Impulse In, Impulse Out Understanding Elastic Collisions Before Energy

Details Impulse In, Impulse Out Understanding Elastic Collisions Before Energy Impulse In, Impulse Out Understanding Elastic Collisions Before Energy

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aas...209.0305p&link_type=abstract

2007 AAS/AAPT Joint Meeting, American Astronomical Society Meeting 209, #03.05; Bulletin of the American Astronomical Society, V

Physics

Scientific paper

Many fine textbooks and teachers of introductory physics postpone discussion of elastic collisions until after the concept of energy conservation has been developed. Even then, the explanations of readily-observed features of one-dimensional elastic collisions, including the signature “velocity swapping” by objects of equal mass, remain buried in some rather daunting algebra. An alternative approach is to focus on impulse, comparing in particular the impulse imparted to each object before the instant of closest approach to that imparted after. For an interaction in which the repulsive force between the objects is a single-valued function of their center-to-center separation, it can easily be proved and/or demonstrated, e.g. by integrating a force-time graph of two carts fitted with force sensors, that these two quantities are equal. Under such circumstances, the standard equations relating final and initial velocities fall out as simple consequences of momentum conservation. Furthermore, a straightforward regrouping of terms shows that Σ(mv2) remains unchanged by the collision, foreshadowing a later discussion of kinetic energy.

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