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More about Momentum Physics 1425 Lecture 15 Michael Fowler, UVa

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Elastic One-Dimensional Collisions 1 An elastic collision is one in which mechanical energy is conserved. First example: two equal masses with opposite velocities: Conservation of momentum tells us they bounce back with equal speeds, and conservation of energy ensures each ball just has its velocity reversed. x After: v -v v -v
Clicker Question Suppose we have two equal masses, one initially at rest , the other approaching from the left at velocity v . What is the velocity of the center of mass ? A. 0 B. 0.5 v C. v D. Something else v

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Clicker Question What is the velocity of the center of mass after the elastic collision ? A. 0 B. 0.5 v C. -0.5 v D. Something else v
Clicker Question What would be the velocity of the center of mass after a completely inelastic collision ? (Assume the balls stick together.) A. 0 B. 0.5 v C. -0.5 v D. Something else v

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Clicker Question Suppose we have a 1 kg mass initially at rest, and a 2 kg mass approaching from the left at velocity v . What is the velocity of the center of mass? A. 0.2 v B. 0.33 v C. 0.5 v D. 0.67 v E. v v 2 kg 1 kg
Looking at Collisions… Collisions of two objects, in one or two dimensions, are often easier to understand (as you’ll see) if we examine the motions relative to the center of mass . This is called working in the center of mass frame of reference . If there are no external forces acting on the system, overall momentum is conserved, and the center of mass moves at constant velocity relative to any given inertial frame.

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Reminder: a Frame of Reference Frame of reference: To measure motion , we must first measure position .
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