Chapter_9

# Chapter_9 - 2 x 1 x y P total = constant (if F total ext =...

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Ch 9: Linear Momentum and Collisions Focus: Systems of Particles, Conservation of Momentum Systems of Particles: F 1 M 1 1 particle: = Total force on M 1 -- determines motion 2 particles: M 2 F 12 F 1ext M 1 F 21 F 2ext 2 on 1 1 on 2 Distinguish internal forces between particles, F 12 and F 21 , from external forces: ext dt d M 1 21 1 1 1 F F F v + = = ext dt d M 2 12 2 2 2 F F F v + = = = 0, 3 rd Law Total external force () ext ext M M dt d 2 1 ) 12 21 2 2 1 1 ( F F F F v v + + + = + add

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Ch 9: Linear Momentum and Collisions Focus: Systems of Particles, Conservation of Momentum Memorize this! Define the Momentum: v p M = 2 2 2 1 1 1 , v p v p M M = = i.e., 1 particle: total dt d 1 1 F p = ext total dt d F P = total or 2 1 total p p P + = where Memorize this! If F total ext = 0 , then P total = constant Memorize this! () ext total ext ext dt d F F F p p = + = + 2 1 2 1 2 particles: Total external force determines rate of change of total momentum Vector Momentum Conservation
Ch 9: Linear Momentum and Collisions Focus: Collisions and Center of Mass Rules for Collisions For 1, what is conserved if masses bounce, stick? For 2, what is conserved if the blue mass slides down without friction? Total momentum for both cases, Total kinetic energy for bounce

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Unformatted text preview: 2 x 1 x y P total = constant (if F total ext = 0): Vector equation (x,y,z components) 1) Total mass conserved 2) If elastic (bounces, slides), total energy conserved : Scalar equation 3) If inelastic (sticks) only P total conserved if F total ext = 0 4) Ch 9: Linear Momentum and Collisions Center of Mass 2 2 1 1 CM r r r m m M + ≡ M = m 1 + m 2 = total mass r CM is the mass weighted position vector or center of mass Why do this? Key idea: The center of mass acts like one particle at r CM acted on by total external force total m m M M dt d P v v v r = + = = 2 2 1 1 CM CM external total total M dt d F a P = = CM Example: Find r CM , a CM if: r 1 = 1 i , m 1 = 1 kg; r 2 = 2 j , m 2 = 2 kg F 1 = 2 N j F 2 = 1N i j i r 2 2 ˆ 1 1 3 CM ⋅ + ⋅ = m 3 1 CM = x m 3 4 CM = y j i a 2 ˆ 1 3 CM + = 2 3 1 xCM m/s = a 2 3 2 yCM m/s = a...
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## This note was uploaded on 05/13/2010 for the course PHYSICS 53L taught by Professor Mueller during the Fall '07 term at Duke.

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Chapter_9 - 2 x 1 x y P total = constant (if F total ext =...

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