Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1...
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Transcript of Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1...
![Page 1: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/1.jpg)
Mรกquina de Atwood
๐
๐
๐1๐
๐2๐
๐1๐ โ ๐ = ๐1๐1
๐ โ๐2 ๐ = ๐2๐2
๐1 = ๐2 = ๐
๐ =(๐1 โ๐2)
(๐1 +๐2)๐
๐ =2๐1๐2
(๐1 +๐2)๐ Que forรงa รฉ
sentida pelo teto?
![Page 2: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/2.jpg)
๐1 m
๐ =(๐1 โ๐2)
(๐1 +๐2)๐
๐1 = 560 g๐2 = 550 g
๐ = 0,088 m/s2
1 m = 12๐ฮ๐ก2
ฮ๐ก = 4,7 ยฑ 0,1 s
๐ = 9,8 m/s2
๐
![Page 3: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/3.jpg)
https://www.youtube.com/watch?v=4ovhEkSIqV0
![Page 4: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/4.jpg)
๐ฟ/2
๐ฟ๐ฟ ๐ฟ/3
Deslocamentos envolvendo polias mรณveis
Obs: cada caso รฉ um caso....
![Page 5: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/5.jpg)
ร possรญvel acelerar ๐1 com ๐1 > ๐ ?
๐1 =๐2
๐1 +๐2๐ ๐1 =
๐2
2๐1 +๐2/2๐ ๐1 =
๐2
๐1/2 + ๐2๐
![Page 6: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/6.jpg)
O caso III em detalhe
ฮ๐ฅ2๐2
๐2
= 2ฮ๐ฅ1
ฮ๐ฅ1
![Page 7: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/7.jpg)
3a Lei de Newton
Mola Slinky
![Page 8: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/8.jpg)
3a Lei = Lei da Aรงรฃo e Reaรงรฃo
โSe o corpo A faz uma forรงa ๐ no corpo B, o corpo B faz uma forรงa โ๐ no corpo Aโ
Evidรชncia experimental: conservaรงรฃo do momento linear total de um par de partรญculas interagentes (veremos mais adiante no curso)
![Page 9: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/9.jpg)
๐ ๐๐ถ
๐ ๐ถ๐(= ๐)
๐ ๐๐๐ ๐๐
๐ ๐๐
๐ ๐๐
![Page 10: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/10.jpg)
Um problema
๐
1
2
3
๐
3๐
๐น โ๐๐ โ ๐21 = ๐๐
๐12 โ๐๐ โ ๐32 = ๐๐
๐23 โ๐๐ = ๐๐
๐ =๐น
3๐โ ๐ ๐23 = ๐32=
๐น
3๐12 = ๐21=
2๐น
3
Qual รฉ a aceleraรงรฃo do conjunto? Quais sรฃo as forรงas entre os elos?
๐น โ 3๐ ๐ = 3๐ ๐
![Page 11: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/11.jpg)
Corda massiva suspensa
Tensรฃo nรฃo รฉ uniforme!
E se a corda estiver em queda livre?
๐ฟ โ ๐ฅ
๐ฅ
๐๐ฅ ๐
๐ ๐ฅ = ๐๐ฅ ๐
๐
๐
๐
๐
![Page 12: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/12.jpg)
Mola Slinky suspensa
demonstraรงรฃo
![Page 13: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/13.jpg)
https://www.youtube.com/watch?v=8UimHnsWSBc
![Page 14: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/14.jpg)
Corda massiva deslizando por um prego
A massa do pequeno trechocircular รฉ desprezรญvel ele nรฃopode estar sujeito a nenhumaforรงa nem a nenhum torque
[๐๐ฅ]๐
[๐ ๐ฟ โ ๐ฅ ]๐ ๐ฅ๐ฟ โ ๐ฅ
๐๐ท๐๐ธ
โ๐๐ทโ๐๐ธ
|๐๐ธ| = |๐๐ท|
![Page 15: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/15.jpg)
[๐๐ฅ]๐
[๐ ๐ฟ โ ๐ฅ ]๐ ๐ฅ๐ฟ โ ๐ฅ
๐๐๐๐ฅ ๐ = [๐๐ฅ]๐ โ ๐
๐ ๐ฟ โ ๐ฅ ๐ = ๐ โ [๐ ๐ฟ โ ๐ฅ ]๐
๐ =2๐ฅ โ ๐ฟ
๐ฟ๐
๐ = 0 quando ๐ฅ = ๐ฟ/2; ๐ = ๐ quando ๐ฅ = ๐ฟ.
![Page 16: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/16.jpg)
Desafio: em quanto tempo o fio abaixo, solto em repouso, vai passar pelo prego?
2๐ฟ/3๐ฟ/3
Obs: Despreze o pequeno trecho sobre o prego
![Page 17: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/17.jpg)
Globo da Morte
![Page 18: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/18.jpg)
https://www.youtube.com/watch?v=qn1jWi_Po9c
![Page 19: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/19.jpg)
๐ฏ๐ก๐๐๐
๐๐ ๐
Qual รฉ a menor velocidade no topo que permite executar o loop vertical?
๐๐ฃ๐ก๐๐๐2
๐ = ๐ +๐๐
๐ ๐๐ฃ๐ก๐๐๐2
๐ โฅ ๐๐
๐ฃ๐ก๐๐๐ โฅ ๐๐
๐ ~ 2m โถ ๐ฃ๐ก๐๐๐ > 16 km/h
![Page 20: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/20.jpg)
https://www.youtube.com/watch?v=oYUfkpyvdOg
![Page 21: Mรกquina de Atwoodยกquina de Atwood ๐ ๐ ๐1๐ ๐2๐ ๐1 โ๐=๐1๐1 ๐โ๐2 =๐2๐2 ๐1=๐2=๐ ๐= (๐1โ๐2) (๐1+๐2) ๐= ... 3a](https://reader031.fdocuments.net/reader031/viewer/2022021600/5c1ad9c609d3f2ea148c3d54/html5/thumbnails/21.jpg)
Os copos nรฃo executam um MCU na vertical
๐๐ ๐
๐ฏ๐ฏ๐ก๐๐๐
|๐ฏ๐ก๐๐๐| โฅ ๐๐
Para a รกgua permanecer no copo no topo:
Obs: no caso da รกgua, ๐ โ ๐
๐ ๐ก๐๐ก
๐ฏ๐๐๐๐ฅ๐ Quem tem que ser |๐ฏ๐๐๐๐ฅ๐|
para isso acontecer?