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Giải bài tập Cơ học - Vật lý (Chương 1: Phương trình chuyển động) môn Cơ điện tử | Trường Đại Học Thái Nguyên

4

Lưu ý rằng, để biết được dạng quỹ đạo chuyển động của một chất điểm nào đó, ta phải đi tìm phương trình quỹ đạo của nó – tức là phương trình biểu diễn mối quan hệ giữa các tọa độ của vật, trong đó ta đã khử mất biến thời gian. Do đó, trong bài tập này ta có thể làm như sau.

Môn: Cơ điện tử 8 tài liệu

Trường: Đại học Thái Nguyên 236 tài liệu

Tác giả:

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Downloaded by mai hoa lý (lymaihoa28@gmail.com)
lOMoARcPSD|22014077

6$FO/=@ABL1Na-c+`
$U</P7AB>AB>1L6;64`
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g
H2
t =
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gH2
H
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2
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t
h
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0
2
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0
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
hD(P>A)C+AB,!+/G1N6eI
,=
2
gt
2
1
s =
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g
h2
t =
8-(P>2!b=1+
,VQ62B-2
$vC+2AB,^0 !I
m04901089
2
1
tg
2
1
s
22
1
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Ft+AB
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s2
89
6192
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lOMoARcPSD|22014077

Tài liệu khác của Đại học Thái Nguyên

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lOMoARcPSD|22014077 !"ω # ϕ $ " $ % !"ω # ϕ%$ "%$ & ' ( ) * + ,- ! $ ϕ . ϕ% %/π0 / 12 !3 4 5 6$ ϕ . ϕ% "%/ # $π5 π $ ϕ . ϕ% "%/ # $ 5 2 ($ ϕ . ϕ% 7 ' 6 / 8 9 : ; 0 6 < , ( ) * 2 7 - = 7 > 12 - 6 ( ? 3 ) @ AB 0 7 C / D 6 < + 8 E 70 62 B- 2 7 12 ! 8 $ F ϕ ϕ% # %/π A2 " $ 7 !"ω # ϕ $ !"ω # ϕ% # %/π$ !"ω # ϕ%$0 % !"ω # ϕ%$ FG 7 x y a = y 2 = x a a a 1 2 1 H . ≤ !"ω # ϕ $ ≤ 4 . ≤ ≤ HB - I $ 2 4 J 6 ( ? 6K a y 2 = x AL . ≤ ≤ a1 6$ 92 M - I $ !"ω # ϕ $
!"ω # ϕ% # %/π#π$ . !"ω # ϕ%$ FG 7 N 4 J 6 ( ? 6K a y 2 = − x AL . ≤ ≤ a1 π $ F ϕ ϕ% # "%/ # $ (? (2 N 6 > 2 x 2 y2 + = 1 a 2 a 2 1 2 2 6 ( ? + 41O- A P 0 7 1L A2 Q ; 4 8 ($ = / D - " $ A2 "%$8 R 3 < / 2 !3 ! " $ A2 "%$
x = cosωt.cosϕ − sinωt.sinϕ "S$ 1 1 a1
y = cosωt.cosϕ − sinωt.sinϕ "T$ 2 2 a 2 U V "S$ AL !ϕ% A2 "T$ AL . !ϕ W A< AL A<
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 x y cosϕ −
cosϕ = sinωt.sin(ϕ − ϕ ) "X$ 2 1 2 1 a a 1 2 9
V "S$ AL ! ϕ% A2 "T$ AL . ! ϕ W A< AL A< x y sinϕ −
sinϕ = cosωt sin(ϕ − ϕ ) "Y$ 2 1 2 1 a a 1 2 Z - "X$ A2 "Y$ W A< AL A< 2 2 x y 2xy + −
cos( ϕ − ϕ ) = sin2 (ϕ − ϕ ) "[$ 2 2 2 1 2 1 a a a a 1 2 1 2 "[$ 6 ( ? + 41O-8 ! " !#$ %#$ # %& !' ϕ() ϕ* %& + , - . /0 12#3 R P P G \ ] < \ Z AL AB 3 A T^/ _ + W 1 G \ Z K A \ ] AL AB 3 A% S^/ _ +8 F AB 3 6 P P 4 + A ]Z0 Z] 7` a ) C + ]Z 6; !8 F !b O AB 3 6 c P > 6 . 4 5 4+ v = 6 5+ +! 4+ . 4 5 0' F , s + s s + s 2 2v v v 1 2 = = = = = 9,5 m 3 / s. t + t s s 1 1 v + v ( A 1 2 + + v v v v 1 2 1 2 F !3 , v = 9,5 m 3 / s. R + > R + J / = X^ + P P5 / P P d f i E Z %^^ + 6e I + a- P P "f .%$8 Z < P P β ] AL AB 3 SY/ _ +8 fQ $ U + - = c α L 2 a- N P P` Z < ; R + AL AB 3 A% ^0g / _ +5 f .% 6$ U + - = AL AB 3 Q 6; 6 4 7 a- , P P` $ R 3 a- N P P Z + + G R L Z - = 6; + P P G ] L Z MB AB = " $ v v 2 1 hD ( ' 1: 2 !3 ! ]ZR 7 MB AB h = , AL sin β = "%$ sin β sinα a FG " $ A2 "%$ N
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 h v1 sinα = . = 0 8 , 33 α XY^S^j a α %S^S^j8 a v2 7 7 5+ 0' ' 8 9 :; <0 α = >:; ? <. 5603 ' 0 ≤ α ≤ 12303 ' 0 3 @ + 5603 ' 0 < α < 12303 ' 0 5+ 0' ' 5 ?+ + 8 h v C / ' +? DE 5+ ' + < F ? <. +G 0' 1 sinα > . 3 a v2 MD AD 1 h v a v :0 = → AD = sinα . M . D 1 > . . A . D 1 = M . D 8 sin β sinα sin β a v h v 2 2 AD MD > 1 - 0 5+ +! 8 ' F 9 5+ +! 5+ ' F#3 v v 1 2 6$ 7 a- , P P AL AB 3 Q k 2 ; 1N 2 + < + l 12 1N c P P L " + a- N P P 2 / P - = + , 1C - O + $0 A AB 0 c - I $ @ L A2 AB 3 + - = 7 ) h v1 sinα = . a v2 H AL m h v h α ! "α$ ≤ 4 1 . ≤ 1 v ≥ v . 2 1 a v a 2 h hv v 1 = = 2 5
, m / s = 9km / h 8 2 min a 9N 2 0 + - = c L Ri0 AL Ri ⊥ ]R8 R AB , = G / O I 6 K S^^ 8 fQ ! 6 1V AB L a 0 < $ n O I 6 14 " c L J > $ AL AB 3 X _!5 6$ n O I 3 " c - J > $ AL AB 3 X _!5 $ n O I > 4 8 n / O I 0 AB K 4 / O I c AB 3 / O I 8 U< / O I 3 ( L AL AB 3 A^ + 2 AB L = C - 6B + 1 v t . + g t 2 . = h 8 0 2 v 2 + 2gh − v o m ( - 2 7 /< ) = t 0 0 = 8 g n / O I 14 4 0 3 ( L a > 4 0 - ( 6 > 2 AL AB 3 6 I A^ .X _!0 A^ X _!5 a A^ ^ A2 7 /< ) = $ g0T! 5 6$ [0S! 5 $ [0g!8 R AB , = G f # c - J > EEj "Ep 12 V f # $8 oq 1N 7 AB > , r 14 G Ep c - J > AL AB 3 A^8 $ fQ AB 3 A^ - = 6; 6 4 AB a- K `
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 6$ FO / = @ AB L 1N a- c + ` $ U< / P 7 AB > AB > 1L 6; 6 4 ` oI L 1 P > M ( $ F + AB G E < a- 12 2H t = l g 6; + AB % G Ej < s0 ( 7 E f 1 + 2 h gt H h h = v t . − g t . → v = + = 2gH 0 s 2 0 t 2 2H 6$ n = @ AB + L / a- , O c ) C + ! A2 !j AB , "f # $ . "! # !j$8 Ej x = (H + h) 1 2 1
− gt − v .t − g.t 2 = + − 0 (H h) v .t 2 2 0 H + h =
( 2H − 2gH .t ) 2H $ hD ( P > ) A0 0 ! J 6 < t v2 − v 2 = 2 a . s . AL AB 3 K M 6; A ^0 . 0 ! ! 0 < / P 0 7 !M = K AB 0 AB % 14 < M 12 v2 ( H + h 2 ) h = = 8 max 2g 4H F = M ( AB G u0Y r 8 FO $ v C + 2 AB , ^0 V I A2 ^0 V 3 + 8 6$ F + I < AB < I A2 3 8 hD ( P > A ) C + AB , ! + / G 1N 6e I , = 1 2 s = gt !b 7 P > ) c A + AB , 2 + 7 / G A' O = 12 2h t = 8 - ( P > 2 !b = 1+ g , V Q 62 B- 2 $ v C + 2 AB , ^0 ! I 1 2 1 s = g t . = 9 8 , 0 . 12 , = 0 0 , 49m 8 1 2 2 Ft + AB 2h 2.19 6 , t = = = 2(s)8 g 9 8 , v C + AB , ^0 ! 3 q 0 , O c ) C + , %.^0 0u ! I 1 s = h − g − , = , − . , . − , = , 8 2 (t 0 )2 1 1 19 6 9 8 (2 0 ) 1 2 1 ( 9 m) 2 2
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 6$ F M 4 s 2 F + AB , I 2.1 t 3 = = = 0 4 , s 5 8 3 g 9 8 , F + AB < 3 2.18 6 , t = t − t = 2 − = 0 0 , s 5 4 6 (I$J< H" 9 8 , FG 6 ]0 Z0 o 4 Ad d + W + = 6 AB 8 HB > c - J > ]R ) V Ad d "f .S$0 AB > c (V ZR0 AB > 6 c (V oR8 fQ AB 2 L R L 4 0 < 6Q ) ! ` ] Z o R f .S v C + A2 3 AB > ! %w0 0 AB > !% ^ ^ ^ ^ %w ! AMB 0 % ! AMB 0 AB > 6 !S %w ! AMB 0 S ! AMC 8 U B 0 + < R AB 12 s 2 4R s 2 s 2 1 2 3 t = = = = t = t = 1 2 3 a g a a 1 2 3 HB 0 6 AB q L R 1N 8 = r AB c - J > G T^ AL AB 3 A^ 6; 6 4 7 L a $ F L τ V ! AL + ,- AB M ( ` 6$ h τ V ! AL + ,- AB M ( ` 9 ^ _!%8 hD ( P > O + < / 62 X v 2 + 2gh − v 2h t 0 0 = A2 P > + M ( t = g g AB !L 0 - = r AB 3 ( L AL AB 3 A^ = C - 2 2h v + 2gh − v 0 0 − = τ → v 2 + g 2 h = gτ − + 0 (v 2gh 0 ) g g
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 Z - A< - , ( 2 g 2 2gh − g gτ ) − 2gτ (v + 2gh + = → = 0 ) τ ( τ ) 2v 2gh 0 v 0 0 2( 2gh − gτ ) $ AB !L 0 - ( AL τ ! 7 10. (
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. 0.40 +10. ) 1 v = = − , / 0 2( 2.10 4 . 0 +10. ) 8 7(m s) 1 HB AB , r J > 14 4 8 R AB J t < ) C + ]Z Y V 8 HB 3 AB / ) ] 6; X _! / ) Z 6; X _!8 F (2 ) C + ]Z8 ( ∆ − − F c ' x 0 3 AB v v v 15 5 5 B A a = = = = ( 2 m / s )8 t ∆ t 6 3 FG 7 7 O ) C + ]Z c P > 1 2 AB = v t + at A 2 F !3 , ]Z Y^ 8 * 9 : ; 0 AB 3 6 J 6 < t 7 P > + a 6 0 6; v v v A B = 0 4 ]Z 7 (2 2 v + v 5 +15 AB = v t A B . = t . = 6 . = 6 ( 0 m) 2 2 R c 1D @ " ; 4 + J $ 0X/ 8 F D + I 0 c 1D (I 0 D + ! c 1D B (I 8 HB 3 1L c 1D @ 7 6; X^/ _ +8 Z < ; ' !3 3 3 4 + 6; 8 FO $ s 3 c 1D 8 6$ F + c 1D < ) C + @ 8 HB 3 6
c 1D 12 v = 50 / 2 = 25km / h 8 F + c 1D < 0X/ 2 12 t = s / v = 15 , / 25 = 0 0 , 6h = 3 6 , B = *(JD 8 v 50km / h max (50 / 3 6 , ) s 3 c 1D m / s a = = = = 0 1 , 29( 2 m / s )8 (t / 2) 18 , B 1 8 , 6 . s 0
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 K +! L ! 8 E! HM! /0 ! N /$ !$ D ! ' A O 2 2 v − v 50km / h 0 ( )2 %+ 6+ G v2 − v 2 = 2 a . s . 2 a = = = 0 1 , 29m / s 8 0 s 2 1 5 , km 1P Q' D 0 E! . 5 ($R <# R c 1D 6e I (I 4 + J ) L a + ) ! > AL I > 8 Z < ; c > ) L a + ) ! < + τ Y V 8 fQ > !b ) L a + ) ! 6 1V ` - ( + ,- [8 sm 1 12 (2 y 0 12 + I ) L a + ) ! 8 - ( - J t 0 7 o (2 > 1 1 2 2 l = at = aτ 1 2 2 o (2 " . $ 1 2 (n − ) 1 l = at n 1 2 − o (2 I 1 2 nl = at 8 n 2 FG 7 ! + > ) L a + ) ! t ∆ = t − t = ( τ n − n − 1 $8 n n n 1 − HL [ 0 7 ∆ [ 0 g!8 R d , r c - ; AL AB 3 A^ X _!8 FO 3 - - < A2 3 <- < d ! 1N r V 8 HB 3 AB c - > ! / r ! A u0g _!8 s7 v α @ AB 3 AB A2 - J > = C x tgα = 8 &c v y Ab 64 8 A^ A α A A α A 8! α 8 !α FG 70 3 - - < A2 3 <- < AB 1N 2 O 12 @ 2 - I < 3
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 g v . 9 8 , 1 . 5 x a = g sinα = = = 8 2 , m / s n ( 2 ) 2 2 2 2 v + v 15 + 9 8 , x y 2 2 2 2 a = g cosα = g − a = 9 8 , − 8 2 , = 5 4 , m / s t n ( 2 ) U + r ) = 67 AL AB 3 A^ ^ _! c - ,- AL a - J ; 7 α T^^8 s = !D ) = 67 , r G a 8 fQ $ 1L 2 ) = 67 7 , 8 6$ FI ) = 67 8 $ F + G 1N r 67 L 1N 67 8 ' , @ 1 , 62 a 0 I 1 : ; 0 7 AB 6 W / 1B- c - J > A2 c - 8 o c - J > 12 J 6 < t AL 3 6; 0 AB 3 6 I 6; A^ A^8! α8 o c - 12 J AL AB 3 / P t 6; A A^8 !α8 $ M A2 + AB \ 1 4 ) < AB 3 6 I c - J > A^ v 2 α 0 y v2 2 .sin y 0 = = = 2, max ( 1 m) 2g 2g v . sinα $ F + 6 AB 0 y 2 v t = 2 0 . = = 1, ( 3 s) g g 6$ oP > I AB r 4 2v sinα v2 .sin 2α L = v t = v 0 0 cosα . = = 10m x 0 g g FG \ - f %X + r d 14 - O 4 AL AB 3 A^ X _! c - ,- AL a - J ; 7 α S^^8 & ' $ F + d 5 6$ n = G V - < y d 5 $ HB 3 d 1N 8 A^ f α z 9 FG \ - A 4 d 14 4 , v 2 α 0 y ( 2 2 v sin .sin 0 ) (15 300 ) h = = = = 2 8 , 7m 2g 2g 2.9 8 ,
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 + d v0 ( 2 H + h) 7 5 , ( 2 25 + 2 7 , 8) t y = + = + = 31 , ( 5 s) g g 9 8 , 9 8 , FI L = v cosα t
. = 15.cos 300.31 , 5 = 4 0 ( 1 m) HB 3 1N v = g 2 + = . , . + , = , / y (H h) 2 9 8 (25 2 78) 23 ( 3 m s) 2 v = v 2 + v 2 = 23 32 , + .cos = , / y x (15 300 ) 26 7(m s) C! +?+ ' %0+ 8 %& HS A3 T N U A V ' /9+ V &< + Q /W3 X ' A ! / 8 U 0' x = v t = v cosα t . x 0 1 1 2 2 y = H + v t − g t .
= H + v .sinα t. − g t. y 0 2 2 Y < 5+ +! +$ +?+ ' = Z3 Y < "< ! < ? [ /, K + 9+ Q $ ! !' < /0 %+ - ! K 3 Y < / L B < \ $ 9 7 - v = v cosα = const x 0 v = v sinα − g t . y 0
!# ]$(JD ^ %# _($(< ^ # *J$2<`D3 FG \ - f S^ 0 + r d 3 AL AB 3 A^ ^ _! c - ,- AL a - J ; 7 α S^^8 F $ F + d L a / G N r ` 6$ n = G V - < y d ` $ E ) * d ` F (q - - - 3 62 . T8 o m z AL z ; V -8 $ AB c 2
x = v t = v cosα .t (1) x 0 1 2 1 y = H − v t −
g.t = H − v .sinα .t − g.t 2 ( 2 ) y 2 0 2 + 0 = - ^ 0 1 30 −10.sin 30 t . − 1 . 0 t2 . = 0 ↔ 30 − 5t − 5t2 = 0 2 o m ( , + d %!8 6$ I { A' O V - 6 4 0 , O 8 x = v cosα t . = 10.cos 300 2 . = 10 m 3 ≈ 17, m 3 0
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 $ 6 < ( ) * A 4 0 I - ) * 2 "- ) @ A2 C / D 6 < + $ n D + - " $ A2 "%$ 6; N G - " $ W A2 "%$ x
(1) → t = v cosα 0 2 1 2 x 1 x
( 2 ) → y = H − v .sinα t . − g t .
= H − v .sinα . − g 0 2 0 v cosα 2 v cosα 0 0 g x 2 .
= H − x t.gα − 2v 2 2 cos α 0 x x 2 = 30 − − ( /9+ 0 ≤ x ≤10 m 3 ) 3 15 2 \ ; 0 ) * A 4 12 - 6 18 fQ - = r AB c - ,- AL a - J ; 7 α 6; 6 4 AL AB 3 6 I L 0 I AB 12 M 8 hD ( P > O I AB , r 4 C 1B- , 62 . S v2 .sin 2α v2 L 0 0 = ≤ g g v 2 HB !b , I M 6; L 0 = / ! %α 0 α TX^8 max g n| 1 } K f2 U 12 %0Y[ r 8 fQ < t > K & 4 c 6 / M " q AB 3 6 I A2 7 4 $0 /| 1 4 !b 12 6 4 ` o 6 < "f2 U $ u0[%[ _!%5 "& 4 c 6 $ u0g ^ _!%8 v2 .sin 2α FG P > I L 0 = B 0 AL 1M } / P t " A^ g / P t $ A2 7 r / P t " r / 7 r 6; TX^$ I 9 !b \ 1 ' AL 3 m + 8 E 7 7 ' , /\ 1 } 2 - 3 & c r 6 g 9 7 , 27 L HN = L = 1 . 2 6 , 7 = 12 5 , XP HN ( 6 m) g 9 8 , 10 XP F AB 3 7 $ F ) ) 7 "F ) Ad ) 7 %T +$8 6$ / + A2 / - N W W5
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 $ Ra F ~ ) ) F "Ra F ~ ) ) F Ad %[ 2 4 $5 ($ A V F ) 4 ) * d AL / 6; gg - N 8 hD ( P > O AB 3 7 2π ω = A2 1 : /• - = t N 3 T AL 12 V "!$ !b , π $ HB 3 7 M ) ) 2. ω = = 7 2
, 6.10−5 (rad / s) 24.3600 6$ o /• ) / - N 12 8 n + ) < Ad 12 % < 4 AB 3 7 / + A2 /
- N 12 T0X 8 ^.X (_!5 0[T 8 ^.S (_! $ ol - ( P > 4 AL /• / 7 AB 3 7 a ~ ) 12 %0[ 8 ^.Y (_! 5 ($ o A 7 / ) 12 gg- N 12 0 u 8 ^.S (_! AB 3 (2 ) 4 a f2 U 8 Z < ; Ax f2 U 12 α % ^8 F c 62 . g AB 3 7 M ) 7 12 ω [0%Y8 ^.X (_!8 Z /O ) * f2 U " c $ 12 ω w z α f 62 . u r = R cosα 8 FG 7 7 AB 3 (2 f2 U 12 A ω8 ω8w8 !α F !3 A2 , A TS^ _!8 Y 0< %0+ + 8 " B a 7 - ! ' A !' ! b < H" G c +L /9+ 7 - ! ' A O %+ 6+ G /9+ DM - !' ϕ !' . 5 D$ / L ω !' / L H0+ /$ +! L β !' +! L 5 ! B d e ! & DL %& % K f 3
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 R AP 1~ ! / 6e I ) , - N , AB 3 [^^ Ad _- N 8 FO 3 7 AP 1~ A2 !3 Ad 2 AP 1~ C ) , - N < AP 1~ 12 (I 8 HB 3 7 AP 1~ ω [^^Ad _- N [^^8%π_Y^ " (_!$ ! + τ - N Y^!8 ω π π R2 1400 / 60 1400 ω β8 τ β = = = = 1 2 , 2( 2 rad / s )8 τ 60 3600 s7 ) , ! + τ - N 12 1 2 1 ϕ = β τ . = .1 2 , 2 6 . 02 = 700π (rad) 2 2 E AB 0 !3 Ad ) , - N 12 ϕ 70 π 0 = = = ]RZ /f 8 *π π 2 R 6 c ) B (I 0 ! - N AB 3 7 = G S^^ Ad _- N 3 g^ Ad _- N 8 F 3 6 c A2 !3 Ad 2 6 c C ) , - N 8 F c ' x A 3 7 7 1 P 3 7 2 ω − ω 180 2
. π / 60 − 300.2π / 60 0 β = = = −0 2 , 1 ( 2 rad / s )8 τ 60 s7 ) , (M A2 3 ) M AL ) A. .! J 6 < t N 2 2 ω − ω . π / − . π / 0 (180 2 60)2 (300 2 60)2 ϕ = = = 240 1/f # 8 2β − 2.0 2 , 1 f a (M A2 P > AB 3 7 6 ω + ω 180 + 300 0 ϕ = .τ = .1 = 240 1/f # 2 2 R 6 c 7 6 /O w ^ 1N I > 4 0 ! 7 ) ) 7 AL 3 7 6; S0 T (_!%8 fQ 0 ! V > $ HB 3 7 A2 AB 3 (2 4 A2 6 ` 6$ s 3 - - < 0 3 <- < A2 3 2 - I 4 A2 6 ` $ s7 @ 3 2 - I A2 6 /O 6 c "> AL q 4 A2 6 ` $ h V > 0 AB 3 7 A2 AB 3 (2 4 A2 6 12 ω = β t. = 31 , 4.1 = 31 , 4 (rad / s) v = ω R . = 31 , 4 0 . 1 , = 0 3 , 14 (m / s) s 3 <- < 7 ' / P t A2 3 - - < α 1N 2 f
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 a = β R . = 31 , 4.0 1 , = 0 3 , 14 ( 2 m / s t ) 2 2 a = ω R . = 31 , 4 .0 1 , = 0 9 , 86 m / s n ( 2 ) od 3 2 - I 6; 2 2 a = a + a = 1 0 , 3 m / s 8 t n ( 2 ) $ s7 @ 3 2 - I A2 6 /O 12 α = C a 0 3 , 14 t sinα = = α [^TYj8 a 1 0 , 3 o / ) 6 c 6 /O X^ 12 ^0 V 8 F $ HB 3 (2 A2 AB 3 7 A2 6 5 6$ s 3 - - < @ 6 /O 8 HB 3 (2 A2 AB 3 7 4 A2 6 +G H0+ ! 4 5 f 2 R π 2π 0 . 5 , v = = = = 31 4 , (m / s) 5+ +! ' 4A f T 0 1 , v 31 4 , ω = = = 62 8 , (rad / s) R 0 5 , 6$ s 3 - - < { 3 L V @ 6 /O 2 2 2 a = ω r = ω R . / 2 = 62 8 , .0 5
, / 2 = 986 m / s 8 n ( 2 ) R 2 2 6e I A2 + d 0 6 /O / 0 (2 Y^^ 0 AL AB 3 XT / _ +8 2 2 < ) C + 7 S^ V 8 F AB 3 (2 0 3 - - < 0 3 <- < 0 3 2 - I A2 3 7 2 2 K 3 ) C + 78 o 2 2 12 (I 8 o w / ^^^ 0 A^ XT/ _ X _!0 ! Y^^ 0 S^!8 hD ( P > A J A2 d 6 < t !b O , 1 , I < 8 1 2 s − v t 2 600 −15 3 . 0 1 2 ( 0 ) ( ) s = v t + a t a = = = m / s 8 0 t t ( 2 ) 2 2 2 t 30 3 HB 3 I 3 + Ad 1
v = v + a t = 15 + .30 = 25 / = / 8 0 t (m s) 90 (km h) 3 s 3 - - < { 3 L V I 2 2 v 25 2 a = ω R = = = 0 6 , 25 m / s n ( 2 ) R 1000 od 3 2 - I 12 2 2 2 2 1 5 a = a + a = + = 0 7 , 08 m / s t n ( 2 ) 3 8 s 3 7 2 I
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 a 1 / 3 t −4 β = = ≈ 3 3 , 1 . 0 ( 2 rad / s ) R 1000 HB 3 41c 4 D P 6; A %0%8 ^g _!8 FO AB 3 7 A2 3 - - < 41c < c ) * 7 12 Ad d 6 /O ^0X8 ^.g 8 €1c A %0%8 ^g _! %0%8 ^Y _!5 w ^0X8 ^.g ^0X8 ^. ^ 8 HB 3 7 A2 3 L V { 3 - - < 1I 1 , ω A_w T0T 8 ^ Y (_!5 ω%w u0Yg 8 ^%% _!% R + 3 • ) !P 7 (d L = 8 U< + • c L G A' O ] ! A' O Z "]Z ⊥ AL (d !P 0 .T$ ! + ^ - N !b L A' O o Z / = ! %^ 8 U< + • A - O , (d ! + % %0X - N !b L N A' O Z8 o AB 3 3 AL (d L 12 / P t 8 FO $ Z 1 !P 5 6$ HB 3 A 3 AL (d L 5 Z o $ HB 3 (d L 3 AL 6+ !P 5 ! ($ s7 γ8 R A H γ FG ] < o < + ] ^ - N 0 ] < Z < + f .T % %0X - N 0 Zo 7 (2 ! Zo %^ 8 V 12 62 t ,- AB 3 8 F W Z o → + q AL (d L AL AB 3 u A2 1 → ! AL (d L "( + • $ AL AB 3 v 8 H A γ o t ,- O 12 3 AL → → → 6+ !P AL AB 3 ] V = v+ u 8 F + ,- > 62 > AL .T 0 + f .T6 ,- > > AL .T68 F c Ab0 7 - ! ! 8 5 1 A8 5 1 "A8 ! γ$8 %5 A8! γ 5 s 120 u = = = 0 2 , (m / s)8 t 600 1 t 10 4
l = v.t = v.cos γ .t → cos 1 γ = = = → γ = 3605 ' 3 1 2 t 12,5 5 2 3 u u 0 2 , 1 sinγ = = → v = = = = 0 3 , 3 (m / s)8 5 v sinγ 3 / 5 3 o (d !P l = v t . = 0 3
, 3.(10.60 ) = 200 m 8 1
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 U + • ) !P c L A P 7 AL 6+ !P AL AB 3 [0%/ _ 8 U L = C A - O P (d / = X^ 8 F $ HB 3 (d L 3 AL 6+ !P 5 6$ F + I ) , !P 8 o 6 < !P 6; ^0X/ 8 Z (d !P 1 ^0X/ X^^ 8 ! X^ 0 H [0%/ _ % _!8 FG Ab Z o u s s 150 ! = → u = v . = .2 = 0 6 , 0 (m / s) 8 v l l 500 A 1 F + < ! !P H AC AB l 500 t = = = = = 250 (s)8 ] V v v 2 - !3 $ ^0Y^ _! 5 6$ %X^!8 f 62 .%[ R 6 6 G A' O ] L A' O Z8 ]Z ; c L FV P A2 / = S^^/ 8 & ' + 6 < $ n P 7 75 6$ o7 7 t c L U Ze 5 $ o7 7 t c L FV P 8 o 6 < AB 3 7 6; A %^ _!0 AB 3 6 3 AL / P / O A% Y^^/ _ 8
]Z S^^/ 0 7 A %^ _! [%/ _ 0 A% Y^^/ _ 8 $ F + 6 6 M <- G ] < Z l 300 t = = = 0 5 , (h) = 30 1 B # 8 v 600 2 6$ F M 62 .%Y0 6 3 L A' O Z0 7 - = 6 < A - O 7 α ! AL - ]Z8 F 7 V = v 2 − v 2 = 6002 − 722 = 596 / 8 2 1 (km h) ] Z F + 6 6 G ] < Z 12 α A s 300 t = = = 0 5 , 03 (h) = 30 2 , B 8 A% V 596 $ s 7 P G FV ! P 8 F + 6 f 62 .%g I (q 12 s 300 t = = = 0 4 , 46 (h) = 26 8 , B 8 v + v 600 + 72 2 1 f .X P = 6 8 $ o 6 < O 78 6$ x @ W ' A2 8 $ h ! AB 3 6 8
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 A % S z f .X A % S z f .Xj $ U A2 W ' = 6 2 12 (I 8 6$ s W ' AL + 6 < + - 8 $ Z 0 12 A q L 8 HB 3 y AB G 1N B / 8 W ' AB 3 2 (3 3 AB 2 1L " 3 6 < !3 7 + J $8 FG W '0 7 ! ! 3 AB S ‚ ‚ %8 f .Y W ' AB 3 8 fC 6 < 4 y z]0 ]Z0 Zo0 oE8 A ] Z o E z f .Y z] AB - + ^ W (I AL 3 / 1L 8 W ' ]Z 6 < AB ! 8 W ' Zo 6 AB B (I 8 W ' oE AB <- B (I AL 3 1L / Zo8 HB (G 1 3 2 8
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 %. 8 R c 7 / 3 1 , %^^^^/ 0 B (I ( L ( 1M 6; Y^^^U0 AB 3 6 I c 6; X _!8 fQ $ s 3 c5 6$ h 6 1V c (G 1 5 $ + c C , / G 1N C < / c (G J 8 $ s 3 c , O c ' 1 B ii Ucƒ „_ .Y^^^_%^^^^ . ^0S _!%8 6$ F + / G 1N C < / (G 1 ∆/ Z ) (R = ∆t = = = RZ (D)3 ! ) Z$] $ v C + / G 1N C < / (G 1 ! A^8 # 8 %_% 8 8 8 S[X 8 %.%8 R y a TuU 6' /…- @ a - J J f %.T > " %.T$8 9M r- J 7 4 y a 12 T[U8 fQ 1M Q I V a y` f !3 ! @ y A2 a r- / ^0%8 9M V ^[0gU 5 1M u0gU „U „f „ „ ! !% f %.T f %.T6 n 3 y 3 I 1M „f L 3 ( L 0 1M ! 4 a y L 14 4 "f %.T $0 d / 3 V y 14 4 1M ! 1 L 3 ( L "f %.T6$8 FG Ab 2 0 1M (q "„f $ A2 V „U y - = 7 ' Q „f F + F − P = 2 × k N . − P = 2 0 . 2 , 1 . 47 − 49 = 9, m 1 s ms2 ( 8 N) „U F + F + P = 2 × k N . + P = 2.0 2 , 1 . 47 + 49 = 107, m 1 s ms2 ( 8 N) %.S8 fQ - = ( 1M 6; 6 4 14 2 > 4 7 (I A2 ! + S^ V 7 , 8 o 6 < 1M ! 2 6; X† m 1 , 2 8 sm „ 12 1M ( 14 2 8 &r c - 0 1M V 3 2 0 c ' 1 B U %0 6; „ . ‡ ! F 7 12 / 3 1 , A2 s 2 a = 12 3 I 8 2 t
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 FG 7 ! 2 s . m . F = f + ma = 5%mg + 8 ms 2 t F !3 ! 0 S^!0 X0Y XY^^/ , „ ≈ g%^^U8 1C " G %0+ + L+ ! ! " %& < = (R$J \ #3 %.T8 R + ( < c AL AB 3 / P t 8 9N I + /r c A - O L 0 ! 7 + } c A - O ! 8 F = + ,-0 2 c ,- AL a - J ; 7 α8 fQ + ,- 2 + - = a 14 c 1M 1L ` Z < ; m 1 , c 12 0 !3 ! @ 6 c A2 a + 12 /8 H < - ' 1 B ii Ucƒ 1M ( A2 c8 F 2 - I 1M t ,- < c - J > A2 ; 6; ^ . / P 7 c - J > 0 c - ./ P 7 3 c - 4 F + ,- /r c A - O L " %. j $ 1M r A P 7 c 14 a + 12 N + F.sin − P = 0 N = P - F.sin H2 F.cosα − F = 0 F.cosα = F ms ms R20 1M ! ( 14 c „ ! /U /" . „! α$ kP
Fcosα = k(P − F sinα )
F = cosα + k sinα U Uj „ α „j „ ! „j ! f %. j f %. j6 F + ,- } c A - O ! " %. j6$ Z; - V O M0 O , 1M ! a 14 c + ,- 2 12 „ ! /Uj /" # „! α$ H2 1M „j I a 14 2 c kP '
F = cosα − k sinα wk 2 „j ‚ „8 U AB + ,- } c A - O ! + - = (q 1M 1L 8 %.X8 R AB 7 / 3 1 , X/ , a 4 a - J 4 ,- AL a - J ; 7 α S^^8 f !3 ! @ AB A2 a - J 4 6; / ^0%8 F 3 AB 4 a - J 4 8
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 F - V O 1M ( A2 AB W S 1M J U > 0 U A P 7 AL a 4 A2 „ ! ; 4 a „ 4 8 ! z ' 1 B ii Ucƒ AB P + N + F α ms = m a . o < - 2 c - A P 7 AL a - J 4 "- z $ A2 - ! ! AL a - J f 62 %.X 4 "- z $ , N = P cosα − P cosα + N = 0 P sinα − F P sinα − F = ma a = ms ms m R2 „ ! /8U 4
P sinα − kP cosα
mg sinα − kmg cosα a = =
= g(sinα − k cosα )8 m m F α S^^0 / ^0%0 u0g O , S0%T _!%8 [ 7 - e ! \'$ +! L ! / e O +e 7 U A /0 L+ ! / 3 %.Y8 R AB , 3 4 a - J 4 ,- AL a - J ; 7 α TX^8 n , , ) C + ! SY0T 0 AB , AB 3 A % _!8 & ' !3 ! @ AB A2 a - J 4 8 - ( P > 3 AB 62 %.X 7 g sinα − a a
a = g(sinα − k cosα ) k = = tgα − 8 g cosα g cosα hD ( / < > i A 3 ) A. .! 7 3 AB , 2 v2 − v 2 2 2 2 − 12 v 0 v a 0 = = = 8 2 S . 2 S . 2 S . v2
k = tgα − 2.gScosα F P !3 C α TX^0 A % _!0 ! SY0T ^0SYT , / ≈ ^0%8 %.[8 R !, (V G , a 4 a 62 ! - I 7 6 P k 3 8 h, (V 6e I , 4 a 62 / (2 - I 6 P k 6; %X† (2 (V 8 & ' !3 ! / @ !, (V A2 a 62 8 ‡ ! f 62 %.[
Downloaded by mai hoa lý (lymaihoa28@gmail.com) lOMoARcPSD|22014077 sm 12 m 1 , = (V 0 12 m 1 , - I 6 P k 8 F c I 62 0 (2 - I 6 P k 6; %X† (2 (V %X† 8 &r c - !, (V 0 (V ' ( 1M A2 ‡ !8 R 3 (V 6e I , - = 7 ‡ ! ‡ ! %X† 8 R20 ‡ ! / 8U /8"[X† $8 FG 7 %X† /8"[X† $ 25 1 k = = ≈ 0 3 , 3 8 75 3 %.g8 $ R P P / 3 1 , 4 + 6; 0 !3 ! @ 6 P P A2 a + 12 ^0 8 FO 1M /r P P + ,- $ ˆ P 5 6$ ˆ P (I AL 3 6; % _!%5 %$ ol V Q 4 + ,- P P A2 $ 94 (3 7 (3 T†5 6$ & 3 (3 78 f !3 ! 6; ^0 ! 3 + 8 → Ft ,- 1M ( 14 P P W 1M /r F P P0 m 1M P 0 - = 1M - - < N a + A2 1M ! a + f 8 ms U Uj „j „ ‡p ! ‡ α ! f 62 %.g → → → → → ' 1 B ii Ucƒ P P 12 F + P + N + f = m a ms o m ( 12 c8 o < - 2 14 - , $ n c 4 + ; F − f = ma F = ma + f = ma + kmg ms ms F !3 ^^^/ 5 / ^0 5 u0g _!%5 A2 $ n 0 ^ „ ug^U8 6$ n (I AL 3 % _!% „ %ug^U8 %$ n c 4 + (3 $ ˆ P 14 (3 F − f − P sinα = ma F = ma + f
+ P sinα = ma + kmg cosα + mg sinα ms ms F 70 ! α ^0^T 12 (3 (3 !α 1 − 0 0 , 42 ≈ 1 0 , F = 1000 × 0 + 0 1 , .1000.9 8 , .1 + 1000.9 8 , .0 0 , 4 = 1372(N) 6$ ˆ P 3 (3 „ "/ !α . ! α$8 F − f + P sinα = ma F = ma + f
− P sinα = ma + kmg cosα − mg sinα ms ms F !3 F = 1000 × 0 + 0,1.1000. , 9 8.1−1000.9,8. , 0 04 = 58 ( 8 N)
Downloaded by mai hoa lý (lymaihoa28@gmail.com)

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