Kufamba kwese kwese - matambudziko nemhinduro

Kufamba kwese kwese - matambudziko nemhinduro

Torque

1. Danda rine urefu hwe 140 cm. Pane masimba matatu anoshandiswa padanda, F ₁ = 20 N, F ₂ = 10 N, uye F ₃ = 40 N ine gwara nenzvimbo sezvakaratidzwa mumufananidzo uri pazasi. Chii chinonzi torque chinoita kuti danda ritenderere pakati pehukuru hwedanda?

Zvinozivikanwa:

Pakati pehukuru pacho panowanikwa pakati pedanda.

Kureba kwedanda (l) = 140 cm = 1.4 metres

Simba 1 (F ₁ ) = 20 N, ruoko rwechitsigiro 1 (l ₁ ) = 70 cm = 0.7 metres

Simba 2 (F ₂ ) = 10 N, ruoko rwechibato 2 (l ₂ ) = 100 cm – 70 cm = 30 cm = 0.3 mamita

Simba 3 (F ₃ ) = 40 N, ruoko rwechitsigiro 3 (l ₃ ) = 70 cm = 0.7 metres

Zvinodiwa: Hukuru hwetorque

Solution:

Torque 1 inotenderera mwenje uchitenderera wachi, saka torque 1 inopa chiratidzo chekusashanda zvakanaka.

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

Torque 2 inotenderera danda richipesana newachi, saka ichipa chiratidzo chakanaka kutorque 2.

τ ₂ = F ₂ l ₂ = (10 N)(0.3 m) = 3 N m

Torque 3 inotenderera mwenje uchitenderera wachi, saka torque 3 inopa chiratidzo chakanaka.

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

Torque yemagetsi:

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

Hukuru hwetorque ndeye 39 N m. Nzira yekutenderera kwedanda inoenderana newachi, saka chiratidzo chekusagadzikana chakapihwa.

2. Chii chinonzi net torque inoshanda padanda. Akisi yekutenderera panzvimbo D. (sin 53 ^o = 0.8)

Zvinozivikanwa:

Kutenderera kwechikamu cheD

F ₁ = 10 N uye l ₁ = r ₁ chivi θ = (40 cm)(chivi 53 ^o ) = (0.4 m)(0.8) = 0.32 mamita

F ₂ = 10√2 N uye l ₂ = r ₂ chivi θ = (20 cm)(chivi 45 ^o ) = (0.2 m)(0.5√2) = 0.1√2 mamita

F ₃ = 20 N uye l ₃ = r ₁ chivi θ = (10 cm)(chivi 90 ^o ) = (0.1 m)(1) = 0.1 mamita

Zvinodiwa: Torque yemagetsi

Solution:

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

(Torque 1 inotenderera danda rinopesana newachi saka tinoisa chiratidzo chakanaka kutorque 1)

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

(Torque 2 inotenderera mwenje uchitenderera wachi saka tinoisa chiratidzo chekusashanda zvakanaka kutorque 2)

τ ₃ = F ₂ l ₂ = (20 N) (0.1 m) = 2 Nm

(Torque 3 inotenderera danda rinopesana newachi saka tinoisa chiratidzo chakanaka kutorque 3)

Torque yemagetsi:

Στ = τ ₁ – τ ₁ + τ ₃

Στ = 3.2 Nm – 2 Nm + 2 Nm

Στ = 3.2 Nm

3. Chii chinonzi net torque kana axis yekutenderera panzvimbo D. (sin 53 ^o = 0.8)

Zvinozivikanwa:

Kutenderera kwechikamu chepakati pechinhu D.

Daro riri pakati peF ₁ ne axis yekutenderera (r _AD ) = 40 cm = 0.4 m

Daro riri pakati peF ₂ ne axis yekutenderera (r _BD ) = 20 cm = 0.2 m

Daro riri pakati peF ₃ ne axis yekutenderera (r _CD ) = 10 cm = 0.1 m

F ₁ = 10 Newton

F ₂ = 10√2 Newton

F ₃ = 20 Newton

Chivi 53 ^o = 0.8

Zvinodiwa: Torque yemagetsi

Solution:

Nguva yesimba 1

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

(Torque 1 inotenderera danda rinopesana newachi saka tinoisa chiratidzo chakanaka kutorque 1)

Nguva yesimba 2

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

(Torque 2 inotenderera mwenje uchitenderera wachi saka tinoisa chiratidzo chekusashanda zvakanaka kutorque 2)

Nguva yesimba 3

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

(Torque 2 inotenderera danda rinopesana newachi saka tinoisa chiratidzo chakanaka kutorque 3)

Torque yemagetsi:

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = 3.2 – 2 + 2

Στ = 3.2 mamita eNewton

Nguva yekusagadzikana

4. Kureba kwewaya = 12 m, l ₁ = 4 m. Usatarise huremu hwewaya. Ndeipi nguva yekusashanda kwehurongwa.

Zvinozivikanwa:

Huremu hweA (mA ₎ = 0.2 kg

Huremu hweB (m _B ) = 0.6 kg

Daro riri pakati peA ne axis yekutenderera (r _A ) = mamita mana

Daro riri pakati peB ne axis yekutenderera (r _B ) = 12 – 4 = 8 metres

Zvinodiwa: Nguva yekusashanda zvakanaka kwehurongwa

Solution:

Nguva yekusagadzikana kweA

I _A = (m _A )(r _A ² ) = (0.2)(4) ² = (0.2)(16) = 3.2 kg ^m2

Nguva yekusagadzikana kweB

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

Nguva yekusagadzikana kwehurongwa:

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

Kutenderera kwesimba

5. Simba re6-N rinoiswa patambo yakaputirwa nepulley ine huremu hweM = 5 kg uye radius R = 20 cm. Chii chinonzi angular acceleration yepulley. Pulley iyi isimbi yakasimba yakafanana.

Zvinozivikanwa:

Simba (F) = 6 Newton

Huremu (M) = 5 kg

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

Zvinodiwa: Kukurumidza kwekona (α)

Solution:

Nguva yesimba:

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

Nguva yekusashanda zvakanaka kwe silinda yakasimba:

Ini = 1/2 MR ²

I = 1/2 (5 kg)(0.2 m) ²

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

Ini = 1/2 (0.2)

I = 0.1 kg m ².

Kukurumidza kwekona:

τ = ini α

α = τ / I = 1.2 / 0.1 = 12 rad s ^-2

6. Bhokisi rehuremu = 4 kg rakarembera kubva patambo rakatenderedzwa nepulley yehuremu = 8 kg uye radius R = 10 cm. Kukurumidza kunokonzerwa negiravhiti ndeye 10 ms ^-2 . Chii chinonzi linear acceleration yebhokisi? Pulley iyi isimbi yakasimba yakafanana.

Zvinozivikanwa:

Huremu hwepulley (m) = 8 kg

Nharaunda yepulley (r) = 10 cm = 0.1 m

Huremu hwebhuroko (m) = 4 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Huremu (w) = mg = (4 kg)(10 m/s ² ) = 40 kg m/s ² = 40 Newtons

Zvinodiwa: Kukurumidza kuwa kwebhuroko

Solution:

Nguva yekusashanda kwe silinda yakasimba:

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

Nguva yesimba:

τ = F r = (40 N) (0.1 m) = 4 Nm

Kukurumidza kwekona:

Στ = I α

4 = 0.04 α

α = 4 / 0.04 = 100

Kukurumidza kwemutsara:

a = r α = (0.1)(100) = 10 m/s ²

7. Bhokisi rine huremu hwe m rakarembera kubva patambo yakaputirwa papulley. Kana kukurumidza kwebhokisi kuri am/s ² , chii chinoitika panguva yekusashanda kwepulley.

Zvinozivikanwa:

huremu = w = mg

Ruoko rwechirevheta = R

Kukurumidza kwekona = α

Kukurumidza kwekuwa kwebhuroko = a ms ^-2

Zvinodiwa: Nguva yekusashanda zvakanaka kwepulley (I)

Solution:

Kubatana kuripo pakati pekuwedzera simba uye kuwedzera simba kwe angular:

a = R α

α = a / R

Nguva yekusaita basa:

τ = ini α

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

Mwero wekona

8. Chidimbu che 0.2-gram chinofamba mudenderedzwa nekumhanya kwakafanana kwe 10 m/s. Radius yedenderedzwa iri 3 cm. Chii chinonzi angular momentum yechinhu ichi?

Zvinozivikanwa:

Huremu hwechidimbu (m) = 0.2 gram = 2 x 10 ^-4 kg

Kumhanya kwekona (ω) = 10 rad s ^-1

Nharaunda (r) = 3 cm = 3 x 10 ^-2 mamita

Zvinodiwa: Kufamba kwekona kwechikamu

Solution:

Kuenzanisa kwe angular momentum:

L = I ω

I = angular momentum, I = nguva yekusaita basa, ω = angular speed

Nguva yekusagadzikana (kwezvimedu):

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

Mwenje wekona:

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

1. Chii chinonzi kufamba kwese kwese kwese?
   • mhinduroKufamba kwechinhu kunoreva kufamba kwechinhu chakatenderedza axis yakatarwa. Ndiwo mhando yekufamba uko poindi yega yega yechinhu inofamba yakatenderedza axis.
2. Kumhanya kwemutsetse kunoenderana sei nekumhanya kwekona mukufamba kwese?
   • mhinduro: Kumhanya kwakatsetseka ($v$) yepoindi iri muchinhu chinotenderera inoenderana zvakananga nedaro rayo ($r$) kubva pa axis yekutenderera uye angular velocity ($\omega$) yechinhu chacho. Hukama hwacho hunopihwa na $v=r\cdot \omega$.
3. Chii chinonzi nguva yekusaita chinhu, uye ine chekuita sei nekufamba kwese kwese?
   • mhinduro: Nguva yekusagadzikana imhando yekutenderera kwehukuru mukufamba kwakatwasuka. Inoyera kuramba kwechinhu kuchinjika mumamiriro acho ekutenderera. Nguva yekusagadzikana inoenderana nehuremu hwechinhu uye kupararira kwacho zvichienderana ne axis yekutenderera.
4. Mutemo wekutanga waNewton wekufamba unoshanda sei pakufamba kwese kwese?
   • mhinduro: Kungofanana nechinhu chiri kufamba mumutsara chinoramba chichifamba kunze kwekunge chashandiswa nesimba rekunze, chinhu chiri kufamba mudenderedzwa chicharamba chiri mumamiriro iwayo kunze kwekunge chashandiswa nesimba rekunze.
5. Chii chinorehwa nehukuru hwe gyration?
   • mhinduro: Radius ye gyration inopa chiyero chekupararira kwehukuru hwechinhu kubva pa axis of rotation yacho. Inotsanangura zvakanyanya kuti huremu hwese hwechinhu hunofanira kuunganidzwa kure sei kubva pa axis kuti huve nenguva imwechete yekusagadzikana seyakatanga kugoverwa.
6. Chii chinonzi angular momentum uye inochengetedzwa sei?
   • mhinduro: Angular momentum inoenderana ne linear momentum. Inobva panguva yekusashanda kwechinhu uye kumhanya kwacho kwe angular. Mu system yakavharwa, total angular momentum inoramba yakadaro kunze kwekunge yashandiswa ne external torque, zvichiratidza kuchengetedzwa kwe angular momentum.
7. Torque inokanganisa sei kufamba kwese kwese?
   • mhinduro: Torque isimba rinotenderera rakaenzana nerokutenderera. Rinokonzera shanduko mukufamba kwechinhu. Hukama hwacho hunopiwa nemutemo wechipiri waNewton wekutenderera: $\tau =I\cdot \alpha$, apo $\tau$ ndiyo torque, $I$ inguva yekusagadzikana, uye $\alpha$ ndiyo kona yekukurumidzira.
8. Pakati pehukuru pacho pasiyana sei nepakati pekutenderera?
   • mhinduro: Kunyange zvazvo zvichigona kuenderana, pakati pehukuru ndipo panoonekwa kuti huremu hwese hwechinhu hwakabatana nechinangwa chekuverenga mukufamba kwakatwasuka, nepo pakati pekutenderera iri poindi (kana axis) iyo chinhu chinotenderera.
9. Chii chinoita basa resimba repakati pemuviri mukufamba kwese ...
   • mhinduro: Simba repakati (centripetal force) isimba rinoshanda pachinhu chiri kufamba munzira yakatenderera, rakanangana nepakati pekutenderera. Rine basa rekuchengetedza chinhu munzira yacho yakakombama uye kuchidzivirira kuti chisafambe mumutsara wakatwasuka nekuda kwekusashanda zvakanaka.

10. Simba rekinetic rinotenderera rinoenderana sei nenguva yekusagadzikana uye angular velocity?

    • mhinduro: Simba rekinetic rinotenderera isimba rinokonzerwa nekutenderera kwechinhu chakatenderedza axis. Rinopihwa nefomura: KE_{rotational​}=1/2 ​I ω², apo $I$ inguva yekusagadzikana uye $\omega$ ndiyo kasi yekona.