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( ) 2 1 (13.14) , , 50, , , 10 ; =20 . .

VA VB - - 1. , :

d d OA = ; OB = - 20;

.

2 d V V OA = ; = d 2 = ; 2,5d 100 = 0,5d; d=50 c.

VB - 20 VB OB 2. :

VA 250 = = = 2.

d 50 : = 2 /, d = 50 .

a = 10 600. .

: , r = 0,5. R=1.

n aA aA aA n aB - - n tg = a, a = ( ) 1. :

3 n aA = a ctg = 10 3 = 10.

A 3 2. B:

n r aA 10 n n aB = aA = = = 5.

R 2 2 n aB = 5.

:

R=10 P, . x = 100t, x , , t . : , t.

- - 1. :

x 100t = = = 10t2 ().

R 2. :

d & = = = 20t ;

dt & && = = =.

.

3. :

c VM = R = 20t 10 = 200t.

4. :

c a = R = 20 10 = ;

a = 2R = 20t 10 = 4000t2 c ;

( ) 22 a = a + a = 2002 + 4000t2 = 200 1+ 400t2 c.

( ) ( ) () c a = 200 1+ 400t: = 20t /, = 20 /2,.

4 (12.18) - , = 4t r = L = 60, MB = L, (t- ), , , = 0.

- - 1. :

x = r + L cos = 60 + 60 cos 4t = 100cos 4t;

y = Lsin = 60sin 4t = 20sin 4t.

2. t :

y x sin 4t =.

cos 4t = ;

100 :

x2 y+ = 1.

1002 100 20 .

3. :

& VX = x = -100 4 sin 4t = -400 sin 4 t, & VY = y = 20 4 cos 4t = 80 cos 4t.

= 0 t = 0. :

.

Vx0 = 0 ; Vy0 = t0 = 0:

2 .

V0 = Vx2 +Vy2 = 0 + 80 = ( ) 0 - - 4. :

& && aX = VX = x = -400 4 cos 4 t = -1600 cos 4 t;

& && ay = Vy = y = -80 4 sin 4t = -320 sin 4t.

t0 = :

;

aY = 0.

aX 0 =- 2 0 t0 = :

.

2 2 2 a0 = aX 0 + ay0 = -1600 + 02 = () 5. t0 = 0:

V V =.

an = an t0 = :

VX 0 aX 0 +Vyo ayo a 0 = = 0;

V an0 = a0 - a2 = a0.

t0 = 0:

V02 ( ) 0 = = = 4 .

( ) a0 6. t0 = 0 :

x0 = 100 y0 = 0.

( ) ;

t0 = .

x2 y , a0 = 1600 2, + = 1, V0 = 0 = 4 .

( ) : 1002 202 - - 5 (12.22) x=300t, y=400t-5t2 (t , x,y ).

:

1) ;

2) ;

3) ;

4) .

, t:

x xxt = y = 400 - ;

300 300 y = x - x3 3002 .

:



t 0 1 2 3 x 0 300 600 900 y 0 395 780 1155 Y VV M h O X L - - :

dx dy .

VX = = 300 ; Vy = = 400 -10t dt dt t0 = 0:

VX 0 = 300 ; Vy0 = 400.

:

V0 = VX 0 +Vy2 = 3002 + 4002 = 500.

:

d y d x ay = = -10.

aX = = ;

dt2 dt :

2 a = a0 = aX + ay = 10.

: x=L; y=0, :

0 = L - L2, 3 3002 L == 2.4104 = 24 .

( ) , h , :

& V = VX Vy = y = ;.

t1 = 40c - Vy , . h = y(t1) = 400 40 - 5402 = 8000 = 8 .

( ) ( ) :

&&& &&& &&& dv xx + yy yy a = = =, && x = .

dt V V :

( -10t (-10) ) a =.

3002 + 400 -10t () - - a = a2 + an, ( -10t ) an = a2 - a2 = 102 - =.

3002 + 400 -10t () 3002 + 400 -10t () t0 = :

3000 an0 == 6.

500 t1 = 40 c :

3000 an1 == 10.

300 :

V V an = =.

; an t0 = 0:

V02 0 = = = 4,167 104 = 41,67 .

( ) ( ) an1 t = t1 = 40 c ( ):

V12 1 = = = 9103 = 9 .

( ) ( ) an1 , a0 = 10, h = 8 , L = 24 , 0 = 41,67 , ( ) ( ) ( ) : V = 1 = 9 .

( ) 1, 2. 2 3, 4.

4 t=1. :

- - x = 5t2 +10t r2 = 10 r3 = 6 ( ) ( ) ( ). :,, r4 = 8 ( ).

rrr 1 2, , :

&& ak = a1 = x =10.

& Vk = V1 = x = 10t +;

2 3 , :

Vk 10t +2-3 = = = t +1 -1 ;

( ) r2 ak 2-3 = = =1 -2.

( ) r2 N 3 4. 3 4 :

VN = 2-3 r3 = 4 r4;

t +1 6 t +1 2-3 r3 ( ) ( ) 4 == = c-1 ;

( ) r4 aN = 2-3 r3 = 4 r4;

- - 2-3 r3 16 4 == = c-2.

( ) r4 8 M:

t +1 ( ) VM = 4 r4 = 8 = 6t + 6 ;

4 t=1c:

c VM1 = 6 + 6 =12.

:

3 aM = 4 r4 = 8 = 6 ;

4 (t +1)3 9(t +1)2 ;

aM = 4 r4 = 8 = 42 t=1c:

9 22 aM 1 == 18 ;

2 aM = a + aM = 62 +182 =18.97.

( ) ( ) :

c VM =12, aM = 18.97.

1 (16.16) , = 1.5, = 40 , = 200 , = 20 .

- - 1. .

VA O P A AB C VB B A O P AB VA VB B , , , , 0.

( ) , . , , . , .

. VA.

:

VA = = .

( ) 1.540 60 == = = = = 0.3015 c-1.

( ) 2002 - 202 39600 BP ( ) -( ) - - :





VB = AB BP = AB h = 0.301520 = 6.03.

2. .

V B VA VA VB VB = VA = OA =1.5 40 = 60.

, :

: VB = 6.03, VB = 60.

- - 2 (16.24) D - OABD. , , = OL .

: D AB, OA=15 .

:

- - . AB ( ) .

:

VA = OA = AB AP;

OA OA AB === = 2.

AP OA c BD :

OA 15 2 VD = VB = AB BP = AB = 2 = 20 3 = 34,6.

cos300 :

VD = 34,6, AB = 2.

c - - 3 (16.35) 0 = 2, , r2 = 15 c ( ), r1 = 5 ( ) .

: , , , D, CE BD , .

VC VD rVA rVE , .

c VA = 0 OA = 0 r1 + r2 = 2.5 5 +15 = 50.

( ) ( ) 0.

1, 2.

1 . .

V VA 50 1 = = = =10.

AP r1 5 .

C, D, E:

VC = VE = 1 CP = 1 r 2 =105 2 = 70,7 ;

- - VD = 1 DP =1010 =100.

, D, , , .

c , VC = VE = 70,7, VD =100.

V = 0, : V = 50 A 4 (18.11) 20 0 = 100 ; .

, , = 450 = 450.

1. :

VA = 0 OA =1020 = 200.

VA 0.

2. .

. .

- - :

VA VA 200 = = = = 2 ;

AP AB 100 :

VB = AB BP = 2100 2 = 282,8 ;

VB .

3. :

aA = aA + aA;

a = 0 AO =102 20 = 2000.

A aA :

aA = 0 = 0, d0 = = 0 = const ,, dt aA = a + aA = 2000.

( ) ( ) A 4. :

:

aB = aA + aB + aB.

() :

aB = AB AB = 22 100 = 400.

:

aB = AB AB.

, :

AB aA - : ;

aA aAB - ;

AB AB - ;

- - B - ;

AB AB - .

().

() 2 AB.

() X Y.

X:

0 =-aA cos 45o + aB cos 45o + aB cos 45o.

aB = aA - aB = 2000 - 400 =1600 / 2.

:

AB B = = = 16 / 2.

AB AB B , , , , .

Y:

-aB = -aA cos 45o - aB cos 45o + aB cos 45o.

B = A + B - B cos 45o = 2000 + 400 -1600 0,707 = 565,6 / 2.

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