9. Iyini indima yamandla aphakathi nendawo ekunyakazeni okujikelezayo?
   • Impendulo: Amandla ase-Centripetal amandla asebenza entweni ehamba ngendlela eyindilinga, eqondiswe enkabeni yokujikeleza. Anesibopho sokugcina into endleleni yayo egobile futhi ayivimbele ukuthi ihambe emgqeni oqondile ngenxa yokungabi namandla.

10. Amandla e-kinetic ajikelezayo ahlobene kanjani nomzuzu we-inertia kanye ne-angular velocity?

    • Impendulo: Amandla e-kinetic ajikelezayo amandla abangelwa ukujikeleza kwento ezungeze i-axis. Anikezwa yifomula: KE_{rotational​}=1/2 ​I ω², lapho $I$ yisikhathi sokungakhathali kanye $\omega$ yijubane le-angular.