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# Яблонский Вариант 18 / Д-5 вар 18 / Д5_18

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5 ( 18) http://www.termeh.ru

V0,

, α . ,

( . 1).

= (t) ! f

t1, t2, t3

t1 ! .

" 0, 1 2, 3

t0, t1, t2, t3 = (t)

.

 : m = 15 , V0 = 13 , t1 = 8 c, t2 = 16 c, t3 = 20 c, 0 = 110 , 1 = 150 , 2 = 0, 3 = 90 , α = 26 , f = 0.22 . α .1 . 2 " , : G, , ! N,

P F, ,. . .

" = (t) 0, 1 2, 3 ( . 2). 1. # , , ,

!

 0 t1: mV1x - mV0x = Six , (1) Six = -Gt1 sinα - Ft1 + Spx . \$ ! = (t): Spx = 0.5×8×(150 +110) = 1040 × . %, F = fN = fG cosα, (1) : mV1x - mV0 x = -mgt1 sinα - fmgt1 cosα +1040, & V1x = V0 x - gt1 sinα - fgt1 cosα +1040 m.

'

V1 = V1x = 13 - 9.81×8×sin 26 - 0.22 ×9.81×8×cos 26 +104015 » 32.41 .

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". ' F ,

, , ,

t1

(V0x > 0), , – .

# , t* < t1,

G, N, F P,

: = ((150-110)/8)t +110= 5t+110.

' , ,

 0 t*: mV - mV = -mgt* sinα - fmgt* cosα + S px , x 0x t* t* Vx = 0, Spx = Px dt = (5t +110)dt = 2.5t*2 +110t*. 0 0 ( t*: 2.5t*2 +110t* - mg(sinα + f cosα )t* + mV = 0, 0x 2.5t*2 +110t* -15×9.81×(sin 26 + 0.22 ×cos 26 ) ×t* +15×13 = 0 t*2 + 6.559 ×t* + 78 = 0.

( , . .

.

2. # t2 ,

, t2 – t1:

 mV2x - mV1x = Six , (2) Six = -G(t2 - t1 )sinα - F (t2 - t1 ) + Spx . " ! t2 – t1 BC P = P(t): Spx = 0.5×(16 - 8) ×150 = 600 × . " (2) mV2x - mV1x = -mg(t2 - t1)sinα - fmg(t2 - t1 )cosα + 600, & V2x = V1x - g(t2 - t1 )sinα - fg(t2 - t1) cosα + 600 m. ' V2 = V2 x = 32.41- 9.81×8×sin 26 - 0.22 ×9.81×8×cos 26 + 600 15 » 22.49 .

". ' F ,

, , ,

(t2 t1)

(V1x > 0), , – . # , t1< t* < t2,

G, N, F

P, : = ((0 – 150)/(16 – 8)t +150 = –18.75t +150.

' , ,

 0 t*: mV - mV = -mgDt* sinα - fmgDt* cosα + S px , x 1x t* t* Vx = 0, Spx = Px dt = (-18.75t +150)dt = -9.375t*2 +150t*. 0 0

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( t*:

 -9.375t*2 +150t* - mg(sinα + f cosα )t* + mV = 0, 1x -9.375t*2 +150t* -15×9.81×(sin 26 + 0.22 ×cos 26 ) ×t* +15×32.41 = 0 t*2 - 6.016 ×t* - 51.859 = 0 t* = -4.8 , t* = 10.8 . 1 2

( t1< t*+ t1 < t2 ,

, 8< t*+ 8 < 16 0< t*< 8. ,

t2 – t1 = 8 .

3. # t3 ,

, t3 – t2:

 mV3x - mV2x = Six , (3) Six = -G(t3 - t2 )sinα - F (t3 - t2 ) + Spx . " ! t3 – t2 = 4 CD P = P(t): Spx = 0.5×(20 -16) ×90 = 180 × . " (3) mV3x - mV2x = -mg(t3 - t2 )sinα - fmg(t3 - t2 )cosα +180, & V3x = V2 x - g(t3 - t2 )sinα - fg(t3 - t2 )cosα +180 m.

'

V3 = V3x = 22.49 - 9.81× 4 ×sin 26 - 0.22 ×9.81× 4×cos 26 +18015 » 9.53 .

". ' F ,

, , ,

(t3 t2)

(V2x > 0), , – . # , t2< t* < t3,

G, N, F

P, : = ((90 –0)/(20 – 16)t +90 = 22.5t +90.

' , ,

0 t*:

 mV - mV = -mgDt* sinα - fmgDt* cosα + S px , x 2x t* t* Vx = 0, Spx = Px dt = (22.5t + 90)dt = 11.25t*2 + 90t*. 0 0 ( t*: 11.25t*2 + 90t* - mg(sinα + f cosα )t* + mV = 0, 2 x 11.25t*2 + 90t* -15×9.81×(sin 26 + 0.22 ×cos 26 ) ×t* +15× 22.49 = 0 t*2 - 0.32 ×t* + 29.987 = 0.

( , . .

(t3 t2) .

: V1 = 32.41 , V2 = 22.49 , V2 = 9.53 .

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