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# Lecture9 - PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 9...

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PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 9

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Momentum: Newton’s 2 nd : Conserved for isolated objects Useful for short times Collisions (p always conserved) Elastic (E conserved too) Inelastic (E not conserved) Last Lecture r p = μ ρ ω ρ F = D r p D t Impulse = Φ τ = ∆ π
Example 6.7 A proton (m =1.67x10 kg) elastically collides with a 0.0 3.0x10 6 m/s

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Elastic collision in 1-dimension 1. Conservation of Energy: 1. Conservation of Momentum: Rearrange both equations and divide: 1 2 m 1 v 1 i 2 + 1 2 m 2 v 2 i 2 = 1 2 m 1 v 1 f 2 + 1 2 m 2 v 2 f 2 (1) m 1 v 1 i + m 2 v 2 i = m 1 v 1 f + m 2 v 2 f (2) m 1 v 1 i 2 - v 1 f 2 ( ) = m 2 v 2 f 2 - v 2 i 2 ( ) (1) m 1 v 1 i - v 1 f ( ) v 1 i + v 1 f ( ) = m 2 v 2 f - v 2 i ( ) v 2 f + v 2 i ( ) m 1 v 1 i - v 1 f ( ) = m 2 v 2 f - v 2 i ( ) (2) v 1 i + v 1 f = v 2 f + v 2 i v 1 i - v 2 i = - v 1 f - v 2 f ( )
Elastic collision in 1-dimension Final equations for head-on elastic collision: Relative velocity changes sign Equivalent to Conservation of Energy m 1 v 1 i + m 2 v 2 i = m 1 v 1 f + m 2 v 2 f v 1 i - v 2 i = - v 1 f - v 2 f ( )

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Example 6.8 An proton (m =1.67x10 kg) elastically collides with a v p =-1.0x10 6 m/s v d = 2.0x10 6 m/s
Example 6.9a The mass M enters from the left with velocity v and a) Just after the collision v ______ v . A) > B) < C) =

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Example 6.9b The mass M enters from the left with velocity v and Just after the collision v ______ 0. A) > B) < C) =
Example 6.9c The mass M enters from the left with velocity v and A) > B) < C) = Just after the collision P ______ M v .

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Example 6.9d The mass M enters from the left with velocity v and At maximum compression, the energy stored in the spring is ________ (1/2)M v A) > B) < C) =
Example 6.9e The mass M enters from the left with velocity v and Just after the collision v ______ v .

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