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lec07a-203-11-impulse-mom-gd-oo-3-28-11

# lec07a-203-11-impulse-mom-gd-oo-3-28-11 - Mass Conservation...

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Recall Newton’s Law : a F = m (m v) t F = a = v t Define momentum: p = m v F = = Newton’s Law written differently p t Note: if F External = 0 Then p t = 0 OR p = 0 No change in p p i = p f if F = 0 initial final p conserved Initial M i = m k = m 1 + m 2 + m 3 + Final M f = m n M i = M f Einstein: E = m c 2 OR m = E c 2 Conservation of (Mass + Energy) Conservation of Mass Momentum Conservation Mass Conservation Will see next semester 7-1

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The System [m 1 v 1 + m 2 v 2 ] t P = p 1 + p 2 (total momentum) F ext = P t = F ext = (p 1 + p 2 ) t F ext = + (m 1 v 1 ) (m 2 v 2 ) t t If F ext = 0, Then P = constant (P conserved) Good for 3 particles: m 1 v 1 + m 2 v 2 + m 3 v 3 Good for 12 particles: m 1 v 1 + m 2 v 2 + … + m 12 v 12 Good for billions and billions particles: m 1 v 1 + m 2 v 2 + … + m N v N Corollary: If there are outside forces and/or particles enter or leave the system, then total momentum is not conserved. (You get the idea.) Generalize 2-Particle System… N-Particle System 7-2
all j j j j j j init final m v m v     =         ∑ ∑ r v 0 P ∆ = ur ( ) ( ) all all j x j j x j j j init final m v m v     =         ∑ ∑ all all j j j j j j init final m v m v     =         ∑ ∑ init final P P = ( ) ( ) all all j y j j y j j j init final m v m v     =         ∑ ∑ ( ) ( ) x init x final P P = ( ) ( ) y init

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lec07a-203-11-impulse-mom-gd-oo-3-28-11 - Mass Conservation...

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