COURS_2DE_files/Chapitre 6

Cours Chapitre 6. Mouvement et forces 2de
!
!
"!
!"#$%&'()*+),-./(0(1&)(&)2-'3(4)
!
*+5+)6()0-./(0(1&)
#$%&!'(!')$*+,-(!.%!/$!0,12+(-!3(!4.1/(4(%,!2(&!'.-*&5!$**(30&!$1&&+!474&80(4)093#1%:.(46!7(!4.1/(4(%,!
(&,!*-0&(%,!*$-,.1,!2$%&!389%+/(-&6!:$-!(;(4*3(!<!
- 3(!4.1/(4(%,!2(&!*3$%=,(&!$1,.1-!21!>.3(+3?!
!
- 3(!4.1/(4(%,!281%!&$,(33+,(!
- !
- 3(!4.1/(4(%,!281%(!@1&0(!
!
- 3(!4.1/(4(%,!281%!$/+.%!(%!/.3!
!
- 3(!4.1/(4(%,!2(&!&*.-,+@&!3.-&!281%!(%,-$A%(4(%,!
- !
- 3(!4.1/(4(%,!2(!')1,(!281%(!B$33(!2(!,(%%+&!
!

Cours Chapitre 6. Mouvement et forces 2de
!
!
C!
7$!,-$D(',.+-(!
!
7.-&!2(!&.%!4.1/(4(%,!1%!'.-*&!20'-+,!1%(!&'#;(3&-%'(+)
7$!,-$D(',.+-(!(&,!38(%&(4B3(!2(&!*.+%,&!.''1*0&!*$-!3(!'.-*&!E&F&,=4(!40'$%+G1(H!3.-&!2(!&.%!4.1/(4(%,6!
!
I%!@.%',+.%!21!4.1/(4(%,5!.%!*(1,!-(%'.%,-(-!*31&+(1-&!&7$(4)<()&'#;(3&-%'(4<!
!
- '(3&%=%>1(4!E1%(!3+J%(!2-.+,(5!'.44(!'(33(!20'-+,(!*$-!3$!B$33(!2(!,(%%+&!3K')0(!L!1%(!'(-,$+%(!)$1,(1-!H!
- !
- 3.'/%=%>1(4!E3$!'.1-B(!20'-+,(!3.-&!21!4.1/(4(%,!(&,!G1(3'.%G1(H6!
- !
- !
9%(!/.+,1-(!G1+!-.13(!&1-!-.1,(!*(1,!$/.+-!1%(!,-$D(',.+-(!-(',+3+J%(6!7.-&G18(33(!*-(%2!1%!/+-$J(!&$!,-$D(',.+-(!
&(-$!'1-/+3+J%(6!
!
#$%&!3$!'3$&&(!2(&!&'#;(3&-%'(4)3.'/%=%>1(4!.%!*(1,!-(%'.%,-(-!2(!,-$D(',.+-(&!*$-,+'13+=-(&!<!
!
- 3%'3.=#%'(4!E3(!&F&,=4(!40'$%+G1(!20'-+,!2(&!'(-'3(&!3.-&!2(!&.%!4.1/(4(%,5!'.44(!*$-!(;(4*3(!3(&!
*3$%=,(&!(%!-.,$,+.%!$1,.1-!21!>.3(+3H!
!
- $#'#?-=%:.(4!E3.-&!2(!&.%!&$1,!3(!&M+(1-!20'-+,!1%(!*$-$B.3(H!
!
!
7(!-0@0-(%,+(3!
!
#$%&!3(!N:!O!7$!-(3$,+/+,0!21!4.1/(4(%,!P!.%!$!/1!G1(!3(!4.1/(4(%,!281%!*.+%,!2(!3$!-.1(!281%!/03.!20'-+,!1%(!
,-$D(',.+-(!'+-'13$+-(!3.-&G1(!38.%!38.B&(-/(!21!/03.!(,!(&,!1%(!'.1-B(!'.4*3+G10(!3.-&G1(!38.%!.B&(-/(!2(!3$!&$33(!
2(!'3$&&(6!!
!Q3!@$1,!2.%'!,.1D.1-&!&*0'+@+(-!*$-!-$**.-,!L!G1(3!'.-*&!.%!20'-+,!3(!4.1/(4(%,!281%!$1,-(!'.-*&5!$1,-(4(%,!2+,5!
28.R!.%!-(J$-2(!!
!!
)6() 3-'$4) $#') '#$$-'&) =(:.(=) -1) <93'%&) =() 0-./(0(1&) <@.1) 474&80() 093#1%:.() $-'&() =() 1-0) <()
'929'(1&%(=+) A-.') $-./-%') 4$93%2%(') =#) $-4%&%-1) <.) 474&80() 093#1%:.() B) 3"#:.() %14&#1&C) -1) #44-3%() #.)
3-'$4)<()'929'(13().1)474&80()<@#D()(&).1()"-'=->(+)
!

Cours Chapitre 6. Mouvement et forces 2de
!
!
S!
!
!
!
!:.1-!2(&!4.1/(4(%,&!2(!'.1-,(!21-0(!ED1&G18L!G1(3G1(&!)(1-(&H!.%!*(1,!1,+3+&(-!'.44(!-0@0-(%,+(3!3(!&.35!.1!
,.1,!.BD(,!@+;(!*$-!-$**.-,!L!3$!N(--(6!T%!$**(33(!'(!-0@0-(%,+(35!'929'(1&%(=)&(''(4&'(6!
!
!7.-&G1(!38.%!2.+,!.B&(-/(-!2(&!4.1/(4(%,&!2(!*31&!3.%J1(!21-0(!E*31&+(1-&!D.1-&5!'.44(!2$%&!3(!'$&!281%!
&$,(33+,(!.1!2(!3$!71%(H!3(!-0@0-(%,+(3!,(--(&,-(!%8(&,!*31&!$2$*,06!U!'$1&(!21!4.1/(4(%,!2(!-.,$,+.%!2(!3$!N(--(!
$1,.1-!2(!&.%!$;(5!4V4(!3(!*31&!&+4*3(!4.1/(4(%,!2(/+(%,!,-=&!'.4*3+G10!3.-&G18+3!(&,!20'-+,!*$-!-$**.-,!L!3$!
&1-@$'(!2(!3$!,(--(!E-0@0-(%,+(3!,(--(&,-(H6!T%!/$!1,+3+&(-!2$%&!'(!'$&!1%!'.-*&!2(!-0@0-(%'(!&+,10!$1!'(%,-(!2(!3$!
N(--(5!'$-!(%!'(!*.+%,!.%!*(1,!+J%.-(-!3(!4.1/(4(%,!2(!-.,$,+.%!'(!'(33(W'+6!9%!,(3!'929'(1&%(=)(&,!$**(30!
>9-3(1&'%:.(6!
!
!>+!38.%!2.+,!0,12+(-!2(&!4.1/(4(%,&!(%'.-(!*31&!3.%J&5!'.44(!*$-!(;(4*3(!3(!4.1/(4(%,!2(&!*3$%=,(&5!3(!
-0@0-(%,+(3!3(!*31&!$2$*,0!&(-$!&+,10!$1!'(%,-(!21!>.3(+36!X8(&,!3(!'929'(1&%(=)"9=%-3(1&'%:.(6!
!!
7$!-(3$,+/+,0!21!4.1/(4(%,!!
!
7(!4.1/(4(%,!281%!*.+%,!281%(!-.1(!2(!/03.!(&,!1%(!'F'3.Y2(!3.-&G18+3!(&,!.B&(-/0!*$-!-$**.-,!$1!-0@0-(%,+(3!
,(--(&,-(!(,!1%!'(-'3(!3.-&G18+3!(&,!20'-+,!*$-!-$**.-,!$1!-0@0-(%,+(3!21!/03.6!!
!
!
!
Z0@0-(%,+(3!,(--(&,-(!
Z0@0-(%,+(3!21!/03.!
!
!
T%!,-.1/(!1%(!&+,1$,+.%!&+4+3$+-(!3.-&G1(!38.%!.B&(-/(!3$!*3$%=,(![$-&!$/('!1%!,03(&'.*(!&+,10!&1-!N(--(6!U!
'(-,$+%&!4.4(%,&!2(!38$%%0(!'(,,(!*3$%=,(!&(4B3(!&8$--V,(-!(,!-(*$-,+-!(%!$--+=-(6!T%!*$-3(!21!4.1/(4(%,!2(!
-0,-.J-$2$,+.%!2(![$-&6!7(!4V4(!*)0%.4=%(!(&,!.B&(-/0!*.1-!,.1,(!$1,-(!*3$%=,(!.B&(-/0(!2(*1+&!3$!N(--(6!
TB&(-/0&!2(*1+&!3(!>.3(+35!,.1&!'(&!4.1/(4(%,&!&.%,!*-(&G1(!'+-'13$+-(&!E(%!-0$3+,05!(33+*,+G1(&H6!
!
!
!
Z0@0-(%,+(3!,(--(&,-(!
Z0@0-(%,+(3!)03+.'(%,-+G1(!
!

Cours Chapitre 6. Mouvement et forces 2de
!
!
\!
!N.1,!20*(%2!2.%'!28.R!.%!.B&(-/(!3(!4.1/(4(%,5!$1,-(4(%,!2+,5!*$-!-$**.-,!L!G1(3!-0@0-(%,+(36!!
))
6#)&'#;(3&-%'()<@.1)474&80()093#1%:.()<9$(1<)<.)'929'(1&%(=)<@9&.<(+)A-.')3(&&()'#%4-1C)%=)2#.&)&-.;-.'4)
4$93%2%(')=()'929'(1&%(=)$#')'#$$-'&)#.:.(=)-1)9&.<%()=()0-./(0(1&+)
)))
*+E+)6(4)2-'3(4)
!
#+)F1&('#3&%-14)(&)#3&%-14)093#1%:.(4)
!
!
),,*<]]$*.26%$&$6J./]$*.2]$*^C"C^_6),43!
!!
!78+4$J(!-(*-0&(%,(!1%!2(&!&$,(33+,(&!3(&!*31&!*-.')(&!2(!`1*+,(-5!Q.6!I33(!$!0,0!*-+&(!*$-!3(!-.B.,!2(!3$!&.%2(!
X$&&+%+!G1+!(&,!*$&&0(!*-=&!2(!`1*+,(-!(%!C^^\6!U!J$1')(!2(!Q.!3$!,K')(!%.+-(!%8(&,!-+(%!28$1,-(!G1(!38.4B-(!2(!Q.6!
>+!.%!0,$+,!L!'(,!(%2-.+,!&1-!`1*+,(-!.%!.B&(-/(-$+,!1%(!0'3+*&(!2(!!>.3(+36!!
!!
!Q.!-(&,(!2$%&!3$!*-.;+4+,0!21!`1*+,(-!J-K'(!L!38$,,-$',+.%!!L!2+&,$%'(!G1+!&8(;(-'(!(%,-(!'(&!2(1;!'.-*&6!X(3$!
&+J%+@+(!G1(!')$'1%!2(!'(&!2(1;!'.-*&!(;(-'(!1%(!$',+.%!40'$%+G1(!&1-!38$1,-(6!
!!
G(.D) 3-'$4) 4-1&) (1) %1&('#3&%-1) 4%) =() 0-./(0(1&) <() [email protected]) <9$(1<) <() =#) $'94(13() <() =@#.&'() (&)
'93%$'-:.(0(1&+)
!"#3.1)<()3(4)<(.D)3-'$4)(D('3().1()#3&%-1)093#1%:.()4.')=@#.&'(+)
!
?+),-<9=%4#&%-1)<@.1()#3&%-1)093#1%:.()
)
H1()#3&%-1)093#1%:.()$(.&)I&'()0-<9=%49()$#').1()2-'3(+)
)
H1()2-'3()(4&)3#'#3&9'%49()$#')J)
– .1()<%'(3&%-1))
– .1)4(14)
– .1()/#=(.')K0(4.'9()(1)L(M&-1)NLOP)
)
H1()2-'3()(4&).1)/(3&(.')QQQ)
)
RD(0$=(J!38$',+.%!40'$%+G1(!(;(-'0(!*$-!!`1*+,(-!&1-!Q.!
!
!
!
!

Cours Chapitre 6. Mouvement et forces 2de
!
!
a!
!
7(!/(',([email protected]'(!(&,!*3$'0!&1-!Q.5!'$-!'8(&,!Q.!G1+!&(%,!'(,,(!$',+.%!40'$%+G1(6!Q3!(&,!2+-+J0!2(!Q.!/(-&!`1*+,(-5!'$-!+3!
(&,!$,,+-0!/(-&!`1*+,(-6!7$!2+-(',+.%!E3$!2-.+,(H!(,!3(!&(%&!E&1-!'(,,(!2-.+,(H!281%([email protected]'(!&.%,!3$!2+-(',+.%!(,!3(!&(%&!
2(!38$',+.%!40'$%+G1(6!
!
7(!2+$J-$44(!.BD(,!W!+%,(-$',+.%&!
!
I%!*)F&+G1(!.%!-(*-0&(%,(!2.%'!3(&!$',+.%&!40'$%+G1(&!*$-!2(&[email protected]'(&5!'8(&,!L!2+-(!*$-!2(&!/(',(1-&6![$+&!3(&!
$',+.%&!40'$%+G1(&!&1B+(&!*$-!1%!'.-*&!E1%!&F&,=4(!40'$%+G1(H!%(!&.%,!*$&!,.1D.1-&!&+4*3(&6!:.1-!$**-(%2-(!
L!-(*-0&(%,(-!3(&[email protected]'(&!.%!*(1,!&8$+2(-!2(&!2+$J-$44(&!.BD(,!W!+%,(-$',+.%&6!!!!
#$%&!'(!2+$J-$44(5!3(&!+%,(-$',+.%&!(%,-(!2(1;!'.-*&!G1+!&.%,!(%!'.%,$',!&(!-(*-0&(%,(%,!*$-!2(&!@3=')(&!
*3(+%(&!(,!'(33(&!L!2+&,$%'(!*$-!2(&!@3=')(&!(%!*.+%,+3306!
!
• L!2+&,$%'(!
!
• 2(!'.%,$',!
!
!
!
RD(0$=(!<!1%!')$-+.,!(&,!,+-0!*$-!1%!J$-b.%6!:1+&G1(!3(!')$-+.,!(&,!,+-0!L!38$+2(!281%!@+35!+3!&(%,!!38$',+.%!21!@+36!Q3!
-.13(!&1-!3(!&.3!&$%&!3(!G1+,,(-6!Q3!(&,!2.%'!(%!+%,(-$',+.%!$/('!3(!&.36!U1&&+!+3!&(!,-.1/(!&1-!N(--(5!2.%'!+3!&(%,!
38$,,-$',+.%!,(--(&,-(!E&$%&!$,,-$',+.%!,(--(&,-(!3(!')$-+.,!*$-,+-$+,!2$%&!38(&*$'(H6!78.BD(,!0,12+0!(&,!3(!')$-+.,6!!
!
T%!/(1,!,-$'(-!,.1,(&!3(&!@.-'(&!G1+!&8(;(-'(%,!&1-!'(31+W'+6!T%!'.44(%'(!*$-!*3$'(-!$1!'(%,-(!21!2+$J-$44(!3(!
')$-+.,6!U1,.1-!21!')$-+.,!.%!/$!*3$'(-!,.1&!3(&!.BD(,&!$/('!3(&G1(3&!3(!')$-+.,!(&,!(%!+%,(-$',+.%!<!3(!@+3!E(%!
'.%,$',H5!3(!&.3!E(%!'.%,$',H!(,!3$!N(--(!EL!2+&,$%'(H6!!
9%(!G1(&,+.%!*(1,!&(!*.&(-!<!G1(33(!(&,!3$!2+@@0-(%'(!(%,-(!O!N(--(!P!(,!O!&.3!P!c!Q3!@$1,!'.4*-(%2-(!G1(!*1+&G1(!
3$!N(--(!$,,+-(!3(!')$-+.,!E'.44(!,.1,!$1,-(!'.-*&H!3(!')$-+.,!2(/-$+,!&8(%@.%'(-!2$%&!3(!&.3!(,!&(!2+-+J(-!/(-&!3(!
'(%,-(!2(!3$!N(--(6!X(!%8(&,!*$&!'(!G1+!&(!*$&&(5!'$-!3(!&.3!E3$!&1-@$'(!2(!3$!N(--(H!(4*V')(!3(!'.-*&!2(!&8F!
(%@.%'(-6!7$!&1-@$'(!(;(-'(!2.%'!1%(!$',+.%!40'$%+G1(!.**.&0(!L!38$,,-$',+.%!,(--(&,-(!(,!2.+,!V,-(!,-$+,0(!
'.44(!1%([email protected]'(!L!*$-,6!!
T%!$!2.%'!1%!2+$J-$44(!G1+!'.%,+(%,!3(!')$-+.,!$1!'(%,-(!(,!3(&!.BD(,&!$/('!3(&G1(3&!+3!(&,!(%!+%,(-$',+.%!$1,.1-!
2(!31+5!'8(&,WLW2+-(!3(!@+35!3(!&.3!(,!3$!N(--(6!>+!3(!')$-+.,!(&,!1%!'.%,$',!$/('!1%!2(!'(&!.BD(,&!.%!3(&!-(3+(!*$-!1%(!
@3=')(!*3(+%(5!&+%.%!*$-!1%(!@3=')(!*.+%,+330(6!T%!.B,+(%,!2.%'!3$!@+J1-(!'+W2(&&.1&!E@+J1-(!2(!J$1')(H6!
!
!
!
!
!
!
)
)