Яблонский Вариант 18 / Д-5 вар 18 / Д5_18
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V0,
, α . ,
( . 1).
= (t) ! f
t1, t2, t3
t1 ! .
" 0, 1 2, 3
t0, t1, t2, t3 = (t)
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: m = 15 , V0 = 13 , |
t1 = 8 c, |
t2 = 16 c, t3 = 20 c, |
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0 = 110 , 1 = 150 , |
2 = 0, |
3 = 90 , α = 26 , |
f = 0.22 . |
α |
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" , : G, , ! N, |
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P F, ,. . .
" = (t) 0, 1 2, 3 ( . 2). 1. # , , ,
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0 t1: |
mV1x - mV0x = Six , |
(1) |
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Six = -Gt1 sinα - Ft1 + Spx . |
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$ ! |
= (t): |
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Spx = 0.5×8×(150 +110) = 1040 × . |
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%, F = fN = fG cosα, |
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(1) : |
mV1x - mV0 x = -mgt1 sinα - fmgt1 cosα +1040, |
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V1x = V0 x |
- gt1 sinα - fgt1 cosα +1040 m. |
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V1 = V1x = 13 - 9.81×8×sin 26 - 0.22 ×9.81×8×cos 26 +1040
15 » 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*: |
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mV - mV |
= -mgt* sinα - fmgt* cosα + S |
px |
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x |
0x |
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t* |
t* |
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Vx = 0, |
Spx = Px dt = (5t +110)dt = 2.5t*2 +110t*. |
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0 |
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( t*: |
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2.5t*2 +110t* - mg(sinα + f cosα )t* + mV |
= 0, |
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0x |
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2.5t*2 +110t* -15×9.81×(sin 26 + 0.22 ×cos 26 ) ×t* +15×13 = 0 |
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t*2 + 6.559 ×t* + 78 = 0. |
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( , . .
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2. # t2 ,
, t2 – t1:
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mV2x - mV1x = Six , |
(2) |
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Six = -G(t2 - t1 )sinα - F (t2 - t1 ) + Spx . |
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" ! t2 – t1 |
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BC P = P(t): |
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Spx = 0.5×(16 - 8) ×150 = 600 × . |
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" (2) |
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mV2x - mV1x = -mg(t2 - t1)sinα - fmg(t2 - t1 )cosα + 600, |
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V2x = V1x - g(t2 - t1 )sinα - fg(t2 - t1) cosα + 600 m. |
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V2 = |
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V2 x |
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= 32.41- 9.81×8×sin 26 - 0.22 ×9.81×8×cos 26 + 600 15 » 22.49 . |
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". ' F ,
, , ,
(t2 – t1)
(V1x > 0), , – . # , t1< t* < t2,
G, N, F
P, : = ((0 – 150)/(16 – 8)t +150 = –18.75t +150.
' , ,
0 t*: |
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mV - mV |
= -mgDt* sinα - fmgDt* cosα + S |
px |
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x |
1x |
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t* |
t* |
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Vx = 0, |
Spx = Px dt = (-18.75t +150)dt = -9.375t*2 +150t*. |
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0 |
0 |
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( t*:
-9.375t*2 |
+150t* - mg(sinα + f cosα )t* + mV |
= 0, |
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1x |
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-9.375t*2 |
+150t* -15×9.81×(sin 26 + 0.22 ×cos 26 ) ×t* +15×32.41 = 0 |
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t*2 - 6.016 ×t* - 51.859 = 0 |
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t* = -4.8 , |
t* = 10.8 . |
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1 |
2 |
( t1< t*+ t1 < t2 ,
, 8< t*+ 8 < 16 0< t*< 8. ,
t2 – t1 = 8 .
3. # t3 ,
, t3 – t2:
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mV3x - mV2x = Six , |
(3) |
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Six = -G(t3 - t2 )sinα - F (t3 - t2 ) + Spx . |
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" ! t3 – t2 = 4 |
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CD |
P = P(t): |
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Spx = 0.5×(20 -16) ×90 = 180 × . |
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" (3) |
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mV3x - mV2x |
= -mg(t3 - t2 )sinα - fmg(t3 - t2 )cosα +180, |
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V3x |
= V2 x - g(t3 - t2 )sinα - fg(t3 - t2 )cosα +180 m. |
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V3 = V3x = 22.49 - 9.81× 4 ×sin 26 - 0.22 ×9.81× 4×cos 26 +180
15 » 9.53 
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". ' F ,
, , ,
(t3 – t2)
(V2x > 0), , – . # , t2< t* < t3,
G, N, F
P, : = ((90 –0)/(20 – 16)t +90 = 22.5t +90.
' , ,
0 t*:
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mV - mV |
= -mgDt* sinα - fmgDt* cosα + S |
px |
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2x |
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t* |
t* |
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Vx = 0, |
Spx = Px dt = (22.5t + 90)dt = 11.25t*2 + 90t*. |
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0 |
0 |
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( t*: |
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11.25t*2 |
+ 90t* - mg(sinα + f cosα )t* + mV |
= 0, |
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2 x |
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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. |
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( , . .
(t3 – t2) .
: V1 = 32.41 
, V2 = 22.49 
, V2 = 9.53 
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