32 Ñònh lyù thu goïn Heä löïc F k khi thu goïn veà moät taâm O töông ñöông vôùi

32 ñònh lyù thu goïn heä löïc f k khi thu

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3.2. Ñònh lyù thu goïn: Heä löïc ( F k ) khi thu goïn veà moät taâm (O) töông ñöông vôùi moät löïc baèng vector chính cuûa heä löïc ( R ’) vaø moät ngaãu baèng vector moment chính cuûa heä laáy cuøng vôùi taâm ñoù : ( F k ) ( R 0 ’, M 0 ). vôùi R 0 ’= F k vaø M 0 = m O ( F k ). 3.3. Caùc tröôøng hôïp ñaëc bieät: 3.3.1 0 R M 0 ( F k ) R . (hôïp löïc R coù giaù vôùi R = R ’ vaø giaù thoûa m O ( R ) = m O ( F k ) ). O F O M F B d Hình 2.3 A
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Baøi giaûng moân Cô lyù thuyeát Hoïc kyø 2, naêm hoïc 2012-2013 15 a) Heä löïc song song: ( F k  Oz ) Neáu R 0 seõ coù hôïp löïc : ( F k ) R . b) Heä löïc phaúng: ( F k Oxy ) Neáu R 0 ( F k ) R (coù hôïp löïc) do ta laáy ñieåm A Oxy laøm taâm thu goïn M A Oxy M A R . c) Hôïp löïc cuûa heä löïc phaúng song song: Cho heä löïc phaân boá nhö hình 2.4: Xeùt phaân toá x k , heä löïc phaân boá treân ñoä daøi naøy töông ñöông: F k = q(x k ). x k ñaët taïi x’ k. . Hôïp löïc R = F = F k = l o dx ) x ( q . Tìm töø M 0 = m O ( F k ) = l o xdx ) x ( q R d = M o l o l o o dx x q xdx x q R M d ) ( ) ( (2.5) Heä löïc phaân boá ñeàu (hình 2.5): Hôïp löïc R I ; R =q o l ; OI = 2 l l q 2 l q o 2 o (2.6) Heä löïc phaân boá tuyeán tính (hình 2.6): Coù ngay q (x) = 2 l q R x l q o I o ; OI = l 3 2 (2.7) Nhaän xeùt: Caùc hôïp löïc coù cöôøng ñoä baèng dieän tích phaân boá, ñi qua troïng taâm cuûa bieåu ñoà dieän tích. 3.3.2. R ’ = 0, M o 0 ( F k ) ngaãu ( Q , Q ’) coù moment baèng moment chính cuûa heä löïc ñoái vôùi taâm O. Chuù yù: Khi R ’ = 0, ( F k ) ngaãu ( Q , Q ’) neân moment chính c uûa heä khoâng phuï thuoäc taâm laáy moment. 3.3.3. R ’ = 0, M o = 0 ( F k ) 0 (2.8) 3.4. Heä ba löïc caân baèng: O l x F q 0 R I I Hình 2.5 O l x F q 0 R I I Hình 2.6 x’ k q(x) F x O l d F k R Hình 2.4 x k
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Baøi giaûng moân Cô lyù thuyeát Hoïc kyø 2, naêm hoïc 2012-2013 16 Heä ba löïc caân baèng thì ñoàng phaúng. Neáu caùc löïc khoâng song song vôùi nhau thì coøn phaûi ñoàng quy. 4 ÑIEÀU KIEÄN CAÂN BAÈNG CUÛA HEÄ LÖÏC: Töø (2.8) chuùng ta nhaän ñöôïc nhöõng ñieàu kieän caân baèng cuûa heä löïc: 4.1. Heä löïc toång quaùt (khoâng gian): R’ x = F kx = 0 R’ y = F ky = 0 R’ z = F kz = 0 M ox = m x ( F k ) = 0 M oy = m y ( F k ) = 0 M oz = m z ( F k ) = 0 Vôùi caùc heä löïc ñaëc bieät moät soá phöông trình coù theå töï thoûa maõn neân soá ñieàu kieän giaûm ñi. 4.2. Heä löïc song song ( F k // Oz ): F kz = 0 0 ( F k ) M x = m x ( F k ) = 0 (2.10) M y = m y ( F k ) = 0 Do 3 phöông trình coøn laïi töï thoûa maõn.
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