bai tap nang cao ly 10

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 Chgn true Ox cd phuong thi

Phan hai mJCR^G M^A!^ G l A l VA D A P s6

DONG HOC CHnt DI€M

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

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 : 6 0 = ^ ' ^ ^ ' " / ^

Chd y : Khdng ldy trung binh hai vto tdc vi thod gian chay khac toau

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 k l 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)

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

X2 = 60t

trong dd t la thdi gian kl tfi lue d td bat ddu chay

X (km)

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 « - ^^2 - ^i) (20 - 25) ^ ^ , 2 , , , u^ ^ ^

1.0 a = — i - = = - 2,5 m/s (chuyen dgng cham dan)

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 1 0 ~ %

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 , 5 t ^ - 3 0 t - 3 0 = 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;

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 - (1)

Xe thfi h a i : X2 = V2t (2) 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

b) Dd thi (xem Hinh 1.3G)

X (km) 250

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

95

VJ x = ^ (2)

2a Thay sd vao cac cdng thfie trdn :

^ ^ v - v g ^ 0 - 1 0 0 ^ ^ ^ ^

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 :

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 :

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 :

/„= 34,3 = |.9,8[n2 - (n - 1)^] = 4,9.(2n - 1)

34 3 Tfi dd t a c d : 2 n - 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 đt, 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 đ sdu cua hang, ti la thđ gian hdn da red dto day, t2 la thđ gian

tid'ng vgng tfi đy hang ldn đ'n midng hang Ta cd :

h = Vật2 = 340t2 (1)

h = - g t f = - 1 0 t f =5tf (2)

Tfiđ to=—I

2 ^ 2 5t

••2

^ 340 Thđ gian tfi luc tha hdn đ 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 đ cd mdt gia tri am

Ta chi ldy gid tri duong ti = 11,66 s

Nhu vay thđ gian tieng vgng di tii đy hang din midng hang la :

t2 = t - tl = 13,66 - 11,66 = 2 s

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 = | 1 0 ( 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 :

v a y hidu cac dd ddd sau 1 s lidn t i l p 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 :

t-,= 1000 1000 (1,2 + 0,5) 1,7 Thdd gian bod ea di va vl la

t = t, + to = ^i"^2 0,7 • 1,7 1000 1000 = 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

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

trong dd Vi la vto tdc cua xe, btog 50 km/h ;

V2 la vto tde cfia gigt mua ddi vdi d td

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

T a c d : VQA = - V A O = ( 4 0 ; 0)

Vay, vto tdc VgA cd cae toa dd sau :

V B A = ( 4 0 ; 6 0 )

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

1.30 Cdch tfto tuong tu bai tdp 1.29

Kit qua tou sau :

40cm +

60 cm 9,82

mii

60cm +

80 em 9,82 m/s^

80em +

100 em 9,82

mii

100 cm +

120 cm 9,65 m/s

120 cm +

140 cm 9,83

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

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 :

0,8

C 20,625

1,2

D 16,875

1,6

E 13,125

2,0

G 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 :

1.36 Dfing cdng thfie tfnh vdn tde tfic thdd Vf du, tfto vdn tde tai vi tri B :

VB = ^C ~ ^ A

t c - t A

0,035 - 0

0 , 0 4 - 0 = 0,875 m/s Tuong tu ta cd : Vc = 0,625 m/s ; Vp = 0,375 m/s

103

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 ;

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

+ Tito gto dfing vdn tdc tfic thdd v = / ~ j^ = 0,43 m/s

(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

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

2.7 Gia tdc cfia bdng trong thdd gian va cham :

a = '^i^^

At Chilu xudng true x (Hito 2.2G) :

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 :

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 ?)

F

107

F = m2a2 ^> m2 = —

a2

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

(2) (3)

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):

2.14 Xem Hinh 2.5G

V (m/s)

1 5 4

-100 200 Hinti 2.5G

300 400 t (s)

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

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

R Luc hdp dto gifla chung lfic sau la

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:

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 ;

ay = g - ; Rfit t tfi bilu thfie eua x thay vao bilu thfie eua y ta dfige

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 ) v g = | = / ^ « 1 0 5 m / s

2.25* Chgn true toa dd tou Hinh 2.9G, phuong trito quy dao

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

Suy r a :

/ 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 ' (1)

Vy = Vgsina - gt = 10,6 - 9,8t (2) Phuang trinh chuyin ddng

cua vat theo true y :

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 trong dd : A/ = —;

r k

A/ F A/ F

A/i = — ; A/2 = —

(1) (2)

Thay (2) vao (1) ta dugc : k = _ ^1^2

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

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.>.'.'JWr^.'77.'.¥7//

F, Fa Hinh 2.1 IG

chto ngudi 1 tdc dung vao "^'i

da't mdt lue ma sdt Fj, mat

ddt tae dung trd lai chto ngudd

1 mdt phto luc ma sat FJ Theo dinh ludt m Niu-ton :

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 :

113

F2=F2 (2)

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 Chilu xud'ng Ox :

F.cos a - F„3t = 0 (1) Chieu xudng Oy :

Luc ddu, tau chuyin ddng diu do lue keo cdn btog vdd luc ma sdt Ito :

Ffc = ^msi = M/Mg (M la khd'i lugng ca doan tau)

Khi phdn dudi tau bi tach khdi doan tau, luc ma sat ham nd vdd gia tdc :

^2

iv/r 3 M

3 3M 3M

4 4 Sau thdd gian t, phto ddu tdu dat vto td'e :

M/g Vg 4

V2 = Vo + a2t = Vg+ ^ - - ^ = ^^0

115

TTT77TTTT77

2.35 a) Lue ma sat nghi F do

td'm van tac dung ldn mdu gd

lam cho mdu gd chuyin sang

trang.thai chuyin ddng ^.^^ 2.14G

- Khi luc keo khdng Ito lam,

gia tdc cfia tdm van va mdu gd cdn nhd, Trong hd quy chilu gto vdd tdin vdn, luc quan tfto tde dung ldn vdt 1 chua dfi thtog lfic ma sat nghi, ndn vdt

1 vto dtog ydn so vdi vdt 2 (Hinh 2.14G)

b) - Trong hd quy chid'u gto

—*

vdd ban, luc ma sat F lam

21

cho vdt 1 chuyin ddng vl

bdn phai (so vdd bto)

- Trong hd quy chilu gan vdd

ed D la dung

2.37 Trong hd quy ehilu gto vdd mdy bay, ngudd

phi cdng chiu tde dung cfia trgng lfic, luc

qudn tfto li tdm (do may bay chuyin ddng

frdn) va phto luc cua ghi ngdi (Hinh 2.16G)

P + NA = Fq

NA = F q - P = m - g = 765N

Itsip

Hinhi.16G

Tai dilm thdp todt B :

Nlu dung hd quy ehilu jgan vdi bto, thi ta lap luto la vat vtog ra khi luc quan tfto li tam thdng lue ma sdt nghi cue dai

Ca hai lap luto cung ddn tdi:

2.39 Phan luc Ncua thato binh dat ldn

vat la luc hutog tam Do cd luc

nay ma xud't hidn luc ma sat nghi

gifl cho vdt khdi bi red xud'ng

mdt lite hfitog tdm cd dd Ito khdng ddi

117

2.41 B dfing

Vdt chuyin ddng chdm dto diu ldn phfa N, tdd mdt dd cao nhdt dinh thi dat

tdd vto tde v = 0 Vi tana > IJ^ ndn vdt se chuyin ddng nhato dto diu

xud'ng phfa M

2.42* Tfi cdng thfie a = g(sina - ^tcosa)

ta rfit ra jit = tana - '• (1)

geosa Khi a = 20°, A/ = D E - C D = C D - B C = B C - A B

a =;= - r - « 5 m/s^

Thay vao (1) ta dugc : ^,2 ~ 0,213

Ta cd gid tri trung bito cfia \i:

„.'^^.a.2

2.43 a) Vdd he 2 vdt

a = " ^ i g - r ™ 5 , l m / s ^ b) Vdi vat 2 :

mi + m2

m2g - T = m2a

T = m2(g-a) = l,41N e) Khi vat 2 cham ddt, vdt 1 cd vdn tdc :

V = \/2ah = 2,26 m/s Gia td'e vdt 1 sau khi vdt 2 cham ddt:

h _ at^

2 ~ 2

t = ^ - 0 , 5 5 s

2.45 a) Nhto xet: P2 > Pix + Fj^g^ n^g^ ^^^ti vat mi chuyin ddng len trdn, vat m2

chuyin ddng xud'ng dudd (Hinh 2.18G) Gia td'e eua he bang :

a =

— P — F

Ix ^mst

mi + m2 _ m2g - migsma - miHtgcosa

2.46 B dung (nd'u tana > n„ thi vdt trugt xudng duge)

2.47* Thato phto cua frgng luc song song vdd mat phing nghidng :

yl2

Px = mgsina = 0,5.9,8.-^ = 3,46 N Gia tri cue dai cua luc ma sat nghi gifla vdt va mat phang nghidng la :

- Hd sd dan hdi ludn bid'n ddi theo dd dan eua day cao su

- Mdi quan hd gifla dd dan vd lue dan hdi khdng don tri

- Khdng thi dung day cao su nay lam luc kl

- Trong khi dd, hd sd dan hdi cua Id xo trong bai da hgc la khdng ddi (trong gidi han dan hdi)

121

TINH HOC VflT ft AN I

t

Hinh 3.1G

3.1 1 a) Nhtog luc ddt ldn hdn bi gdm : luc \^

etog eua sgi ddy T hutog ldn frdn va

trgng luc P hutog xud'ng dudd

b) Do hdn bi ehi chiu tac dung cua hai

lue eho ndn dilu kidn cto btog cua nd la

f + P = 6, hay f = -P

Hai luc tac dung cd cfing dd Ito, cung

phuong toung ngugc chilu

c) Tfi cdng thfic frdn, ta ed dd Ito cfia hai

luc la T = P = 0,2.9,8 = 1,96 N

2 a) Luc k l do gia tri cua luc do sgi ddy dat ldn mdc C Sgi day cd khd'i lugng khdng dang kl, luc dd bilu thi lue etog eua sod day tai mgi dilm cua day So ehi eua lue k l la 1,96 N

b) Luc k l do gid tri cfia lue etog eua sod ddy, bdy gid btog 2i,2 N Dilu kidn cto bang cua hdn bi bay gid la :

b) Cac luc dat ldn quyln frdn (1) gdm :

- Trgng luc Pi do Trdi Ddt hfit nd

- Phto luc do quyln dudi (2) tdc dung N

Suyra F21 = -P,, va |F2I| =

|?I|-Lue do quyln dudd tdc dung ldn quyln

frdn ed dd Ito btog frgng lugng quyln

frdn va hutog ldn frdn Ta ed F21 = 10 N

Cdc lue dat ldn quyln dudd gdm :

-Trgng luc P2 do Trai Ddt hut

-Luc do quyln frdn tac dung F12

- Phto luc do mat bto tde dung N

Quyln dudd ndm can btog, vay ta cd :

P 2 + F i 2 + N = 6 theo dito luat III Niu-tan, tac dung tuong hd gifla hai vat (1) va (2) eho :

Fi-2 - -F21 (2) vay luc F12 ed dd Ito btog dd Ito eua luc Fji, btog 10 N va hutog

xudng dudd

Theo cdng thfic (1), ta cd :

N = -(P2+Fi2) (3) Phto luc N hutog ldn frdn va vl do Ito thi N = P2 + F12 = P2 + Pi =

= 18 + "lO = 28N

2 a) Cac lue dat ldn hd gdm :

-Lite hut cfia Trdi Ddt P

- Phto lite cua mat bto N

e) Theo dinh luat tae dung tuong hd, hd tac dung ldn mat bto mdt lue bto§

va ngugc chilu vdd phto luc N, tfic la btog P

(Khdng ndn todm Ito gitta lfic cfia hd ddt ldn mat bto vdd frgng luc cua hd, tuy rtog hai luc dd btog toau ea vl dd Ito Ito phuong, chilu)

3.3 Tuong tu bai tap 3.1 Luc Id xo dat ldn vat btog frgng lugng vat va cd ehilu nguge lai

3.4 1 Luc k l chi frgng lugng eua vdt P = mg = p7tr hg

Thay cac gid tri vao edng thfic, ta dugc :

P = 2700.3,14.0,01^0,2.9,8 = 1,66 N

2 a) Xem Hinh 3.3.G

b) Cdc luc dat ldn hito tru gdm :

Trgng lue P, luc ddy Ae-si-met A va luc etog T

P + A + f = 6

f = -(p + A)

Do P va A ngugc chilu toau ndn gid tri eua T btog :

T = P - A = 1,66 - 0,62 = 1,04 N Vdy sd chi cua lue k l la 1,04 N

3.5 a) Lidt kd cac luc dat ldn vat:

- Trgng lue P dat d frgng tam, hutog thing dtog xudng dudd ;

- Lue etog T cd phuong cua sod day, hutog ldn phfa trdn ;

- Luc didn F ed phuong nam ngang, keo vat lam day Idch khdi phuong thtog dtog (xem Hito 3.4G)

b) Do vat ndm cto btog, ta cd :

P + f + F = 0 (1) Chgn mdt hd toa dd xOy, cd gdc trung vdd vat, true Ox nam ngang hutog

theo ehilu lue F, true Oy thtog dtog hutog ldn frdn Phuong trinh vecto (1)

cd hai thato phto la :

- Trdn true Ox : 0 + (-T.sina) + F = 0 (2)

- Trdn true Oy : - P + T.eosa + 0 = 0 (3)

Tfi hai phuong tiito (2) va (3), ta suy ra :

F tana = — Thay cac gia tri cua P va F vao edng thfie frdn, ta

3.6 Hgp hai luc song song Fi va F2 cung chilu cd gia tri btog :

F = Fi+F2 (1) Dutog tde dung cua hgp lue F chia frong hai luc Fi va F2 theo edng thfic ti Id

nghich vdd dd Ito hai luc Ta cd :

V2

Fl _ F 2 F i + F ,

(Cdc bai tdp 3.6 va 3.7 giai' dugc tod ede cdng thfic (1) va (2))

Cac dtt kidn cua bai tdp 3.6 la : d = di + d2 = 0,2 m ; Fi = 13 N ; d2 = 0,08 m

Tfi cac cdng thfie frdn, ta cd :

F, = F - F, = 32,5 - 13 = 19,5 N

125

3.7 Theo ddu bai, Fi + Fj = 20 + 30 = 50 N ; d2 = 0,8 m Sfi dung edng thfie (2)

6 b M , a p t t n , c 6 : d = d , + d , = ( F , F , ) ^

Thay sd vao, ta dugc : d = 2 m

3.8 Cdch giai tuong tu ede bai tap 3.6 va 3.7 Chu y cac etog thfic lidn quan la :

F = i F 2 - F i |

d = ldn — dd

Fl _ F2 _ F

(1) (2)

(3)

Theo dl bai tap 3.6, bilt d = 0,2 m ; Fi = 13 N ; d2 = 0,08 m

Kit qua cho : F = (0,2.13): 0,08 = 32,5 N

F2 = F + Fl = 32,5 + 13 = 45,5 N

dj = d + d2 = 0,2 + 0,08 = 0,28 m Theo dl bai tap 3.7, bilt Fi = 20 N ; F2 = 30 N ; d2 = 0,8 m

Kit qua eho : F = 10 N ; d = 0,4 m ; di = 1,2 m

3.9 a) Cae lue dugc bilu didn frdn hito 3.5G

A / ' = i ^ = 0 , 0 2 m = 2em / = /n + A/' = 50 + 2 = 52 em '0

3.11 a) Ddu trfi (momen lue dm),

b) M = F.OA sina

J 3

e ) M = 3 ^ « 2 , 6 N m

3.12 a) Ddu cdng (momen luc duong)

b) Dutog vudng gdc cua hai gid

3.15* a) Ggi Pg la trgng luc cua qua cto Mi la momen dd'i vdd true I eua ttgng luc

phto phfa AI cua cto ; M2 la momen dd'i vdd true I cfia trgng lue phto phfa

BI cua can Khi Pg treo d O thi cto thtog btog Ta cd :

Mi = M2 + Pg.I0 (1) Treo mdt vat frgng lugng P tai K thi phai dat Pg tai vi tri B Can nim thang

_ R A I _ 2 a 5 _

^^ ^0 - OB " 20 ~ ^

^-3.16* a) Xet vidn gach 4 nam frdn cfing

Nd chi ed thi tod ra ngoai vidn

gach 3 nhilu todt btog nfia ehilu

dai L cua gach : a^ = — L Tilp

theoi dl hd hai vidn gach 3 va 4

nim cto btog tiii gidd han ngoai

cfing cua dutog tde dung eua frgng ^,^^ ^ ^^

127

luc hd hai vidn gach 3 va 4 la mep phai eua vidn gach 2 Vi tri cua dutog do duge xae dito btog quy tde tdng hgp hai luc song song, cung chilu (btog toau, bang trgng lugng cua mdi vidn) Dutog nay ndm each mep phai cua

vidn gach 2 mdt doan a^ = J^- Tuong til, di hd ba vidn gach 2, 3, 4 nam

cto btog thi hgp luc cua ehung cd gidd han ngoai etog cua dutog tac dung ehi cd thi di qua mep phai cua vidn gach 1 dudd cung Cung bang phip tfto hgp lue, ta cd thi xdc dinh duge khotog each nhd ra cua vidn 2 so vdi vidn 1

la a2 = 77 L Cud'i cfing, frong tdm cfia hd 4 vidn gach each mep bto nhilu

6 todt chi cd thi ndm trdn dutog thtog dtog each mep bto mdt doan ai = ^ L

o

(xem Hinh 3.6G)

b) vay khotog each ^ = [ji'^'4'^'^'^ g j ^ " 24 ^ '

3.17 B dung (xem bai hge 27 SGK)

3.18 B dung Hai lue dat vao qua edu

3.19 C dung Vi khi cto btog ta cd Pidi = P2d2 ; ma di < d2, do dd Pi > P2

3.20 B dung Cd thi tfto dugc dd dtog

3.21 Chu y vai frd cua lue ma sdt gifla ngdn tay vdd cdy gdy va dp luc de ldn

mdi ngdn Su dich chuyin eua edy gdy phu thudc vao vi trf cud trgng tam eua nd dd'i vdi hai ngdn tay

- Khi dich ngdn tay phai vl phfa tay trai, gia sfi ban ddu ngdn tay phai dich chuyin so vdd gay, cay gay dtog ydn so vdd ngdn frdi, thi :

+ Din mdt luc nao dd, cay gay se dtog ydn so vdd ngdn phai vd trugt ttdn ngdn ttai

+ Tid'p theo, edy gdy lai dtog ydn so vdd ngdn frai va dich chuyin so vdi ngdn phai

+ Qua tiinh lap lai luan phidn eho dlji khi hai ngdn tay cham nhau ma cay gay khdng rod

- Nlu sau dd dich ngdn phai theo chilu ra xa ngdn frai thi cdy gdy ludn dtog ydn so vdd ngdn frai va se rod khi ngdn phai ra ngoai ddu gdy

3.22 - T a i D phai ed lue ma sat du Ito dl gifl D khdng trugt D frd thanh tdm quay cua vdt

- Dilu kidn cdn btog momen luc ddi vdd dilm D eho :

CAC DJNH L U A T BflO T O A N

4.1 B dung Cfing ddng lugng, ndn vat cd khdi lugng tod thi vto tdc Ito Khd'i

lugng tod thi luc ma sat cflng tod, lai thdm vto td'e Ito ; do dd thdd gian

chuyin ddng trudc khi dtog se dai hon

4.2 D dfing

4.3 Vecto B Dua vdo ding thfic vecto: P2 - Pi = FAt, suy ra F cd hutog eua B

4.4 Khi chim bay ldn, hgp luc N - P theo phuong thing dtog (N la phan luc

cua thanh ngang dat ldn chan chim) tdc dung hutog ldn trdn gay ra bid'n

thidn ddng lUgng Ap luc tfi chto chim dat len thato ngang se Ito ban

trgng lfic, do dd sd chi tfic thdd cua lfic k l ttog ldn Ngugc lai, khi chim

bay xudng, sd chi tfic thdd cfia luc k l giam (xem thdm bai tap 4.8)

4.5 Cdto quat cd cdu tao dang xoto, do dd khi quay tao ra mdt ludng khdng khf

bi ddy vl phfa sau Ddng lugng ma ddng khf mang theo vl phfa eudi may

, bay trong 1 s btog phto luc cua ddng khf tde dung ldn cato quat cua ddng

CO gto vdd cato may bay va lam mdy bay chuyin ddng vl phfa trudc

Nhu vdy, nguydn nhto chuyin ddng cfia mdy bay dung cdto quat la phan

I luc tfi phfa ddng khdng khf bi cdnh quat ddy vl phfa sau tao thato luc keo

cfia may bay Ddi vdi tau thuy, nguydn tic hoat ddng cua chan vit cung

gidng nhu cdto quat cua mdy bay

4.6 Chia dia thanh totog cap nguydn td cd khd'i lugng Am btog toau, nim ddi

xtog qua tam frdn mdt dutog kfto bdt ki cfia dia Vto tdc dai v = ror (r la

khotog cdch tdd tdm dia) cua mdi nguydn td Am cd dd Ito btog toau, toung

ed hutog nguge toau Vi thi, tdng ddng lugng cua ttog cap nguydn td khdi

lugng la btog khdng Suy ra ddng lugng cua ca dia cung btog khdng

4.7 Ap dung dmh ludt bao toto ddng lugng eho hd kin gdm prdtdn va hat a, ta cd :

mpVp = -nipVp + maVa

^ ^ M ! p i i > = ^>6^-lQ"\^-^-^0^ = 6,68.10- kg

MTVL10(NC)-A 129