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Škola: Šablona: Název projektu: Číslo projektu: Autor: Tematická oblast: Název DUMu: Kód: Datum: Cílová skupina: Klíčová slova: Anotace: Gymnázium, Brno, Slovanské náměstí 7 III/2 – Inovace a zkvalitnění výuky prostřednictvím ICT Inovace výuky na GSN prostřednictvím ICT CZ.1.07/1.5.00/34.0940 RNDr. Bc. Miroslav Hruška Dynamics of particles (dynamika hmotných bodů) Law of conservation of linear momentum VY_32_INOVACE_FY.3.06 20. 10. 2013 Žáci středních škol s CLIL výukou fyziky v angličtině Linear momentum of a system, isolated system, Newton’s third law of motion, conservation of linear momentum, reactive engine Prezentace slouží k uvedení do problematiky zákona zachování hybnosti. Je vhodné ji použít při probírání nového učiva. 1 Dynamics of particles 6. Law of conservation of linear momentum Revision What is the most important quantity of dynamics? Is it a vector, or a scalar? What is its unit? What are the names of Newton’s laws of motion? What does Newton’s first law of motion say? What does inertia mean? 3 Revision – answers Force; it is a vector; unit is newton Law of inertia, law of acceleration, law of action and reaction Law of inertia: A body is at rest or in uniform rectilinear motion unless made to change its state by external forces Inertia is a property of matter by which it remains at rest or continues moving uniformly in a straight line unless acted on 4 by an external force Linear momentum of a system System (of bodies) (soustava těles) = usually more than one body Linear momentum of a system of two bodies with linear momenta p1 and p2 is p = p1 + p2 (addition of vectors) Note: p can be even a zero vector (o) when p2 = –p1! 5 Exercise I A wagon (1) with a mass of 10 tonnes is going at 10 m/s to the north. A wagon (2) with a mass of 15 tonnes is going at 8 m/s to the south. Find the linear momentum of the system of the wagons. Solution I p1 = m1v1 = 100 t.m/s (↑) p2 = 120 t.m/s (↓) p = 20 t.m/s (↓) 6 Laws of conservation Isolated system = system that exchanges neither energy nor matter with its surroundings (s okolím) Isolated system obeys laws of conservation of (zákony zachování) energy electric charge mass linear momentum 7 Conservation of linear momentum Law of conservation of linear momentum: “The linear momentum of an isolated system is (a) constant: p = const.” If a system of two bodies is isolated, and bodies exert forces (F1,2 and F2,1) on each other, then F1,2 equals the net force acting on body 2 F2,1 equals the net force acting on body 1 8 Conservation of linear momentum Have a look: F2 ,1 F1 ,2 p1 p2 t t p1 p2 p1 p2 o (p1 p2 ) o p1 p2 const. 9 Exercise II Have a look at the Exercise I. If the wagons collide and connect, what will their velocity be? Solution II Linear momentum of the system is p = 20 t.m/s (↓). After collision momentum doesn’t change! Direction is southward, and magnitude v = p ÷ (m1 + m2) = 20/25 m/s = 0.8 m/s 10 A cannon and a cannon ball After shot: opposite directions, and equal magnitudes of linear momenta: MV = mv v m http://www.youtube.com/watch?v=Tsql5Wv0TiE 1 min M V Zdroj: archiv autora 11 Action and reaction around us •reactive engines http://www.youtube.com/watch?v=p1TqwAKwMuM •walking http://www.youtube.com/watch?v=rQXis2u7F0E http://www.youtube.com/watch?v=Fbb3631ew_4 •swimming •paddling (canoeing) http://www.youtube.com/watch?v=qH3HnhEaeok •inline skating etc. http://www.youtube.com/watch?v=sWv6em9EZGE http://www.youtube.com/watch?v=ZHPvR7DKISU 12 That is all for now Thank you for your attention Materiál je určen pro bezplatné používání pro potřeby výuky a vzdělávání na všech typech škol a školských zařízeních. Jakékoliv další využití podléhá autorskému zákonu. Zdroje: Bednařík, M., Široká, M. Fyzika pro gymnázia, Mechanika. Dotisk 3. vyd. Praha: Prometheus, 2004. 288 s. ISBN 807196-176-0 Hornby, A. S. Oxford Advanced Learner’s Dictionary of Current English. 5. vyd. Oxford: Oxford University Press, 1995. 1428 s. ISBN 0-19-431423-5 Autor nezaručuje funkčnost webových odkazů! 14