bai tap nang cao ly 10

Phan hai mJCR^G M^A!^ GlAl VA DAP s6

DONG HOC CHnt DI€M

1.1. Sit dung edng thfic tfto v t o td'e trung binh :
y

^ ^2 - ^1 ^ Ax
*

t2 - tj

At

a) Ax = 2,3 m ; At = 1,0 s ; v = 2,3 m/s.
b) Ax = 57,5 - 9,2 = 48,3 m ; At = 3 s ; v = 16,1 m/s.
e) A X = 57,5 m ; At = 5,0 s ; Vji, = 11,5 m/s.
1.2. Chgn true Ox trung vdi dutog chay va cd gd'c la dilm xudt phat cua ngudi
Vi chuyin ddng theo mdt chilu ndn dd ddi trung vdd qutog dutog chay
cua ngudd dd.
a) Qutog dutog chay trong 4 min ddu la :
51 = 5.(4.60) = 1200 m
Qutog dutog chay trong 3 min sau la :
52 = 4.(3.60) = 720 m
Qutog dutog ngudd dd chay duge la :
S = Sl + S2

= 1200 + 720
= 1920 m =1,920 km
b) Vi chuyin ddng chi theo mdt chilu ndn trong ca thcd gian chay vdn tic
trung bito btog tdc dd trung bito va bdng :

s
1920 , ^^ ,
^'^'=1=7:60=^'^^'"/^
Chd y : Khdng ldy trung binh hai vto tdc vi thod gian chay khac toau.
90


1.3. Chgn true Ox trtog vdd ehilu dgc cua bl boi, gd'c O la dilm xudt phat.
a) Ax = 50 m ; At = 40 s ; Vji, = — = 1,25 m/s ;
As = 50 m ; tde dd trung bito = -;— = -TTT = 1,25 m/s.
At 40
b) Ax = - 50 m ; At = 42 s ; Vtb =

= - 1,19 m/s ;

As = 50 m ; tdc dd trung bito = -r— = -rr- =1,19 m/s.
^
At 42
c) Ax = 0, Vtb = 0 ; As = 50 + 50 = 100 m ;
100
At = 40 + 42 = 82 s ; td'e dd trung bito = —— « 1,22 m/s.
82

1.4.

1,5

2,0

2,5

3,0

3,5

4,0 t(h)

Hinh 1.1 G

Theo dd thi, hai xe dudi kip toau sau 3 h 30 min, tai vi tri each Ha Ndi 210 km.
Chii y :
Cd thi giai bang tfto todn tou sau : Xe thfi hai dtog lai d vi tri.each
Ha Ndi la 70.1,5 = 105 km. Khi xe nay bat ddu chang tilp theo thi xe thfi
todt d vi tri each Ha Ndi 60.2 =120 km. Phuong trinh chuyin ddng cua
hai xe kl tfi lue dd la :
91


Xl = 120 + 60t
X2 = 105 + 70t
Xe thfi hai dudi kip xe thfi nhdt khi Xi = X2. Tfi hai phuong tnnh trdn ta tim
dugc t = 1 h 30 min va x = Xi = X2 = 210 km.
Vdy thod dilm dudi kip toau kl tfi lfic xudt phat tai Ha Ndi la
2 h + 1 h 30 min = 3 h 30 min, vi tri lfic dudi kip toau each Ha Ndi la 210 km.
1.5. a) Phuang trito chuyin ddng cua ngudd di bd va cua ngfidi di xe dap Ito lugt la:
Xl = 20 + 5t
(1)
(2)
b) Tfi dd thi ta thdy hai ngudd gap toau sau t = 4 h va tai vi tri x = 40 km.
e) Giai hai phuong trinh (1) va (2), ta dugc kd't qua t = 4 h va x = 40 km,'

dung tou cau b.
1.6. a) Cach giai tuong ttt bai tap 1.4. Dd thi cho trdn Hito 1.2G, dilm gd'c 0
tuong tog vdd luc 6 h.
b) Nhin trdn dd thi ta thdy d td va tau gap nhau khi t = 2 h 50 min ; x = 120 km;
tfic la chung gap nhau luc 8 h 50 min, cdch Thato phd Hd Chf Minh 120 km,
c) Xl = 30 + 45t
X9 = lOt

X2 = 60t
trong dd t la thdi gian kl tfi lue d td bat ddu chay.
X (km)

92


1.7. a) Chgn true Ox cd gdc tai Ha Ndi, chilu hutog vl phfa Hai Phdng.
Phuong trmh chuyin ddng cua hai xe la :
Xe di tfi Hai Phdng :

Xi = 105 - 60t

(1)

Xe di tfi Ha Ndi:

X2 = 75t

(2)

b) Hai xe gap nhau khi Xi = X2.

Giai (1) va (2), ta tim dugc t = 0,777 h « 46,2 min ; x = 58,33 km.
e) Hgc sito tu ve dd thi.
1«
1.0.

^ ^ m/s, 2 (chuyen
, . . dgng
,, cham
u^ dan).
^-- ^
a. =- ^^2 -—^i)
i - = (20 - 25) = - 2,5

1.9. a) Tuong tu bai tap trdn, ta tfnh dugc : a^j^ =

= 4 m/s^ (chuyin

/

ddng nhanh ddn).

b) Khdng. Gia tdc tinh dugc la gia tdc trung binh. Nd'u gia tdc dd la khdng
ddi thi chuyin ddng la biln ddi diu. Khi dd trung binh cua hai vto td'e nay
dtung bang vto td'e trung bito trong khoang thdi gian dd. Tuy nhidn, ta
khdng ed co sd dl ndi chuyin ddng cua chdt dilm la biln ddi diu.
1.10. a) Chgn true Ox trung vdd dutog di cua dlectron. Dung cdng thfic lidn hd
gifla vdn td'e, dd ddd va gia tdc trong chuyin ddng thing biln ddi diu :
V-

VQ

= 2a(x - Xg) = 2as

Thay sd, ta cd :
(5.10V - (3.10V = 2a.(2.10~^)
Tfi dd suy ra gia td'e a » 6*25.10 m/s
b) Cd thi dfing cdng thfic v = Vg + at dl tfto thod gian t. Ta ed :
^ v - v g ^ 5.10^-3.10^
~ a " 6,25.10^^
t«8.10~%
Chii y : Ta todn thd'y, tuy gia tde rdt Ito toung hat chi todn gia tdc nay
trong mdt thod gian rdt tod (ed phdn ti giay). Gid tri nay la gia tri diln hito
cfia gia tdc cac hat tfch didn trong cdc may gia td'e hidti nay.
1.11. a) Chgn true toa dd trung vdd dutog di, gdc toa do trung vdi vi tri cua
ato cato sat giao thdng, gd'c thod gian la luc ato xudt phdt. Khi dd d td da
93


d vi trf each ato cato sat 30 m. Phuong trinh chuyin ddng cua d td va eua
ato cato sat ldn lugt la :
Xl = 30 + 30t

(1)

3t^
x,= ^

(2)

Khi ato cato sat dudi kip thi Xi = X2. Ta cd :

30 + 301 = — , hay la
2
l,5t^-30t-30 = 0

(3)

Giai phuong trinh nay, ta dugc ti = 20,95 s vd t2 = - 0,95 s. Vdy, sau 21 s
anh cato sat dudi kip d td.
b) Thay t = 21 s vao cdng thfic (1) hoac (2), ta tim dugc qutog dudng;
di dugc.
Kit qua la : s = 661 m.
Chii. y : Cd thi giai bang ve dd thi.
'^'y2

1 c2

1.12. a) Tuong tu bai tdp 1.10, ta ed : a =

= 3,6 m/s .
2.70

1 2 , bidt s, a, Vg, ta tfnh duge t.
b) Dung edng thfie x - Xg = s = "Vgt +—at
Kit qua la : t = 3,3 s.
1.13. a) Phuang trinh chuyin ddng cua hai xe la
Xe thfi todt: Xl = 40 + Vit = 40 + 40t
Xe thfi h a i : X2 = V2t

Lue dudi kip toau thi x"i = X2 = 200 km.
Cdng thfic (1) cho t = 4 h.

Cdng thfie (2) eho 200 = V2.4.
Tfi dd V2 = 50 km/h.
94

-

(1)
(2)


b) Dd thi (xem Hinh 1.3G)
X (km)

250-200--

100--

6t(h)

1.14. Dung edng thfic v = Vg + at.
2

a) Ta cd a = 3 m/s ; t = 2,5 s ; Vg = 5,2 m/s. Thay vao cdng thfic trdn,
ta dugc :
V = 12,7 m/s
b) Thay a = - 3 m/s ; t = 2,5 s ; Vg = 5,2 m/s vao edng thfie tren, ta dugc :
V = -2,3 m/s
1.15. Phuang trinh chuyin ddng cua chdt dilm la :
X = -6t + 4t^
a) Thay t = 2 s vao cdng thfic trdn, ta dugc :

X = - 6.2 + 4.2^ = 4 cm
b) Vdn tdc V = - 6 + 8t. Thay t = 3 s vao cdng thfie nay, ta dugc :
v= 18 cm/s
1.16. a) V = 3.10^ + 8.10^^t = 5,4.10^
10.

Tfi dd suy rat = 3.10 '"s.
b) Cd thi dung mdt trong hai cdng thfie sau
1 2
X = vot + 2 ^*

(1)
95


VJ

x

=

^

(2)

2a
Thay sd vao cac cdng thfie trdn :
(1) cho
X = 3.10^t + 4.10^V ; vdi t = 3.10"^° s.
(2) cho

X=

L_[(5,4.105)2 - (3.10^)2].
2.8.10^^

Kit qua la :

x = 1,26.10"'* m. Quang dutog tuy nhd nhung rd't Ito so

vdd kfch thudc nguydn tu (10

m).
^

2

1.17. a) Thdi gian nhd nhdt khi gia tdc can Ito nhdt, bang - 5 m/s . Ta ed :
^ ^ v - v g ^ 0-100^^^^
a
-5
b) Quang dutog chay tren dutog bang cung la nhd nha't. Ta cd :
s = 100.20 + - .(-5).20^ = 1000 m = 1 km
2
Nhu vay khdng thi ha eanh vdd dutog bang dai 0,8 km dugc.
1.18*. a) Chgn true Ox cd phuong thing dtog, hutog ldn trdn. Gd'c toadg d mat
ddt. Phuang trinh chuyen ddng cua qua bdng la :
X = Vgt - 4,9t^

Luc t = 1,5 s thi X = 4 m. Thay cae gid tri dd vao edng thfic trdn, ta cd :

4 = vo.l,5-4,9.1,5^
Tfi dd suy ra :
Vg = 10,0 m/s.
b) Ta ed V = Vg + (-9,8).t = 10,0 - 9,8.1,5 = -4,7 m/s.
Dd la vto tdc eua qua bdng khi ban nay bat duge. Ddu trfi cd nghia la qua
bdng dang roi xud'ng.
1.19. a) Ta cd V = Vg - gt = Vg - 9,8t.
Thod dilm ti lue vdn tdc qua bdng bang 2,5 m/s la :
v-4
2,5-4
'^ = ^ 9 j = ^ 9 : 8 - = ^'^^^ ^

Thod dilm t2 luc van tdc dat gia tri -2,5 m/s (khi di xudng) btog :

96


Khotog thdd gian gifla hai thod dilm dd la :
t = t2 - tl = 0,663 - 0,153 = 0,510 s
b) Dd cao lfic dd btog toa dd cfia qua bdng :
v^ - Vn 2 5^ - 4^
x-x„ = x = ^ ^ = ^ - ^ =

0,497m

1.20*. Chgn true Ox ed phuong thing dtog hutog xudng dudd, gdc O tai vi tri
tha vdt. Ggi n la sd giay vat rod xudng din ddt.
Toa dd cua vat sau n gidy la :
1

2

1

2

Toa dd eua vdt sau ( n - l ) giay la :

^n-l = 2^1-1

=\s(n-if

Trong gidy cudi cung (tfic la tfi luc (n - 1) giay dd'n luc n giay), vat rod duge
34,3 m, ta cd :
/„ = 34,3 = x„ - x„_i
hay la:
/„= 34,3 = |.9,8[n2 - (n - 1)^] = 4,9.(2n - 1)
Tfi dd tacd:

34 3
2n-1 = ^
= 7,

hayn = 4.

vay thdi gian rod la 4 s.
1.21. Chgn true toa dd Ox cd gd'c tai vi tri tha hdn da va chilu hutog xudng
dudd. Phuong trito chuyin ddng cua hdn da va cua hdn bi thep Ito lugt la :
xi = ^gt^ = 4,9t2

(1)

X2 = V o t + | g t ^ = 1 5 t + 4,9t^ '

(2)

Khi hdn da rod din ddt, Xi = 8 m, thdd gian rod la ti btog :
.• = j i = 1,277 s

7-BTVL 10(NC)->^

97


Khi hdn bi thep rod xud'ng din ddt, X2 = 8 m, thdi gian red t2 dugc tfnh theo
edng thfic (2), tfic la :
8 = 15t2 + 4,9t^, hay la
4,9t^ + 15t2 - 8 = 0

(3)

Giai (3), ta dfige hai gid tri eua t2, ta chi ldy gia tri dfiong cua t2 btog :
t2 = 0,463 s
Hai vdt rod cdch toau khotog thdi gian la :
At = tl - t2 = 1,277 - 0,463 = 0,814 s
1.22*. Ggi h la dd sdu cua hang, ti la thdd gian hdn da red dto day, t2 la thdd gian
tid'ng vgng tfi ddy hang ldn dd'n midng hang. Ta cd :

Tfidd

h = Va^.t2 = 340t2

(1)

h = - g t f = - . 1 0 t f =5tf
2 ^
2

(2)

5t

to=—I
••2
^

340

Thdd gian tfi luc tha hdn dd din lfic nghe thdy tidng vgng bang :,
t = t i + t 2 = 13,66 s
Thay t2 vao bilu thfic vfia toto duge, ta cd :
5t2
^ 340
hay la
5tJ + 340 tl - 13,66.340 = 0

(3)

Giai phuong trito (3), ta duge hai gia tri cua tj, trong dd cd mdt gia tri am.
Ta chi ldy gid tri duong ti = 11,66 s.

Nhu vay thdd gian tieng vgng di tii ddy hang din midng hang la :
t2 = t - tl = 13,66 - 11,66 = 2 s
98

l^BTVL 10(NC)*


Dd sdu cua hang la :
h = 340.t2 = 340.2 = 680 m
1.23*. Chgn true toa dd cd phuong thing dtog, gdc O trfing vdd vi tri eua hdn bi
lfic t = 0.
.
a) Sau 1 s, hdn bi rod dugc mdt ddan Si = /i = :j.l0.1^ = 5 m.
Sau 2 s, hdn bi rod duge mdt doan dutog la :
/ 2 = | . 10.(2)^ =4.5 = 20 m
Nhu vay trong giay thfi hai, hdn bi rod thdm dfige mdt doan la :
S2 = / 2 - / i = 2 0 - 5 = 15m
Ta vilt lai tou sau :
52 = / 2 - / i = 5(2^-1^) = 15 m
Dd chinh la dd ddd eua hdn bi trong giay thfi 2.
Sau 3 giay, hdn bi rod duge mdt doan dutog la :
/3=|.10.(3)2=5.(3)V
Nhu vay trong giay thfi 3, hdn bi da red dugc thdm mdt doan dutog la :
53 = /3-/2 = 5[3^-2^] = 25m
S3 Cfing la dd ddd cua hdn bi trong giay thfi 3.
Ta tito duge dd ddd cua hdn bi trong giay thfi n :
Sn = ^„ - ^n-1 = 5[n2 - (n - if] = 5(2n - 1 ) m
b) Ta cd:
52 - S l = 5[(2.2 - 1 ) - ( 2 . 1 - 1 ) ] = 2.5 = 10 m
53 - S2 = 5[(2.3 - 1) - (2.2 - 1)] = 2.5 = 10 m

Sn - s„_i = 5 { ( 2 n - l ) - [2(n - 1 ) - 1 ] } = 2.5 = 10 m
v a y hidu cac dd ddd sau 1 s lidn tilp b t o g 10 m, b t o g hai ldn dd ddd sau
gidy thfi todt.
Ghi chii : Cd t h i dp dung cdng thfic d bai 7 SGK la A/ = ax , trong dd ld'y
2

A/ = Sn - Sn_i ; a = 10 m/s ; x = 1 s.
99


1.24. Khoang cdch AB la :
s = vt = 100.(2.3 600 + 20.60) = 840 000 m = 840 km
Khi trd vl thdi gian bay la t' = 2 h 30 min, Ito hon 10 min do cd gid can.
Ggi vdn tde gid la VQ , ta cd :
S = (v-VG).t'

840 000 = (100 -

VG).(2.3

600 + 30.60)

Tfi dd tfto dugc VQ :
VQ =

6,66 m/s

1.25. Thdi gian bed nguge ddng la :
1000
t, =

1 (1,2-0,5)

1000
0,7

Thdd gian boi xudi ddng la :
t-,=

1000
1000
(1,2 + 0,5) 1,7

Thdd gian bod ea di va vl la
1000 1000
t = t,^i"^2
+ to = 0,7 • 1,7 = 2 016,8 s = 33,6 min
Nd'u sdng ydn lang thi thdd gian bod di va vl la :
t' = ^ ^ = 1666,67 s = 27,78 min
1,2
1.26. a) Hutog bay thoa mto cdng thfic tdng hgp cac vecto vdn tdc nhfi sau :
V = Vj + v^

trong dd v cd hutog Tdy, la ydn tde
tdng hgp ; v. la vdn tdc cfia may bay
theo hfitog cto xdc dinh (gia tri cua
Vj btog 200 km/h) ; V2la vdn tdc
cua gid theo hutog Nam.

^""-^^
" " - ^.

So dd vdn td'e tou hito ve 1.4G.
Hinh 1.4G

100


Dd dtog thd'y gdc a Idch khdi hutog Tdy cfia vdn tde Vi (tfic la hutog
Tdy - Bdc) dugc tfto bdng :
sma =

'2

_

50
= 0,25 ; a = 14,48°
200

v^ = vJ - v^ = 200^ - 50^

b)Taed:

V = 193,65 km/h
1.27. a) So dd vto tdc cua gigt mua ddi vdd xe eho
trdn Hinh 1.5G.
Theo so d6, ta cd : sin 60°P-lL
= —^•,
V2

trong dd Vi la vto tdc cua xe, btog 50 km/h ;
V2 la vto tde cfia gigt mua ddi vdi d td.

Hinh 1.5G

Tfi dd tfnh duge V2 = 57,73 km/h.
b)VB =

V,
'I

tan 60°

=_ 28,87 km/h.

1.28. Chgn hd true toa dd gto vdd mat ddt cd true Ox theo hutog Tay - Ddng,
true Oy theo hutog Nam - Bae. Vecto vto tdc cua xe A cd cac toa dd la
v^o = (-40 ; O) ; vecto vto td'e cua xe B cd cac toa dd la VgQ = (O ; 60).
Vto tdc VgA cua xe B dd'i'vdd xe A dugc tfnh theo cdng thfic cdng vto tdc
tou sau :
VBA = VBO + VQA
Tacd:

VQA = - V A O = ( 4 0 ; 0)

Vay, vto tdc VgA cd cae toa dd sau :
VBA=(40;60)

Dl dtog tfto duge dd Ito cua VgA va phucmg, chilu cua nd.
Kit qua la:

VBA = 72,11 km/h, hutog Ddng - Bac lam mdt gdc 56,3°so vdd hutog Ddng!
101


1.29.
Khotog each
20cm + 40cm 40 cm + 60 cm
(tii... din...)
2
^2

2
-'^l

a = —^

0,412 m/s^

0,396 m/s^

60 cm + 80 cm 80cm+100em
0,384 m/s^

0,389 m/s^ ,

2s
Nhu vay, trong pham vi sai sd ed htog mm/s , ta cd thi coi gia tdc cua
chuyin ddng la khdng ddi va btog gid tri trung bito cfia cac gia tdc la
0,395 ml%
1.30. Cdch tfto tuong tu bai tdp 1.29.

Kit qua tou sau :
Khotog cdch
(tfi... din...)
2
2
^2 - ^1

^

2s

20em +
40 cm

40cm +
60 cm

60cm +
80 em

80em +
100 em

100 cm +
120 cm

120 cm +
140 cm

9,84

9,82

9,82

9,82

9,65

9,83

m/s^

mii

m/s^

mii

m/s

mii

Trung bito eua gia td'e g la 9,79 m/s Cd thi coi rod tu do theo quy luat
cua chuyin ddng bid'n ddi (Jiu (gia tdc khdng ddi).
1.31. E dfing. Gia tdc cd gid tri am btog - 2 mii, vto tdc ban ddu cd gia tri
duong btog 10 m/s. Gia td'e va vdn td'e ban ddu ngugc ddu, ehdt dilm
chuyin ddng chtoi dto diu theo chilu cua vto td'e, tfic la ehilu duong
cfia true Ox. Vto tdc giam ddn dd Ito cho dd'n khi btog khdng, cdn gia
,^

ty

tdc ludn ludn btog - 2 m/s , ehdt dilm tdng dto vdn tde theo chilu am cua
true Ox.
1.32. a) Sai. D6 thi vto tdc cfia chuyin ddng thing diu la mdt dutog thing song
song vdd true thdi gian.
b) Dung. Trong khotog thdd gian tfi 0 s - ti «, ca hai xe diu cd vdn tdc
duong va gia tde dm, trdi ddu toau, do dd chuyin ddng la chdm dto diu.
e) Sai.
d) Dung. Hai dutog bilu diln song song vdd toau, hd sd gdc btog toau
ndn gia tdc cua hai xe la tou toau.
102


e) Sai. Hai xe dudi kip toau lfic t =
^OA

^OB

1.33. B dung. Ta cd v^ = 2as = 2.0,5.100 = 100 (mlsf, tii dd v = 10 m/s.
1.34. D dtog. Ta cd - v^ = 2a's', hay -100 (mlsf = 2a'.50. Tfi dd suy ra a' = -1 mii
1.35. a) Vdn tdc tfic thdd tai B duge tfto gto dfing theo cdng thfic :
Xp - X A

21-1,5

' » = 1 ^ = 0 : 8 3 0 - = 24.375 cm/s
Tfto tuong tu cho cac vi tri khac, ta cd kit qua sau :
Thdi dilm (s)

0,4
0,8
1,2
Vitri
Vdn tdc (cm/s)

1,6

2,0

B

C

D

E

G

24,375

20,625

16,875

13,125

9,375

Vdn tdc giam ddn, chuyin ddng la cham ddn.
b) Gia td'e trung binh trong khotog thdd gian t = 0,4 s dd'n t = 0,8 s, tfic la
tfi vi tri B din vi tri C, dugc tfnh theo cdng thfic sau :
ai =

Vc - Vg _ 20,6 - 24,4
= -9,5cm/s^
0,8 - 0,4
tc ~ tg

Tfto tuong tu cho cac khotog-khac, ta cd duge kd't qua sau
Khotog each
2

a (cm/s )

BC

CD

DE

EG

- 9,375

- 9,375

- 9,375

- 9,375

Gia tdc trung bito la khdng ddi, do dd chuyin ddng la chdm dto diu.
1.36. Dfing cdng thfie tfnh vdn tde tfic thdd. Vf du, tfto vdn tde tai vi tri B :
VB =

^C ~ ^ A

tc-tA

0,035 - 0
= 0,875 m/s
0,04-0

Tuong tu ta cd : Vc = 0,625 m/s ; Vp = 0,375 m/s.
103


1.37. a) Hito 1.6G.
b ) f = ^ = -M^.0,75s-l
'
2n
2.3,14
T = l = 1,33 s.
f
e) V = r© = 5.4,7 = 23,5 cm/s.
1.38. Tdc dd gdc :

Hinh 1.6G

( 0 = 5 vdng/giay = 5.27i rad/s = IOTI rad/s.
Td'e dd dai: v = r© = 0,4.10.71 = 4n m/s = 12,56 m/s.
Gia tdc : a = Tti = 0,4.(107t)^ « 394,4 m/s^, hutog vao tdm dutog trdn.
1.39. a = — = — = 12 mii
r
3
1.40. a) v^ = ar = 7gr = 7.9,8.5 = 343 (mlsf, tfi dd v = 18,5 m/s.
b) ro = - = 3,7 rad/s = ^f-.dO vdng/phfit = 35,4 vdng/phut.
r

271

1.41. v = Vo,15.3,5.10^^^ = 7,25.10^ m/s.
1.42. a) Trong indt ngay ddm (86400 s), mdt dilm d xfeh dao ve mdt vdrtg theo
chu vi cua Trdi Ddt. Tdc dd dai eua nd bdng ;
\3.

_ 27tRp _ 271.6400.10^
m/s = 465,2 m/s = 1674,7 km/h
Vxd =
86400
^D
Tai vi dd 45°, ban kfnh dutog vi tuyin la :
R^^o =RD.eos45°
Tdc do dai cua mdt dilm d vi do 45° btog :
V

104

2TtR o

= ^ =

27iRr,.eos45°
86400
'329m/s=1184JbWh


b) Ta todn thdy, trong chuyin ddng quay cua Trai Ddt xung quanh true eua
nd, tdc dd dai cd gia tri Ito todt d xfeh dao. Ngudd ta lgi dung dilu nay dl
phdng cdc eon tau vu tru. Vi If do dd ndn Guy-an nam gto xfeh dao dugc
chgn lam noi dat bd phdng tdn Ifia vu tru eua Trung tain Nghidn cto Vu tru
chdu Au.
c) Hutog phdng cdc con tau la hutog Ddng vi Trdi Ddt quay theo chilu tfi
Tdy sang Ddng. Nhu thi Igd dung dugc tdc dd quay cfia Trdi Ddt.
1.43. - Cdch 1 : Tinh theo bang sd lidu.
+ Ldy gid tri Ito cdn cua t = 0,2 s.
n o 2 - 2 2'>
+ Tfnh gdn dung vdn tdc tfic thdi v = ^ .'
' ^ = 0,40 m/s.
- Cdch 2 : Tihh theo dd thi.
+ Trdn dfitog cong, ldy dilm M tog vdd t = 0,2 s.
+ Tai M, ve tilp tuyd'n vdd dutog cong, cdt true t tai t = 0,08 s.
+ Ta todn thdy la tog vdi s = 30 cm thi t « 0,78 s.
~ j^ = 0,43 m/s.
+ Tito gto dfing vdn tdc tfic thdd v = /
(0,78 — 0,08)
Trong hai each tfto kd't qua cd sai khdc toau. Trong pham vi sai sd, ed thi
chdp todn dugc.
1.44. - Tfi dd thi, ta cd todn x l t :
+ Cd ba dfitog bilu didn tog vdd ba chuyin ddng khac nhau cua bgt khf

trong d'ng.
+ 6ng cd dd ngljidng Ito thi dutog bilu diln ddc hon, chtog td vto tdc
' cua bgt khf Ito hon.
+ Vto tde chi ddng biln vdd dd nghidng chfi khdng ti Id thuto vdd dd nghidng.
+ Tfi day cd thi tfnh vto td'e eu thi cfia mdi chuyin ddng.

105


&uMiig.Il
DONG LUC HOC CHAT DICMi

.1. Xem m t o 2.IG.
Trgng lue P dugc phto tfch thato hai thato

phto f^ va f^^ Ito lugt can btog vdd cac

////////////////////////M
J20«

K

lue etog eua day ABva day AC. Theo hito
ve, ta cd :
TAC =

mg

~ 56,6 N
''"*-'" „

TAB = mgtan30° « 28,3 N
^

or>0

Hinh2.1G

2.2. C dung.
2.3. Khi xe dang chay nhanh ma dtog ddt ngdt, ngudd ngdi trdn xe se bi xd vl
phfa trudc (do qudn tfto), cd thi bi lao khdi ghi hoac bi chto thuong do
va cham mato vao cdc bd phdn cfia xe d phfa trudc chd ngdi eua mito.
Ddy an toto cd tae dung gifi cho ngudd khdi xd vl phfa trudc khi xe dtog
ddt ngdt.
2.4. Do cd quan tfto, mdy bay khdng thi tfic thdd dat tdd ydn tdc du Ito dl cdt
cdto. Nd phai tang tdc dto trdn dutog btog mdd cdt canh dugc. Khi ha
canh, nd dang cd vdn td'e Ito ndn phai ham dto trdn dutog btog mdd dtog
lai duge.
2.5. Luc do bua tac dung truyin qua dinh tdd tdm vto. Vi tdin vto mdng va toe c6
khdi lugng tod ndn lue nay gdy cho vto mdt gia tdc dtog kl etog chilu vdi
chuyin ddng cua dmh. Vi vdy ma khd ddng dugc dinh vao van.
Nhung nd'u ta dp vao bdn kia tdm vto mdt vdt khac (tiiutog la mdt tdm g6
ntog hoac mdt vidn gach...), tiii tdm vaff cfing vdd vdt nay hgp thanh mdt hd co
khdi Ifigng Ito. Khi ta ddng dinh, hd nay cd gia tdc rdt tod (cd till coi gdn nhil
dtog ydn) ndn ta dd ddng dugc dinh ngdp vao vto.
(Hay lidn hd vdi cdu tiiato ngfl dto gian : Dao sdc khdng btog chdc kd).
2.6. D dung.
10#


2.7. Gia tdc cfia bdng trong thdd gian va cham :

Vo

a=

'^i^^
At
Chilu xudng true x (Hito 2.2G) :

P

Vt

Hinh 2.2G

F = ma = 0,2.800 = 160 N
-^o ^
2.8. a)

T7
0,8-0,4
Fl = mai = m.
= m.0,5
0,0

F2 = ma2 = m. — - — = m.0,1
^ = 5
b)
2.9.

Av = ajAt = 0,1.1,1 = 0,11 m/s.

Fi

81 A

VA

F2

32

B

VB

Hinh 2.3G

Chgn ehilu chuyin ddng ban ddu eua vdt lam ehilu duong cua Ox. Luc
FJ lam cho vdn tdc cua vdt giam, chtog td Fi nguge ehilu chuyin ddng.
Gia td'e cua vdt trong giai doan ddu :
VR-VA
--^—A.-

5-8

,2
= _5_ cm/s''

0,6
Khi vat tdd B, lue gifl hutog nhu cu va ttog dd Ito ldn gdp ddi, ndn gia tde
cua vdt etog tang gdp ddi:

2
a2 = 2ai = -10 em/s
van td'e cua vat sau 2,2 s :
t.

V = VB + a2t2 = 5 + (-10).2,2 = - I 7 cm/s
Ddu am chtog td vat da ddi ehilu chuyin ddng.
(C6 ihi khai thac thdm : Vdt ddi ehilu chuyin ddng vao lfic nao, d ddu ?).
2.10.

F = miai =>mi =

F

(1)
107


F = m2a2 ^> m2 = —
a2

(2)

F = (mi + m2)a, suy ra : mi + m2

(3)

Tfi (1), (2), (3) t a c d :
1
1

+

a2

= ^ 1 ^ = ^ : 1 = 2,67 m/s2
ai+a2 8 + 4
F

9

9

2.11. a ± -^ = ^ = 3 mii
m 3
at^
S = Vgt + —

3t^
Thay sd : 10 = 2t + -—— Giai ra, ta duge : t = 2 s (loai nghidm dm).
^2

2.12. a) Thay sd vao edng thfic : s = Vgt + — , tfnh ra a = 2 m/s
Thay a vao cdng thfic : Fi^ - F^. = ma, tfto ra Fj^ = 1,5 N.
b) Sau 4 s ddu, vdt dat tdi vto td'e,:
V = Vg + at = 10 m/s
Khi lite keo thdi tdc dung, luc can gdy cho vdt gia tdc :
-

-0.5

,

,2

" = " 0 3 " " -^'^'
Sau thdi gian t' vdt se dtog lai:
v' = v + a't' = 0
Thay sd, ta dugc t' = 10 s.
2.13. Theo dito If ham sd edsui (Hinh 2.4G):
Y^^ = Ff + F | - 2F1F2 cos 150°
Tfi dd tfnh dfige : F12 « 6,8 N.
a = ^ = 3,4m/s^
m
at^- « ^2,45m
,r
s=—
108

Hinh 2.4G


2.14. Xem Hinh 2.5G.
V (m/s)
154-

100

200

300

400 t (s)

Hinti 2.5G

2.15. Luc etog cua ddy khi dd la 50 N. Day khdng dfit.
2.16. 9,78 mii ; 4,36 mii.
2.17. 3,5.10^^ N.
2.18. Ggi khdi Ificmg mdi qua cdu lfic ddu la m^ va m j ; luc sau la mj va m2.
Khotog cdch gifla tdm cfia ehung lfic ddu la R, luc sau la R'. Khi ban kfto
mdi qua cdu giam di 2 Ito, thi tfch cfia nd giam 8 Ito, do dd khdi lugng
etog giam 8 ldn : mi - - ^ \

^2 = ~ ^ ' Ngoai ra, theo ddu bai thi

Luc hdp dto gifla hai qua cdu luc ddu la : F = G tnim2
^
R
Luc hdp dto gifla chung lfic sau la

mi m2
p.^oi^hEi = G 8 8
R

= 1 G ^ ^ = : ^ . Vdy B dung
16
16
R^
2.19*. Luc hdp dto giam 9 Ito, tfic la khoang each

tfi vdt din tam Trdi Ddt ttog ldn 3 Ito. Luc
ddu, vdt each tam Trai Ddt mdt doan R, thi
sau dd, nd cdch tdm Trdi Ddt 3R, tfic la d
dd cao 2R so vdi mat ddt. Vdy B dung (xem
mto2.6G).

_

Hinh 2.6G

109


2.20. B dfing.
2.21. Ggi X la khotog each tfi dilm phai tim din tdm Trdi Ddt (Hinh 2.7G). Luc
hdp dto do Trdi Ddt tac dung ldn vdt:
_
GMim
Lue hdp dto do Mat Trang tdc dung ldn vdt:
GM2m
Ml
2

^2=

Tfidd

11
.2
X-

Fl m F2 M2
- « t > —9

Q-

(60R - x)^
1

!R|

(60R -x)^

60R

Giai ra ta dugc : x = 54R.
2.22. O cdch tam Trdi Ddt mdt khotog d :
^ GMm
F=
r—
6 mat ddt

^

Hinh 2.7G

GMm

Tfidd:

550

gt^
2.23. h = ^
= 44,1m.
L = Vgt = 75 m.
2.24. a) + Nd'u chgn he true toa dd tou d Hinh 2.8Ga (gdc toa dd d dilm tha vdt.
Ox hutog theo Vg, Oy hutog thtog dtog xud'ng dudi) thi :
a, = 0 ;
X = Vgt = 120t
ay = g - ;

y = - ^ = 4,9t2

Rfit t tfi bilu thfie eua x thay vao bilu thfie eua y ta dfige
120^
Nd'u chgn hd true tou d Hito 2.8G b (gdc toa dd la hinh chilu cua
dilm tha vdt trdn mat ddt. Ox song song vdd Vg, Oy hudng thing dtog ldn
trdn) thi:
110


a. = 0 ;

X = Vgt = 120t

ay=-g;

^ _2 .5 0 0 - 4 , 9 t
y = y g - gVt =

4 9 ->
y= 2500--^x2
120^

Tfidd

O

Vo

r

Vo

g

M$t(lSt
77T

\

Trf^rrrTrrrrTrrrrrrTTTTTTrrrTTTTTTTTT*-

X

y

a)

b)
Hinh 2.8G

2h
+ Thdd gian tfi lue tha vat dd'n luc vat cham ddt la : t = , — « 22,6 s.
g
Tfi dd : / = Vgt = 120.22,6 = 2712 m.
b)vg=| = /^«105m/s.
2.25*. Chgn true toa dd tou Hinh 2.9G, phuong trito quy dao
0

2v;0
Khi vidn sdi di tdd vi tri cua bfic

g

i2

X

Vo
\\
\V
\\
\

tfitog (x = /) thi y =

h

\ ""fa
•

Vidn sdi lgt qua cfia sd nlu :
j2

h-a-b<

ST < h - b

2v:0

//// ///j///n///r
I

(/////////

y

Hinh 2.9G

111


Suy ra:
/.

g
g
'2(h-b) ^ ' ' o ^ W 2 ( h - a - b )

Thay sdta ed: 1,66 m/s < Vg < 1,71 m/s.
2.26. Chgn hd true toa dd nhu Hito 2.10G (gdc toa dd la dinh thap). Phuong
trito vdn tdc cfia vdt:
^ Vx = Vgcosa = 10,6 mis

'

Vy = Vgsina - gt = 10,6 - 9,8t
Phuang trinh chuyin ddng
cua vat theo true y :
^2

y = (vosina)t - - ^
= 10,6t - 4,9t^
Khi hdn da tdd ddt:
y = -12 m. Ta cd :
10,6t-4,9t^ = -12.
Phuong ttito nay cd mdt
nghidm duong : t = 2,98 s.

Hinh2.10G

Thay vao (2), ta cd :
Vy =-18,6 m/s
Dd Ito cfia van tdc khi vat cham ddt:
V = ^vJ+Vy.= ^10,6^+18,6^ = 21,4m/s
Vdn tde nay hgp vdd phfiong nam ngang mdt gdc P :
cosP = ^5. ~ 0,5

hay

V

2.27.

= FAB
kAA/A = kBA/B
FRA

kp = - ^ - - ^ = 500 N/m
112

p « 60°

(1)
(2)


2.28. Ggi Al^, A/2 la dd dan cfia cac Id xo Li, L2 khi bi keo vdd luc F.
Ta cd :
A/ = A/i + A/2
F
A/
F
A/
F
trong dd : A/ = —;
A/i
=

—
;
A/2
=
—
.
r
k

(1)
(2)

_ ^1^2
Thay (2) vao (1) ta dugc : k =
kl +,k2
2.29. Vi eac vdng Id xo gidng hdt toau ndn khi Id xo bi keo vdi mdt luc F todt
dito, dd dan cfia mdi phto cua Id xo ti Id thudn vdd chilu dai ban ddu
cua nd.
A/i _ /i
A/g

Nhung mat khac
Tfidd:

/g

k - ^ -

k-

•"i - A/i ' ^ - A/n
^1 _ ^lo_ _ }o_
k
A/i /i
_ k / g _

k, =

Tuong tu:

= 300 N/m

k/„
k, = - 2 - = 150 N/m

2.30. Trong bai nay, phai chfi y tdi
vai trd cua luc ma sdt do mat
ddt tac dung vao mdi ngudd
(Hito 2.110).
Khi ngfidd 1 dap vao mat ddt, v^^^^wM^.'.'^/.>w.'.'.i^.'///y'///.'/^.^77f.>7w.>.'
F,
Fa
chto ngudi 1 tdc dung vao "^'i
da't mdt lue ma sdt Fj, mat

Hinh 2.1 IG

ddt tae dung trd lai chto ngudd
1 mdt phto luc ma sat FJ. Theo dinh ludt m Niu-ton :
F;

= Fl

(1)

Tuong tu, ngudd 2 tdc dung vao ddt lue ma sat F^, mat ddt tdc dung vao
chto ngudi 2 mdt phto luc F2, ta cd :
a-BTVL 10(NC)-A

113


(2)

F2=F2

Nd'u ngudi 1 dap mato hon ngudd 2 : Fi > F2, thi theo (1) va (2), Fi > F2.
Khi dd hgp luc do mat ddt tae dung ldn hd gdm hai ngudi ya ddy se hutog
sang trai, va hd chuyin ddng sang trdi (ngudi 1 thtog cudc).
vay ai dap vao ddt mato hon thi se thtog cudc (mudn frd chod dugc edng
btog, phai dam bao cho mat ddt d chd hai ngucd dtog ed dd rap gidng toau).
2.31. - Xe dtog ydn : khdng cd luc ma sat nghi.
- Xe chuyin ddng toato dto diu : F^j^n do sto xe tdc dung da gdy cho
hdm gia tde a (btog gia tdc cua xe).
Fmsn = ma
(Fmsn hutog cung chilu chuyin ddng cua xe).
Nd'u a > Ung thi vat trugt vl phfa sau so vdi sto xe.
- Xe chuyin ddng chtoi dto diu : F^sn = ma.
Fmsn hutog ngugc chilu chuyin ddng cua xe. Nd'u lai > \i^g (chtog han
khi xe ham gdp) thi vdt trugt vl phfa trude so vdd sto xe.

- Xe chuyin ddng thtog diu : khdng cd F^^^^.
2.32. Hdm chiu tac dung cua lue keo F,
frgng luc P, phto luc phap tuyin
N value ma sat Fmst (Hinh2.12G).
Vi hdm chuyin ddng diu ndn :
F + P + N'+Fmst = 0

N
*/77/y//////////

Chilu xud'ng Ox :
F.cos a - F„3t = 0

(1)

Chieu xudng Oy :

Hinh 2.12G

F.sina - mg + N = 0 (2)
Ngoai ra :
114

Fj^^t = IhJ^

(3)
8-BTVL 10(NC)-i