R: Re: vector quantities and energy

[Paolo Cavallo <ton0621@IPERBOLE.BOLOGNA.IT>]

-----Original Message-----
From: GARY HEMMINGER <Hemmig@D-E.PVT.K12.NJ.US>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Thursday, January 21, 1999 3:33 PM
Subject: Re: vector quantities and energy


> Since we study momentum before energy I've had kids ask me the
> question - why isn't energy (particulary kinetic energy)  a vector?
> It strikes me that this is a great question because it can be
> addressed at so many levels.  Feynman would no doubt say something
> rather different to his colleagues than I would to my weakest 10th
> graders and so on.     How would you answer this?


Being an Italian teacher, I'm not sure about the age of your pupils.
Mine are 14-15. I'd say:
a) How do you add energies? With the same rule you use for numbers (scalars).
Energy would not be conserved if you used a different rule. That's the biggest
reason for energy being a scalar.
b) Computing kinetic energy, you must take the scalar product of velocity times
itself - so you get a scalar.
c) You can change energy doing work. But again, work is the scalar product of
force times displacement, so...
d) Consider a disintegration event (in the center of mass frame). Two equal
fragments travel in opposite directions. Would kinetic energy be a vector, the
sum would be zero, not equal to the energy of the system before disintegration.
Before disintegration, the system had zero momentum, not zero energy!

Of course, every argument works only in the light of conservation principles.
Without that, energy could be everything you prefer, even a tensor.

Well, I tried...

Paolo Cavallo
ton0621@iperbole.bologna.it