PH 201 Dr. Cecilia Vogel Lecture 16

OUTLINE  Momentum Conservation  Collisions

Momentum  momentum of an object  p=mv  If no net external force,  the total momentum of a system is  CONSERVED – the same all the time  so, for a system of particles moving separately:

Conserved?  I drop ball, is momentum conserved?  What is its initial momentum?  What is its momentum a moment later (before hitting ground)?  ??

Collisions  Is momentum conserved in a collision?  Yes, if no external force  Even if external forces are acting,  collisions usually happen so fast, that effect of forces is negligible  But be sure to look at momentum just before and just after the collision  if there is a net external force (like friction) the momentum will be different later

Collisions & Momentum  Momentum is conserved during a collision:  Notice that this one equation alone does not let you determine both v1f and v2f

Collisions & Energy  In most collisions, kinetic energy is lost to thermal energy (dissipated)  The ideal case, in which no kinetic energy is dissipated  is called an ELASTIC collision for ELASTIC collisions only

Elastic Collisions  In 1-D problems (both objects moving along a line)  conservation of p and K  provide two equations  in two unknowns  if initial condition is known.

Elastic Collisions Eqns  Solve these two equations  you get:  and: for ELASTIC collisions only

Special Cases  CASE I:  1-D elastic collision with equal masses  trade v’s!  DEMO

Special Cases  CASE II: 1-D elastic collision with one mass much larger m 1 +m 2 ≈ M,  Heavy object - unchanged motion  Light object – turns around & may go flying!  DEMO m 2 -m 1 ≈ M, m 1 -m 2 ≈ -Mm 1 /(m 1 +m 2 ) ≈0

Special Cases  CASE III:  1-D elastic collision with much larger mass at rest  same as previous, but with v 2i =0.  Heavy object - unchanged  Light object – bounces back

Inelastic Collisions  In most collisions, kinetic energy is lost to thermal energy, dissipated  These collisions are inelastic  Can all the kinetic energy be lost?  usually no  Totally inelastic collision means  maximum amount of K lost  generally not all of it  Object stick together/move together after collision

Totally Inelastic Collisions  Totally inelastic collision implies  stuck together  To conserve momentum

Special Cases  CASE I:  1-D totally inelastic collision with equal masses  average  DEMO

Special Cases  CASE II:  1-D totally inelastic collision with equal masses moving in opposite dir at same speed   stop

Special Cases  CASE III:  1-D totally inelastic collision with one mass much larger  m 1 +m 2 ≈ M,  Heavy object - unchanged motion  Light object - joins it in motion m 1 /(m 1 +m 2 ) ≈0

Summary  momentum  p=mv  Total momentum of a system is conserved, if no net external force acts.  Collisions  Momentum is conserved in collisions.  Kinetic energy is conserved in elastic collisions.