Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Cours M1 : présentation
Chute libre
Repère cartésien

→
−
ez
O

→
−
ey

→
−
ex
−
−
−
||→|| = 1 ; ||→|| = 1 ; ||→|| = 1
ex
ey
ez
Figure 1
−→
−
Vecteur position OM en coordonnées
cartésiennes
z

M
→
−
ez
→
−O
ex

→
−
ey

x
Figure 2

y
−
Vecteur vitesse → en base cartésienne
v
z
− (M)
→
v
−→
−
dOM

M(t + dt)
M(t)

→
−
ez
O

y

→
−
ey
Figure 3
Bilan des forces du problème 1 à l’instant initial
→ →
−
−
R = F M/O

→ →
−
−
P = F T /O
Figure 4
Bilan des forces lors de la chute libre pour le
problème 1

→ →
−
−
P = F T /O
Figure 5
Illustration de la troisième loi de Newton
→
−
F M/O

→
−
F O/M
Figure 6
Base cartésienne en 2D

z

→
−
ez
O

→
−
ey
Figure 7

y
Conditions initiales du problème n◦ 2
z

→
−
v0
z =h
→
−
e

α

→
−
P

z

O

y

→
−
ey
Figure 8
Trajectoire parabolique d’un projectile
z
4
3

→
−
v0

2
α
z =h
1
→
−
ez
0 →
ey
0− 1

2

3

4
Figure 9

5

6

7

8

y
Trajectoire parabolique pour différentes vitesses
initiales
h = 1, 5 m ; α = 45◦

z

Plusieurs vitesses testées

3
2
1
O

1...
Trajectoire parabolique pour différentes hauteurs
initiales
v = 8 m.s−1 ; α = 45◦

z

Plusieurs hauteurs testées

3
2
1
O

...
Trajectoire parabolique pour différents angles de
tir (h > 0)
z
h = 1, 5 m ; v = 8 m.s−1

5

Plusieurs angles testés

4
α =...
Trajectoire parabolique pour différents angles de
tir (h = 0)
z
h = 0 m ; v = 8 m.s−1

3

Plusieurs angles testés

2
1
O

1...
Parabole de sûreté
z
4
3
2
1
→
−
ez
0 →
ey
0− 1

2

3

4

5

Figure 14

6

7

8

y
Upcoming SlideShare
Loading in …5
×

M11 presentation

101,262 views

Published on

mécanique 1 : chute libre : présentation

Published in: Education
  • DOWNLOAD THIS BOOKS INTO AVAILABLE FORMAT (2019 Update) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { https://soo.gd/irt2 } ......................................................................................................................... Download Full EPUB Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download Full doc Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download PDF EBOOK here { https://soo.gd/irt2 } ......................................................................................................................... Download EPUB Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download doc Ebook here { https://soo.gd/irt2 } ......................................................................................................................... ......................................................................................................................... ................................................................................................................................... eBook is an electronic version of a traditional print book THIS can be read by using a personal computer or by using an eBook reader. (An eBook reader can be a software application for use on a computer such as Microsoft's free Reader application, or a book-sized computer THIS is used solely as a reading device such as Nuvomedia's Rocket eBook.) Users can purchase an eBook on diskette or CD, but the most popular method of getting an eBook is to purchase a downloadable file of the eBook (or other reading material) from a Web site (such as Barnes and Noble) to be read from the user's computer or reading device. Generally, an eBook can be downloaded in five minutes or less ......................................................................................................................... .............. Browse by Genre Available eBooks .............................................................................................................................. Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, ......................................................................................................................... ......................................................................................................................... .....BEST SELLER FOR EBOOK RECOMMEND............................................................. ......................................................................................................................... Blowout: Corrupted Democracy, Rogue State Russia, and the Richest, Most Destructive Industry on Earth,-- The Ride of a Lifetime: Lessons Learned from 15 Years as CEO of the Walt Disney Company,-- Call Sign Chaos: Learning to Lead,-- StrengthsFinder 2.0,-- Stillness Is the Key,-- She Said: Breaking the Sexual Harassment Story THIS Helped Ignite a Movement,-- Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones,-- Everything Is Figureoutable,-- What It Takes: Lessons in the Pursuit of Excellence,-- Rich Dad Poor Dad: What the Rich Teach Their Kids About Money THIS the Poor and Middle Class Do Not!,-- The Total Money Makeover: Classic Edition: A Proven Plan for Financial Fitness,-- Shut Up and Listen!: Hard Business Truths THIS Will Help You Succeed, ......................................................................................................................... .........................................................................................................................
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • DOWNLOAD THIS BOOKS INTO AVAILABLE FORMAT (2019 Update) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { https://soo.gd/irt2 } ......................................................................................................................... Download Full EPUB Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download Full doc Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download PDF EBOOK here { https://soo.gd/irt2 } ......................................................................................................................... Download EPUB Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download doc Ebook here { https://soo.gd/irt2 } ......................................................................................................................... ......................................................................................................................... ................................................................................................................................... eBook is an electronic version of a traditional print book THIS can be read by using a personal computer or by using an eBook reader. (An eBook reader can be a software application for use on a computer such as Microsoft's free Reader application, or a book-sized computer THIS is used solely as a reading device such as Nuvomedia's Rocket eBook.) Users can purchase an eBook on diskette or CD, but the most popular method of getting an eBook is to purchase a downloadable file of the eBook (or other reading material) from a Web site (such as Barnes and Noble) to be read from the user's computer or reading device. Generally, an eBook can be downloaded in five minutes or less ......................................................................................................................... .............. Browse by Genre Available eBooks .............................................................................................................................. Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, ......................................................................................................................... ......................................................................................................................... .....BEST SELLER FOR EBOOK RECOMMEND............................................................. ......................................................................................................................... Blowout: Corrupted Democracy, Rogue State Russia, and the Richest, Most Destructive Industry on Earth,-- The Ride of a Lifetime: Lessons Learned from 15 Years as CEO of the Walt Disney Company,-- Call Sign Chaos: Learning to Lead,-- StrengthsFinder 2.0,-- Stillness Is the Key,-- She Said: Breaking the Sexual Harassment Story THIS Helped Ignite a Movement,-- Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones,-- Everything Is Figureoutable,-- What It Takes: Lessons in the Pursuit of Excellence,-- Rich Dad Poor Dad: What the Rich Teach Their Kids About Money THIS the Poor and Middle Class Do Not!,-- The Total Money Makeover: Classic Edition: A Proven Plan for Financial Fitness,-- Shut Up and Listen!: Hard Business Truths THIS Will Help You Succeed, ......................................................................................................................... .........................................................................................................................
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • DOWNLOAD THAT BOOKS INTO AVAILABLE FORMAT (2019 Update) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download Full EPUB Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download Full doc Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download PDF EBOOK here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download EPUB Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download doc Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... ......................................................................................................................... ................................................................................................................................... eBook is an electronic version of a traditional print book that can be read by using a personal computer or by using an eBook reader. (An eBook reader can be a software application for use on a computer such as Microsoft's free Reader application, or a book-sized computer that is used solely as a reading device such as Nuvomedia's Rocket eBook.) Users can purchase an eBook on diskette or CD, but the most popular method of getting an eBook is to purchase a downloadable file of the eBook (or other reading material) from a Web site (such as Barnes and Noble) to be read from the user's computer or reading device. Generally, an eBook can be downloaded in five minutes or less ......................................................................................................................... .............. Browse by Genre Available eBooks .............................................................................................................................. Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, ......................................................................................................................... ......................................................................................................................... .....BEST SELLER FOR EBOOK RECOMMEND............................................................. ......................................................................................................................... Blowout: Corrupted Democracy, Rogue State Russia, and the Richest, Most Destructive Industry on Earth,-- The Ride of a Lifetime: Lessons Learned from 15 Years as CEO of the Walt Disney Company,-- Call Sign Chaos: Learning to Lead,-- StrengthsFinder 2.0,-- Stillness Is the Key,-- She Said: Breaking the Sexual Harassment Story That Helped Ignite a Movement,-- Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones,-- Everything Is Figureoutable,-- What It Takes: Lessons in the Pursuit of Excellence,-- Rich Dad Poor Dad: What the Rich Teach Their Kids About Money That the Poor and Middle Class Do Not!,-- The Total Money Makeover: Classic Edition: A Proven Plan for Financial Fitness,-- Shut Up and Listen!: Hard Business Truths that Will Help You Succeed, ......................................................................................................................... .........................................................................................................................
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • If you want to download or read this book, copy link or url below in the New tab ......................................................................................................................... DOWNLOAD FULL PDF EBOOK here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download EPUB Ebook here { http://bit.ly/2m6jJ5M } .........................................................................................................................
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • DOWNLOAD THIS BOOKS INTO AVAILABLE FORMAT (Unlimited) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... Download Full EPUB Ebook here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... ACCESS WEBSITE for All Ebooks ......................................................................................................................... Download Full PDF EBOOK here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... Download EPUB Ebook here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... Download doc Ebook here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... .............. Browse by Genre Available eBooks ......................................................................................................................... Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult,
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here

M11 presentation

  1. 1. Cours M1 : présentation Chute libre
  2. 2. Repère cartésien → − ez O → − ey → − ex − − − ||→|| = 1 ; ||→|| = 1 ; ||→|| = 1 ex ey ez Figure 1
  3. 3. −→ − Vecteur position OM en coordonnées cartésiennes z M → − ez → −O ex → − ey x Figure 2 y
  4. 4. − Vecteur vitesse → en base cartésienne v z − (M) → v −→ − dOM M(t + dt) M(t) → − ez O y → − ey Figure 3
  5. 5. Bilan des forces du problème 1 à l’instant initial → → − − R = F M/O → → − − P = F T /O Figure 4
  6. 6. Bilan des forces lors de la chute libre pour le problème 1 → → − − P = F T /O Figure 5
  7. 7. Illustration de la troisième loi de Newton → − F M/O → − F O/M Figure 6
  8. 8. Base cartésienne en 2D z → − ez O → − ey Figure 7 y
  9. 9. Conditions initiales du problème n◦ 2 z → − v0 z =h → − e α → − P z O y → − ey Figure 8
  10. 10. Trajectoire parabolique d’un projectile z 4 3 → − v0 2 α z =h 1 → − ez 0 → ey 0− 1 2 3 4 Figure 9 5 6 7 8 y
  11. 11. Trajectoire parabolique pour différentes vitesses initiales h = 1, 5 m ; α = 45◦ z Plusieurs vitesses testées 3 2 1 O 1 2 3 4 5 Figure 10 6 7 8 y
  12. 12. Trajectoire parabolique pour différentes hauteurs initiales v = 8 m.s−1 ; α = 45◦ z Plusieurs hauteurs testées 3 2 1 O 1 2 3 4 5 Figure 11 6 7 8 y
  13. 13. Trajectoire parabolique pour différents angles de tir (h > 0) z h = 1, 5 m ; v = 8 m.s−1 5 Plusieurs angles testés 4 α = 45◦ 3 2 z =h 1 → − e O z→ − ey 1 2 3 4 5 Figure 12 6 7 8 y
  14. 14. Trajectoire parabolique pour différents angles de tir (h = 0) z h = 0 m ; v = 8 m.s−1 3 Plusieurs angles testés 2 1 O 1 2 3 4 5 Figure 13 6 7 8 y
  15. 15. Parabole de sûreté z 4 3 2 1 → − ez 0 → ey 0− 1 2 3 4 5 Figure 14 6 7 8 y

×