Here is how Chabay and Sherwood approach the problem you pose at first.
Their text is a momentum first text.
They define momentum p as gamma*m*v
Then for a low speed situation, its easy to show gamma ~1 and we have p
= m v.
What's the motivation for defining p as gamma*m*v?
What's the motivation for defining p as m*v in say a H&R style text?
The motivation in either case is that that is a useful conserved
quantity.
________________________
Joel Rauber
Department of Physics - SDSU
Joel.Rauber@sdstate.edu
605-688-4293
| -----Original Message-----
| From: phys-l-bounces@carnot.physics.buffalo.edu
| [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
| Of Rick Tarara
| Sent: Wednesday, February 27, 2008 12:53 PM
| To: Forum for Physics Educators
| Subject: [Phys-l] momentum first and relativistic mass
|
| OK--here is my question about starting with momentum and
| force = delta-p/delta-t.
|
| When asked something like: "What is the necessary average
| force needed to stop a 1000 kg car from a speed of 30 m/s in
| 10 seconds?" aren't you forced to return to p = mv? Once
| there, introducing the relativistic observations that the
| momentum of a given object (an electron for example) is not
| linear in velocity since both the velocity and momentum can
| be measured experimentally, isn't there a very strong
| temptation to look at something going on with the mass? That
| is, if one almost always pulls momentum apart into mass and
| velocity at low speeds, why not at high speeds?
|
| Related, I think, is the notion of how WE would experience
| and the 'logically' explain relativistic phenomena. To the
| point--the twins. In my presentation we have twin brothers,
| Harlie and Charlie. Harlie gets hungry and wants a pizza.
| He knows a great pizza joint on Alpha Seti 6, a mere 30 light
| years away, and dashes off at relativistic speeds. He
| returns with the pizza (still hot). Charlie is now 60 years
| older, whereas Harlie has experienced an hour's time. Harlie
| KNOWS that Alpha Seti 6 is 30 light years away (and he knows
| he has undergone a bunch of accelerations). He knows Charlie
| is now 60 years older--which basically precludes a conclusion
| that he has been traveling much faster than light (he knows
| that rule too). He might consider that the distance to AS-6
| somehow shrunk considerably, but with his knowledge of the
| universe, he knows that can't really be true and besides
| Charlie has been measuring that distance each year using
| parallax techniques. Isn't the
|
| only thing Harlie is left with as a workable conclusion is
| that HIS CLOCK has been running slower than Charlie's. I
| don't see how 'geometry' can help here--he is 1 hour older,
| Charlie is 60 years older, Harlie is holding the pizza box
| clearly marked with an Alpha Seti 6 address that required a
| 60 light-year round trip. Slow clocks seem the only way for
| Harlie to resolve this puzzle. ??
|
| Rick
|
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| Richard W. Tarara
| Professor of Physics
| Saint Mary's College
| Notre Dame, IN
| rtarara@saintmarys.edu
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