Dinh luat bao toan dong luong cua he eo lap

^ Xet mdt he cd lap gdm hai vat nhd, tuong tac vdi nhau qua cdc ndi luc F, va F, true dd'i nhau Hinh 23.2 (Hinh 23.2). Theo djnh luat III Niu-ton :

F2 = - F ,

Dudi tdc dung ciia cac lue F^ va F2 trong khoang thdi gian Ar. ddng lugng eiia mdi vat cd do bid'n thidn ian lugt la Ap, va A/?2 • Ap dung edng thiic (23.3b) cho timg vat, ta cd :

Ap, = F,Ar (23.4) Ap2 = F,Af (23.5) Tir djnh luat III Niu-ton. ta suy ra Api = -Ap, hay

Ap|.-i- A/?2 = 0. Nd'u p = Pi + P2 Id ddng lugng ciia he thi bid'n thidn ddng lugng eiia he bdng tong cac bid'n thidn ddng lugng ciia mdi vat :

A/5 = A/5, + A/5-, = 0. Bie'n thidn ddng lugng eua he bdng khdng, nghla la ddng lugng eiia he khdng ddi.

Pi+P2= khdng ddi (23.6)

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Kd't qua nay cd thd' md rdng cho mdt he cd lap gdm nhidu vat va duge phat bieu nhu sau :

Dong luirng cua mot he co lap Id mot dai lucmg hdo todn.

Phat bie'u trdn dugc ggi la dinh lucit bdo todn ddng lucmg.

Djnh luat bao toan ddng lugng cd nhieu iing dung thue td': giai cdc bai todn va cham, lam co sd eho nguydn tde chuydn ddng phan lue...

3. Va cham mem

Xet vf du mdt vat khdi lugng m,, chuydn ddng trdn mdt mat phdng ngang nhdn vdi van tdc i^,, ddn va cham vdi mdt vat khdi lugng m.., dang ndm yen tren mat phdng ngang a'y. Bidt rdng sau va cham hai vat nhap lam mdt, chuyen ddng vdi eiing van tdc v . Xae djnh v.

Vl khdng cd ma sat ndn cac ngoai luc tac dung gdm cd cdc trgng luc va cac phan luc phap tuyd'n, chiing can bdng nhau ; he {A?;,, m^} la mdt he cd lap. Ap dung djnh luat bdo toan ddng lugng :

w,c;i = (w;, -I- m2)v m^v^

suy ra v =

m, + nh

Va cham trdn day ciia hai vat A?r, vd m-, dugc ggi la va cham mem.

4. Chuyen dong bang phan lue

Cai dieu bay ldn dugc la nhd cd khdng khf da tao ra

luc nang tac dung Idn dieu. Trong khoang khdng Y : m M gian vu tru (khdng cd khdng khf), nha vat If Xi-dn- j '

edp-xki (ngudi Nga) da ndu ra nguyen tac chuydn ~

ddng bdng phan luc ciia eae ten lira. "

Gid sir ban ddu tdn lira dirng yen. Ddng lugng ban dau ciia cd tdn lira bdng khdng. Sau khi lugng khf khdi lugng m phut ra phfa sau vdi van tdc v , thi tdn lira khdi lugng M chuydn ddng vdi van tdc V (Hinh 23.3). Ddng lugng ciia he liie dd la :

mi' + MV

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Nd'u xem tdn lira la mdt he cd lap (trong khoang khdng vu tru, xa ede thidn the) thi ddng lugng cua he dugc bao toan :

mv + MV ^0

hay V = - — V (23.7) M

Cdng thii:c (23.7) ehiing td rdng 'V^ nguge hudng ran Giai thich hien tugng simg vdi v, nghia Id tdn lira bay ldn phfa trude nguge vdi giat khi ban. hudng khf phut r a . S 3

Nhu vay, cdc con tau vu tru, tdn lira,... cd the' bay trong khoang khdng gian vii tru, khdpg phu thudc mdi trudng bdn ngoai la khdng khf hay la chan khdng.

Ddng luong p cua mdt vat la mdt vecto ciing hudng vdi van tdc ciia vat va dupc xac dinh bdi cdng thirc p = m r .

Luc dii manh tac dung len mdt vat trong mpt khoang thdi gian thi cd t h ^ gay ra su :, . bien thien dong luong cua vat do.

\; ? Ddng luong cua mdt he co lap la mpt dai lupng bao toan.

CAU HOI VA BAI TAP

A. N/s. B. N.s.

^•"^ C. N.m. D. N.m/s.

1. Neu djnh nghla va y nghla ctia dpng lugng. ^hpn dap an diing.

2. Khi nao dpng lugng cua mpt vat bien thien ? g. Mpt qua bdng dang bay ngang vdi dpng lugng 3. He cd lap la Qi ? - .. - ^ . u . ^ - .u^

• ^ ^ p thi dap vuong goc vao mpt buc tuong thang 4. Phat bie'u dinh luat bao toan dpng lugng. dimg, bay ngugc trd lai theo phuong vudng gdc

Chirng to rang djnh luat do tuang duang vdi vdi birc tudng vdi cimg dp Idn van tdc. Op bien djnh luat III Niu-tan. thien dpng lugng cua qua bong la

5. Dpng lugng dugc tinh bang 1 2 6

A. 0 . C. 2 p .

Chpn dap an dung.

B.p.

D.-2p

7. Mpt vat nho khdi lugng m = 2 kg trugt xudng 8. Xe A cd khdi lugng 1 000 kg va van tdc mpt dudng ddc thang nha'n tai mpt thdi diem 60 km/h ; xe 6 co khdi lugng 2 000 kg va van xac dinh co van tdc 3 m/s, sau do 4 s co van tdc 30 km/h. So sanh ddng luang ciia chiing.

tdc 7 m/s. tiep ngay sau do 3 s vat co dpng 9_ ^^^ ^^ ^ ^^ khdi luang 160 000 kg, bay luang kg.m/s la .; . \.. ' , ,. ru .> i

-' vai van toe 870 km/h. Tmh dpng lugng cua A. 6. B. 10. may bay.

C. 20. D. 28.

Chpn dap an dimg.

o

CHUYEN O O N G CLJA T E N LlJA * t \

\ I

Nguyen tac chuyen dpng ciia ten Ida khae v = Q ' I

han vai nguyen tie chuyen dpng cua 6 to, tau i \ \ hoa. Khi 6 tp tang tdc, mat duang tac dung - i i"\ r

cac luc ma sat thep phuang ngang len cac I {«•<{ ' \ ^ banh xe thea huang chuyen dpng va cac i-\ i] : ^ J

ngoai luc nay gay ra gia tdc chp 6 to. ^ ^ . ^ ^ ,[ ] C\

Con ten lira can phai tang tPc trpng / I 'i i ';\

khoang khOng gian vu tru chan khOng, d dd ^ j ' < ^ ^ l ^ ^ \ l-^

khong cp mpt tac nhan ben ngpai nao ca de [- • ^\^ • ]

"day ngupc lai". Mpt ten lira chuyen dpng i j | k f r l bdng each phPng ra mpt bp phan cua chinh " ^ ' ^^

no theo huang nguac vai huang chuyen dpng. Bp phan nay chinh la khdi cac nhien

lieu duac dat chay - tap thanh khf thai. Khdi - - . ^

khf thai nay va bp phan cpn lai ciia ten lira tac ^ 5 Hmh 23.4 dgng len nhau cac luc true ddi (dinh luat III Ten ICta nhieu tang Niu-tan). Luc do khdi khf thai tac dung len

phan con lai ciia ten lira gpi la luc day cua dpng eaten lira. Luc nay day phan can lai ciia ten lira len phia truac, lam cho ten lira tang toe. Su thay doi tac dp ten lira khi np dang

hoat dpng duac tfnh theo cong thuc Xi-6n-cdp-xki sau : V -VQ = 'dc\--^ ; trong do y - f^ la M do tang tdc dp ten Ida khi khdi lupng thay doi Xd MQ den M, u la tdc dp phut khf ddi voi ten lira. 6 day ta thay uu diem ciia ten lira nhi&u tang, trong do M duac giam do lien tie'p bo di cac tang da hei nhien lieu. Mpt ten lua duac gpi la If tudng khi v^ tai dfch chi con lai nhung khai lupng huu fch.

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