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 = m r v r F = " r p " t Impulse = F ! t = ! p
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Example 6.7 A proton (m p =1.67x10 -27 kg) elastically collides with a target proton which then moves straight forward. If the initial velocity of the projectile proton is 3.0x10 6 m/s, and the target proton bounces forward, what are a) the final velocity of the projectile proton? b) the final velocity of the target proton? 0.0 3.0x10 6 m/s
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Elastic collision in 1-dimension 1. Conservation of Energy: 2. 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 ( )
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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 p =1.67x10 -27 kg) elastically collides with a target deuteron (m D =2m p ) which then moves straight forward. If the initial velocity of the projectile proton is 3.0x10 6 m/s, and the target deuteron bounces forward, what are a) the final velocity of the projectile proton? b) the final velocity of the target deuteron? v p =-1.0x10 6 m/s v d = 2.0x10 6 m/s Head-on collisions with heavier objects always lead to reflections
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The mass M 1 enters from the left with velocity v 0 and strikes the mass M 2 =M 1 which is initially at rest. The collision is perfectly elastic. a) Just after the collision v
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Lecture9 - PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 9...

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