[PDF] [PDF] Cinématique en mécanique newtonienne - cpge paradise

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x=a0t2+x0y(t) =v0t z(t) =z0: t1= v1= ā t2= t3=02591206 t(s)a(ms2)

ā āāā ȕāāaa=; āta=;

ātu= ā āāāā ȕāā ad=; ātdȕ ȕć

ā ā ātd

ā āā a ȕ

t1ȕ ā āāě āā ć v v0 2 tt0 t0 2 = 1

ā ȕ v

ȕćt

0v 00tv

ȕ ā v1v2

ć l ć ā

v1=v2=l= I

ěāāāāěL

ȕ Ox

D ā ā

āM v

ȕ' #v

ȕOy 0

/2'A 2A 1L D# Vxy M

āxy A2M

ȕtxɵ MA2 ā

ȕtyɵ ā MA2 ā

ā v(') ā ȕā ā

ā v0 ā ā ā

ā ȕ v(') ' ȕ

v(') v=KV (')ɵ Kā DL

āv0DLLDȕ'

āā#a=g#ez g ā

ȕ ȕ x= 0;z=h ā #v0=v0(()# ex+()#ez) 2[;] Ā ȕā

ā ȕxC z= 0 ȕ zS

zS ȕv0 ā h h= 0 xC v0ȕg=; xC ā ā R C

Oxāāȕ(t)

x ā x=x+R 0xy x+ C HA

R ā ě ā ȕO M

āā ŧ = 0O ȕ

R āā ȕāā

M

ȕāāMɵ

ě āMȕ ā āāā āā

R #aȕāā M

ě ā ā M

ā x0v0 M Ā

M ȕ ā x0v0

EI

ě (Ox)(Oy) ȕt= 0 O

ȕ(Oy) v ć ȕ A ȕ(Ox)

ā aO ţ 2v

ā ā x;y

ţ xM;yM ā(x;y)

ȕā ā 1 +

y x 2 = 4x2 2y x2 2

ā ā y=x3/2/3px/+

r=a0t2+r0(t) =0+!t z(t) =v0t:

Mā ȕā (r=bet/;=!t) ;!

ā ȕā ȕO M

0 ȕ ȕ ā ā O

ā ȕāā M

āȕ# OM

ā R O ā

ā O = 0 ȕ

ȕ (t) ȕ v0 ȕ

ȕ ā v=ktk

ȕ D

R=; vţ ;

ā āā a= 3g g=;

ě ā MAMBā ć O

TATB

ā ā ā MAMB ā ȕ O

MAMB

ā ā ā TV= TT=

ě R O !

āāR ā ā

v

O = 0 ā ā r(t)(t)

āāR

ć ȕ ā v ȕ r0

O ć = 0 ȕ

ā āā āā R

ā āā R

ȕāā ā g=;v=;!=/!

r(t1)r(t2)(t1)(t2)0P(t1)P(t2) r(t1)r(t2)(t1)(t2)0P(t1)P(t2)

ϔό ȕ t1t2 P

ěd=;foretmorscorps

d l fl pR p

ā lf=; ȕā lp=;

Rp=; ȕ ȕ

ā ȕ ā ȕ ě RT āā '

#v

ȕ v

I E

ā V

āā R0 āt0

āā R āt ā

MM0 O

0Ox0xR

R0L H B

ȕ t0= 0 ǃ

ā D ā ȕt= 0

R ǃ O0 OO=O0

ȕ āāR0 ě ȕ c

T0 ě ǃ

c āāR0 ā MR

RcL T ě ǃ R

Ā Vc āT

T= T0 = 1/ q 1V2 c2 ŋ āŌ RR0 _x= 2a0t_y=v0_z= 0 x= 2a0y= 0 z= 0 v= q (4a20t2+v20)a= 2ja0j

ā a=v

t ā v(t)v(t= 0) = tZ t=0 a(t)t:

ě a(t) ā ā

v(t2) =v(t1) +2/3

2=: v(t3) =v(t1) +=:

ţ ā āta tu

āţ ā td ātd ć

ta ȕ ȕ x

ȕt x(t)x(0) =x(t) =

tR =0v v(t)v(0) =v(t) = tR =0a ȕ ȕāā x t= ȕāā 2x t2= āā xȕ 3 1 2 tatutd t() a() 31016
6 tatutd t() v() 31016
9 51
69
tatutdt() x() t6t1:vx=at t>t1:vxat1=a(tt1)!vx= 2at1at:

ȕ t= 2t1āā

8>>>>><

t6t1x(t)0 = tR t=0v(t)t= tR t=0att=1 2at2 t>t1x(t)x(t1) = tR t=t1 v(t)t= tR t=02at1tatt= 2at1(tt1)1

2a(t2t21)

x(t) =at21+ 2at1t1 2at2

āāāȕāvx

x(2t1) =at21/2 x=vx!x(2t1) = x(2t1)Z x=0 x= 2t1Z t=0 vxt:

ȕ ȕ vx(t) ȕ ā ȕ

2t1 at1at1

ā ȕāā v

v0 2 tt0 t0 2 = 1

ā 0t12t10at

1tv

Ā t12t10at

212at

21tvĀ

āā v= 0;t= 0v= 0;t= 2t1v=v0;t=t0 v0

t0ā ȕ ȕ ā v v=v0 s 1 t t01 2 x(t)0 = tZ t=0 v(t)t=v0 tZ t=0 s 1 t t01 2 t: t/t01 =(u) t=t0(u)u u2[/2;/2]t2[0;2t0] p1(u)2=jcos(u)j=(u) (u)>0 ȕɵ x(t) =v0 /2Z u=/2 q

1(u)2t=v0t0

/2Z u=/2 (u)2u=v0t0 /2Z u=/2

1 +(2u)

2u =v0t0 2 + [(2u)/2]/2 u=/2 =v0t0 2:

āā ā ȕ v(t)

ā ȕ ȕ v0t0 ā v0t0

āR2āŋŌā

ā x1(t) āx1(t) =v2t

D ȕ ě

t= 0x2=(D+l) ȕ(D+l)/v1 ȕ ȕ v2(D+l)/v1 l < v2(D+l)/v1D >(v1/v21)l=; #v(M) =v((')#ey+(')# ex):

ā ȕ t= 0ɵM=O

ā v=

# OM(t)#0 = tZ t=0 #v(M)=v((')#ey+(')# ex); yM(t) =v(')txM(t) =v(')t: #v(A2) =V# ex# A2(0)A2(t) =V t# ex xA2(t) =D+V t yA2(t) =L: xM=xA2tx=D Vv(') yM=yA2ty=L v(') tx V=v(') ā ā ȕ

ć Ox ćty '=/2 ā ȕOx

ā ā ȕ y=L ȕ tx> ty

D

Vv(')>L

v('): v(')ā tx=tyv(') =V L

D(') +L('):

ā ȕ'v(') āā v(')

D(') +L(') ȕā

D(') +L(') =D(') +L

2 pD2+L2 ȕā' =L/D

D(') +L(') =pD2+L2(')v(') =V LpD2+L2('):

v0=v('=) =V LpD2+L2:

DLāāȕā()

1 ȕ ' ě 1 ā Oy

v0'V L/D ā ć ā L/D

LD ()1 '=ě /2 ā

Ox ě v0'V

ě ě āā #a

ě ȕā ā2# OM

t2=g#ez x=v0t()z=h+v0t()gt2 2

ŋ ţŌ ět

t=x v0()zh=x()g

2v202()x2:

ā ȕ ȕāz= 0

h=x()g

2v202()x20 =x22v20()()

gx2hv20()2 g:

ȕ ā ā ȕ xC

xC=v20 g 0 @(2) 2+ s(2) 2 2 +2gh v20 2() 1 A zh=x()g

2v202()x2=g

2v202()

x22v202()() gxquotesdbs_dbs47.pdfusesText_47

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