W7.3 - Physics for Scientists & Engineers 1 Spring Semester...

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February 18, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2008 Lecture 25
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February 18, 2008 Physics for Scientists&Engineers 1 2 Momentum Conservation Momentum Conservation Remember, again: Momentum is conserved in all kinds of collisions In totally elastic collisions, kinetic energy is conserved as well. Question: What is the opposite limit, one that one can define as totally in elastic? Can one remove all kinetic energy? Answer is NO! (usually) p f ,1 + p f ,2 = p i ,1 + p i (1d) ! p f ,1 + ! p f = ! p i ,1 + ! p i (more general)
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February 18, 2008 Physics for Scientists&Engineers 1 3 Totally Inelastic Collisions Totally Inelastic Collisions A totally inelastic collision is defined as one in which the two collision partners stick together after the collision Example: Bug on your car’s windshield If both partners stick together, their final velocities after the collision must be identical Please note: in this case, the final relative velocity is zero Momentum conservation results in ! v f ,1 = ! v f ,2 ! ! v f ! v f = m 1 ! v i ,1 + m 2 ! v i m 1 + m 2
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February 18, 2008 Physics for Scientists&Engineers 1 4 Derivation Derivation : : Totally Inelastic Collisions Totally Inelastic Collisions Momentum conservation Use and get: Now use Thus: ! p f ,1 + ! p f ,2 = ! p i ,1 + ! p i ! p = m ! v m 1 ! v f ,1 + m 2 ! v f = m 1 ! v i ,1 + m 2 ! v i ! v f ,1 = ! v f ! ! v f m 1 ! v f + m 2 ! v f = m 1 ! v i ,1 + m 2 ! v i ( m 1 + m 2 ) ! v f = m 1 ! v i ,1 + m 2 ! v i ! v f = m 1 ! v i ,1 + m 2 ! v i m 1 + m 2 q.e.d.
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February 18, 2008 Physics for Scientists&Engineers 1 5 Example Example : Head-On Collision (1) : Head-On Collision (1) Head-on collision of full-size SUV, M =3,023 kg, and compact car, m =1,184 kg. Each had initial speed of 50 mph (=22.35 m/s), moving in opposite directions (SUV: -v ; car: +v ) . Two vehicles crash into each other and become entangled => totally inelastic collision.
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This note was uploaded on 04/06/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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W7.3 - Physics for Scientists & Engineers 1 Spring Semester...

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