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elastic collisions



Hi everyone,

Here's a question that has been on my mind for a year, but which I am just getting around to posting to this wonderful group.

In the 5th edition of Physics, by Resnick, Halliday and Krane, major changes are made from the previous editions. One of the most significant is the moving of all discussion of energy to the end of the mechanics section, where it is used as a unifying theme. This is, I know, in vogue among physics teachers these days, and, while I'm not excited by it, I'm not unhappy about it either.

Discussing momentum and collisions before energy does raise a question, though. What do we do about elastic collisions, which are usually defined as collisions that conserve total kinetic energy, or so I've always thought. For collisions between particles, it turns out that elastic collisions are especially simple in the center of mass frame, where the particles simply reverse their motions after the collisions, at least in the one-dimensional case. Now we have an august textbook that defines elastic collisions as collisions in which, "in the cm frame, the velocity changes in direction, but not in magnitude." (p129) Later, in the discussion of energy, RHK states that as "an alternate definition of an elastic collision: In an elastic collision, the total kinetic energy of the two bodies remains constant..."

This might be a sort of "chicken and egg" quibble except for the issue of collisions where some of the initial translational KE ends up in rotation, like the old puck and stick collisions. For example, suppose, on a horizontal, frictionless surface, a puck of mass m is moving with speed vo perpendicular to the axis of a stick of mass m, initially at rest in the LAB frame. The puck strikes the stick at one end. If we simply say that the puck and stick rebound with speed vo/2 in the CM frame, we don't simultanteously conserve angular momentum and total KE. Interestingly, the 5th edition of RHK omits all mention of puck and stick collisions, which were included in the 4th edition and also on past AP Physics exams.

I did send an e-mail to Krane through the text website about this last year. I know Prof. Krane and the editors at Wiley are very busy, though and so...

Best to all for a great academic year,

Jeff Weitz

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.